Discussion Paper No. 512

DOES THE FREE-RIDER PROBLEM OCCURIN CORPORATE TAKEOVERS?
EVIDENCE FROM LABORATORY MARKETS
Shin’ichi Hirota
Tatsuyoshi Saijo
Yasuyo Hamaguchi
Toshiji Kawagoe

June 2000

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Does the Free-rider Problem Occur in Corporate Takeovers?
Evidence from Laboratory Markets*

Shin’ichi Hirota (Waseda University)
Tatsuyoshi Saijo (Osaka University)
Yasuyo Hamaguchi (Osaka University)
Toshiji Kawagoe (Future University - Hakodate)June 13, 2000

* Earlier drafts of this paper were presented at the Japanese Economic Association annual meetings (June1998), the first Japan Experimental Economics Conference (September 1998), a conference on ‘New
Developments in Experimental Economics’ held in Osaka, Japan (March 1999), the third Japan
Experimental Economics Conference (March 2000), and seminars at the Economic Planning Agency ofJapan, the Finance Research Workshop, the Institute for Posts and Telecommunications Policy, Osaka
University, University of Tsukuba, and Waseda University. We would like to thank Bram Cadsby forreading the entire text in its original form. We also thank Ken Koga for reading the earlier drafts andmaking a number of valuable comments. We are also indebted to Kazunori Araki, Colin Camerer, Dan
Friedman, Koichi Hamada, Kohei Kawamura, Motonari Kurasawa, Elizabeth Maynes, Naoko Nishimura,Charles Plott, Kazuhiko Ohashi, Wataru Ohta, Akira Okada, Arthur Schram, Shyam Sunder, Toshio
Yamagishi, and seminar participants. Kohei Kawamura provided research assistance. The first author
wishes to acknowledge the financial support of Grant-in-Aid for Encouragement of Young Scientists
09730067 of the Ministry of Education, Science, Sports and Culture in Japan, and a grant from the Zengin
Foundation for the Studies on Economics and Finance.
Correspondence:

Shin’ichi Hirota, School of Commerce, Waseda University,
1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo, 169-8050, JAPAN.
E-mail: shirota@mn.waseda.ac.jp1Abstract

We explore experimentally whether the free-rider problem occurs in corporate takeovers. While
Grossman and Hart’s (1980) classical proposition states that due to the free-rider problem
takeovers never succeed, we observe a considerable number of successful takeovers in realcapital markets. To solve this paradox, we conducted an experimental study by constructing
simple laboratory markets of atomistic shareholders. We found the following. First, free-rider
problems did occur in our laboratory; only 20% of takeovers were successful and consequently
80% of social value disappeared. Second, a bidder’s initial shareholdings significantly mitigated
the free-rider problem; the probability of takeover success rose to 71.3% when a bidder initiallyheld the shares of the target firm. Based on these experimental results, we argue that the freerider problem potentially exists in real takeover markets as well, but that the bidder’s initialshareholdings may make takeovers successful in reality.

2

I. Introduction
In a widely held firm, the separation of ownership and control is a serious matter for
shareholders. Corporate managers do not necessarily pursue shareholders’ wealth. To cope withthis matter, shareholders have two alternatives, “voice” and “exit” (Hirschmann (1970)). Even if
a small shareholder cannot take the former option, she can take the latter (much easier) route by
selling her shares. If the buyer purchases progressively more shares from these shareholders andsucceeds in holding half of the company’s shares, the buyer obtains control and can improve themanagement of the firm. Thus, small shareholders do not have to worry about the risk of
incurring loss due to bad management.
This is the well-known story of the takeover mechanism. About twenty years ago, however,
Grossman and Hart (1980) challenged this “optimistic story”. They suggest that this type ofcorporate takeover never succeeds. The reason is that if a small shareholder knows that her
share value will rise due to the improvement in management after the takeover success, she
prefers to hold on to her shares rather than selling them. That is, no shareholder sells her own
shares when she expects others to sell. In other words, the shareholder attempts to free-ride on
the benefit of a successful takeover. This selfish behavior of shareholders, however, results inthe socially inefficient outcome that takeovers will never be successful. This is the free-rider
problem in corporate takeovers that Grossman and Hart (1980) discuss.1
Grossman and Hart’s (1980) story is widely known, and their theoretical conclusion seems tohave already become a classical proposition.2 It is accepted as a starting point for a considerable
number of theoretical models of corporate takeovers (e.g., Shleifer and Vishny (1986), Bradley,
Desai, and Kim (1988), Bagnoli and Lipman (1988), Bebchuk (1989), Hirshleifer and Titman(1990), Holmstrom and Nalebuff (1992), etc.).3 However, turning to real takeover markets, wehave to be skeptical of this proposition. We observe that a significant number of corporate
takeovers have been successful over the past few decades. Hoffmeister and Dyl (1981) find thatamong 84 cash tender offers made during 1976 and 1977 in the U.S., 73.8% of them (62 offers)
were successful. Walking (1985) reports that using his U.S. sample of 108 takeover offers
during 1972-76, 66.7% of them (72 offers) succeeded. Duggal and Millar (1994) examine 287
tender bids involving firms listed on the New York Stock Exchange or the American Stock
Exchange during the period 1984-1987, and show that the probability of takeover success is
1

Bradley (1980) presents a similar idea. He also suggests that synergy gains from consolidating thetwo firms make a takeover successful even if the free-rider problem exists.

2

For example, Bebchuk (1989) states in the introduction to his paper, “In an already classical paper,
Grossman and Hart (1980) advanced the proposition … ”.

3

Hirshleifer (1995) presents a good survey of various takeover models.

3

55.4% (159 of 287 succeeded). Also, Jensen (1993) convincingly shows that the market forcorporate control was especially active in the U.S. during the 1980s and suggests that a lot of
successful takeovers play roles in improving corporate efficiencies and raising social welfare.
These results and views, at first glance, seem to support the “optimistic story” of takeovers
rather than Grossman and Hart’s classical proposition: the takeover mechanism actually works
and there is no serious free-rider problem preventing takeover success4.
Observing this reality, people outside the economics would criticize Grossman and Hart’s
result. In particular, among other things, they would insist that the assumption of rational
shareholders is unrealistic. Some would say, “I do not agree with Grossman and Hart. I would
guess that some shareholders sell their shares and takeovers may be successful, because
shareholders are not as rational as economists say.” Others would say, “In reality, shareholders
do not know how high their share values will rise after the takeover, so they would choose to
sell shares if the price offered by the bidder (buyer) is higher than the current market price.” We
consider that these critics should not be ignored, since recent developments in experimental
economics indicate that people do not necessarily behave rationally (see, for example, Thaler(1992)).
Against these critics, financial economists would argue as follows, “Grossman and Hart’s
proposition is right. But in real capital markets there are several economic factors or
institutional environments that do not appear in Grossman and Hart’s model. These factors orenvironments must mitigate the free-rider problem and produce a successful takeover”. Indeed,
subsequent takeover models give some theoretical foundations for this argument. Shleifer and
Vishny (1986) and Hirshleifer and Titman (1990) suggest that a bidder’s initial shareholdings
may overcome the free-rider problem. Bradley, Desai, and Kim (1988) also show that two-tiered
offers may resolve the free-rider problem. Bebchuk (1989) indicates that with unconditional
offers, takeovers succeed with positive probabilities. Bagnoli and Lipman (1988) andHolmstrom and Nalebuff (1992) find that when the number of shareholders is finite, the freerider problem is alleviated and successful takeovers are possible. Also, Grossman and Hart
(1980) themselves suggest that a dilution opportunity for a bidder may make takeovers
successful. Thus, it is possible that we may observe successful takeovers in real capital markets
even if free-rider problems in the Grossman and Hart’s sense potentially exist.
Therefore, from our casual observations, it is not clear whether Grossman and Hart’s story
4

Interestingly, the well-known corporate finance textbooks, Brealey and Myers (1991) and Ross,
Westerfield, and Jaffe (1996) do not mention the free-rider problem in corporate takeovers although
they discuss mergers and acquisitions and present empirical evidence on the effects of takeovers.
Also, in a survey article for corporate takeovers in the Journal of Economic Perspectives, Jarrell,
Brickley, and Netter (1988) do not cite Grossman and Hart (1980) either. Do these imply that thefree-rider problem is less important in actual takeover markets?

4

applies to corporate takeover markets. We consider it necessary to examine the appropriatenessof Grossman and Hart’s model by presenting empirical evidence, because the results of such an
examination would have important implications for real takeover markets and financial
economics. Let us suppose that we find Grossman and Hart’s model rejected in reality. Then, we
can believe the optimistic story of takeovers, and investors do not have to worry about bad
management. At the same time, however, we must question the value of recent takeover models
since these models have evolved from Grossman and Hart’s model. Next, let us suppose theopposite case, that is, we find that Grossman and Hart’s model is accepted in reality. Then,bidders must be serious about the free-rider problem and need to find ways to mitigate thisproblem. In this case, we recognize the significance of takeover models that show bidders how
to succeed in takeovers and give us insights into appropriate public policies to prevent the freerider problem.
Numerous empirical studies on corporate takeovers5, however, have made few contributions
to testing Grossman and Hart’s model. This must be because empirical research uses field data
affected by many different factors in complicated real takeover markets (some of which may be
the factors pointed out by subsequent takeover models), and hence it is difficult to test
Grossman and Hart’s model directly. On the other hand, experimental studies, in general, havean advantage in controlling factors that do not appear in the model and testing the model
directly. For this reason, we adopt an experimental approach in this paper. We construct simple
laboratory markets for corporate takeovers comparable to Grossman and Hart’s model, andexamine how severe the free-rider problem is in our laboratory markets.6
In addition, we explore the effect of a bidder’s initial shareholdings on takeover success. The
bidder’s initial shareholdings are regarded by financial economists as one of the means ofsolving the free-rider problem. As we briefly mentioned above, Shleifer and Vishny (1986) and
Hirshleifer and Titman (1990) argue that when a bidder initially holds the shares of the target
firm, she can internalize the benefits of the takeover, thus overcoming the free-rider problem(takeovers may be successful). We examine whether their story is actually supported in ourlaboratory. In real U.S. capital markets, Walking’s (1985) empirical study finds a positive effectof the bidder’s initial shareholdings on takeover success, which is in line with the prediction of
the above two models. This positive effect, however, may stem from various other factors inreality, such as the bidder’s influence on the target management or the shareholders’ fear of
becoming inactive minorities, as Walking (1985) suggests. Our experiment gives an opportunity

5

See, survey articles by Jensen and Ruback (1983) and Jarrell, Brickley, and Netter (1988).

6

As for the free-rider problem in the provision of public goods, there have been a huge number ofexperimental studies and several interesting findings are reported (see survey articles by Davis andHolt (1993) and Ledyard (1995)). We will mention them later.
5to test Shleifer and Vishny’s (1986) and Hirshleifer and Titman’s (1990) models directly. Also,
conducting experiments in this initial shareholdings case as well as in the Grossman and Hartcase (with no initial shareholdings), we can check whether the Grossman and Hart case shows aseverer free-rider problem than the initial shareholdings case, as theory suggests.
In attaining our aim, we must confront one problem with experimental settings: how toconstruct an atomistic shareholders world in the laboratory. The models we test (Grossman andHart (1980), Shleifer and Vishny (1986), and Hirshleifer and Titman (1990)) all assume thateach shareholder is atomistic in the sense that she ignores her impact on the outcome of the
takeover in making her tender decision. We should notice that the results of these models (e.g.
Grossman and Hart’s proposition) crucially depend on this atomistic shareholders assumption,
as Bagnoli and Lipman (1988) point out. The atomistic shareholders assumption is naturally
satisfied in the case where there are an infinite (or a very large) number of shareholders, each ofwhom owns a negligible (very small) proportion of the firm. In conducting experiments,
however, we cannot gather an infinite number of participants, and hence it seems difficult tocreate the atomistic shareholders’ world in the laboratory. We deal with this difficulty by
developing an original experimental device where each shareholder takes her decision as if shewere an atomistic shareholder even in the finite-participant laboratory. We believe that thisdevice is innovative and can be applied to other experiments dealing with atomistic agent
markets.
To our knowledge, there have been two experimental studies of corporate takeovers. One isKale and Noe’s (1997) study which compares the predictions of finite (non-atomistic)
shareholder models (Bagnoli and Lipman (1989) and Holmstrom and Nalebuff (1992)) with theoutcomes of laboratory experiments. Their experimental results support these models in somedesigns, but do not in other designs. Also, Cadsby and Maynes (1998) test Holmstrom andNalebuff’s (1992) model in a laboratory environment where shareholders own more than one
share, and find that their experimental results are inconsistent with that model’s predictions. Our
study differs from Kale and Noe (1997) and Cadsby and Maynes (1998) in four respects. First,
most importantly, we test the takeover models of atomistic shareholders as discussed by
Grossman and Hart (1980), whereas the previous two studies test the models of non-atomistic(finite) shareholders. Second, as we mentioned above, we also investigate the effect of abidder’s initial shareholdings on mitigating the free-rider problem. Third, our experiments
involve a bidder’s bidding behavior as well as shareholders’ tendering decisions following thestory of the takeover models, while the previous two studies only involve the latter. Fourth, we
introduce informational asymmetry about the share value after a successful takeover (only abidder knows it) because this setting seems more realistic in corporate takeover markets.
From our laboratory, we find the following. First, the free-rider problem is severe in our

6laboratory markets: only 20% of takeovers are successful when a bidder has no initial shares(Grossman and Hart’s case). This result indicates that corporate takeovers tend to fail andconsequently most of the potential social value from successful takeovers disappears due to thefree-rider problem. In this sense, we can say that Grossman and Hart’s model contains valuable
message in understanding the nature of takeover markets. Second, the initial shareholdings by abidder considerably mitigate the free-rider problem in corporate takeovers: about 70% of
takeovers succeed when a bidder initially holds shares in the target firm. This result is consistent
with the theoretical predictions presented by Shleifer and Vishny (1986) and Hirshleifer andTitman (1990). It also suggests that the initial shareholdings held by the bidder may be one
reason for the successful takeovers observed in real takeover markets.
This paper is organized as follows. Section II reviews theoretical models of corporate
takeovers that analyze the free-rider problem in atomistic shareholders markets. Section III
describes our laboratory takeover markets and explains experimental procedures. Section IV
presents the hypotheses to be tested. Section V discusses our experimental results. Section VI
analyzes each participant’s behavior and points out some anomalies observed in our laboratory.
Finally, Section VII summarizes our findings and examines their implications.
II. Theoretical Overview
In this section, we briefly review three takeover models that analyze the free-rider problem
under the atomistic shareholder assumption. First, we illustrate Grossman and Hart’s (1980)classical proposition that corporate takeovers never succeed. We show that their proposition
holds under both symmetric and asymmetric information. Second, we discuss the results ofShleifer and Vishny (1986) and Hirshleifer and Titman (1990) in which initial shareholdings by
the bidder play the crucial role in solving the free-rider problem.
A. Corporate Takeovers and the Free-rider Problem
Suppose that one bidder (raider) attempts to take over the firm by purchasing the firm’s sharesfrom atomistic shareholders. The bidder does not initially hold any shares of the target firm, andshe offers a bid price per share x to the shareholders. The shareholder observes x and decides
whether to tender her shares. If the bidder can successfully purchase 50% of the total number ofthe firm’s shares, S, then she succeeds in the takeover, gains control of the firm, and improves
the value of the firm by the amount z > 0 per share. If she cannot acquire 0.5 of the shares, thenshe fails in the takeover, does not purchase any shares (the bidder makes a conditional offer)7,7

In this paper, we explore Grossman and Hart’s (1980) model under a conditional offer. This seems
7and cannot realize the increase in firm value. We assume, for simplicity, that the pre-takeovervalue of the firm under the incumbent management is zero8. Since z is positive, it is obvious thatthe success of the takeover produces social benefits. Then, the important point to explore iswhether or not such a value-increasing takeover can succeed in a world of rational bidders andshareholders.
Grossman and Hart (1980) argue that this type of takeover never succeeds. They deduce thisstriking result by pointing out there is a free-rider problem among shareholders as follows.
If the takeover is successful, the bidder’s profit is 0.5S (z - x). Therefore, to obtain some gainfrom this takeover, the bidder must make the bid x smaller than the post-takeover value of theshare z, i.e., x < z. In Figure 1-A, this bidder-profitability condition is shown as the area under
the x = z line.
Next, let us consider the shareholders’ decisions. First, suppose that the takeover issuccessful. Then, the shareholder can obtain the bid price x per share if she has chosen to tendershares whereas she obtains z per share if she rejects the offer and holds on to her shares. On thecontrary, suppose that the takeover is unsuccessful. Then, no transactions occur between thebidder and shareholders, and hence the shareholder earns zero profits whether or not she haschosen to tender her shares. This shareholder’s payoff is summarized in Table 1. In addition,
since each shareholder is atomistic, her tender decision has no impact on the outcome of the
takeover. Under these conditions, the (weakly) dominant strategy for the shareholder is to accept
the offer if x ≥ z, and to reject the offer if x < z. This shareholder-acceptability condition (x ≥ z)
is indicated by the area above the x = z line in Figure 1-A.
Observing Figure 1-A, we realize that there is no x which satisfies both the bidderprofitability and the shareholder-acceptability conditions for any z, that is, takeovers which
benefit the bidder can never succeed. To understand this impossibility result, suppose that thebidder makes the bid, x0 < z0, to earn the profits 0.5S (z0 - x0). Shareholders, however, will reject
this offer. Each shareholder, while on the one hand holding his shares, on the other hand expects
other shareholders to accept the offer and make the takeover successful, and attempts to obtain
the post-takeover value z0 which is greater than the bid price x0. That is, she does not contributeto the success of the takeover, but seeks to free ride on the benefit of its success. This selfinterested behavior of each shareholder, however, leads to the socially inefficient outcome that avalue-increasing takeover always fails. This is Grossman and Hart’s (1980) classicalto be standard among recent treatments of the free-rider problem in takeovers, although Grossman
and Hart themselves assume an unconditional offer (an offer committing the bidders to purchasetendered shares whether or not takeovers succeed). See, Hirshleifer (1995) and Grinblatt and Titman(1998).
8This assumption is the same as that in Hirshleifer and Titman (1990).

8

proposition.
Grossman and Hart (1980) show this proposition under the assumption that the post-takeovervalue of the target firm z is known to both the bidder and the shareholders. In our paper,
however, we wish to explore whether this proposition holds under the assumption that there isinformation asymmetry regarding z between a bidder and the shareholders. We assume that thebidder, who attempts to takeover the firm and to earn considerable profits, knows z, but
atomistic shareholders do not. The reason why we examine this asymmetric information case isthat it is closer to real-world capital markets. In actual takeover markets, it is plausible thatshareholders do not know the post-takeover value (z), and hence whether they can predict z is adisputable issue. Indeed, subsequent theoretical models of corporate takeovers, such as Shleiferand Vishny (1986), Hirshleifer and Titman (1980), and Chowdhry and Jegadeesh (1994),
assume asymmetric information regarding the post-takeover value and examine how
shareholders formulate their expectations of that value. Therefore, throughout this paper, we
explore the free-rider problem and the possibility of takeover success under this information
asymmetry setting.
Does Grossman and Hart’s (1980) proposition still hold in the world of asymmetric
information? The standard answer of modern economics would be “Yes”. In the world where z
is private information for a bidder, a shareholder must have some prediction of z in order todetermine her action. However, as long as the shareholder is rational, she realizes that thebidder makes the offer x < z to earn profits, and hence the shareholder predicts that x is lower
than z. Thus, the shareholder prefers to reject the offer, hoping to free ride and obtain z if the
takeover is successful. Therefore, even under asymmetric information, the free-rider problem
among rational shareholders means that takeovers never succeed.9
This prediction that takeovers never succeed also implies that there is no relation between theprobability of takeover success and the bid price x. Whatever x the bidder chooses, rational
shareholders expect that x is lower than z. Hence shareholders reject the offer and takeovers
always fail. Therefore a high bid price offered by a bidder does not increase the probability of
takeover success at all.
From the above discussion, we restate Grossman and Hart’s (1980) proposition under theasymmetric information setting.
Proposition 1 (Grossman and Hart (1980))
When the post-takeover value z is unknown to atomistic shareholders and the bidder has
no initial shareholdings,
1-1. takeovers can never be successful, and9Shleifer and Vishny (1986) show this result as a special case of their model.
91-2. no relation exists between a bid price x and the probability of success.
Proposition 1 implies that “the free-rider problem remains when asymmetric information is
introduced” (Hirshleifer (1995), pp.845). We believe that this proposition is persuasive for mostacademic economists, since the model is based on the usual assumption of economics that“people are both rational and selfish” (Dawes and Thaler (1988), pp.187). In the above model,
in deriving the proposition, we assume that shareholders (i) maximize their own profits, (ii)fully understand that they gain x by accepting the offer and z by rejecting it in a successful
takeover, and (iii) rationally predict that x is lower than z.
This presumption, however, is not without its critics. People outside the economics profession
may consider that human beings do not behave as economists assume, but that they sometimes
choose irrational or altruistic behavior. If this is true, some shareholders may not satisfy theabove conditions, (i), (ii), or (iii), and might indeed sell shares to the bidder if offered a positivebid (x). Considering the possibility of such behavior, it is probable that takeovers sometimes
succeed and that the probability of success is increasing with the bid level x. In addition, as we
mentioned in the introduction, we observe a considerable number of successful takeovers in real
financial markets. This evidence also makes us skeptical of whether there exists a severe freerider problem in corporate takeover markets, motivating our experiments.
B. The Bidder’s Initial Holdings and the Takeover Success.
Next, consider the case where the bidder initially holds some shares of the target firm. Let α
represent the proportion of the firm’s shares owed by the bidder (we assume 0 < α < 0.5). Then,the bidder’s profits from the successful takeover can be written as[αz + (0.5 - α)(z - x)] S(1)

Notice that the bidder obtains some gains (αz) from her initial holdings if takeovers are
successful. In other words, the bidder can internalize a part of the increase in firm value
generated by successful takeovers. This means that the bidder with initial holdings has a greater
incentive to make the takeover succeed and can also afford to offer a higher bid to facilitateshareholders’ acceptance. In fact, the bidder-profitability condition (which assures the bidder of
positive profits from successful takeovers) in this case can be written as
x < [0.5/(0.5-α)]z.

(2)

As [0.5/(0.5-α)] is greater than 1, (2) implies that the bidder can make the bid x greater than z.
This bidder-profitability condition is shown in Figure 1-B.
Noting that the shareholders’position is the same as in the previous case, we also show theshareholder-acceptability condition (x > z) in Figure 1-B is exactly the same as that in Figure 1-

10

A. The point to observe is that there are x’s which satisfy both the bidder-profitability and theshareholder-acceptability conditions for all z. This suggests that when both the bidder and theshareholders know z (information is symmetric), the bidder can always make a bid which isaccepted by the shareholders. For example, as shown in Figure 1-B, to succeed in a takeover,the bidder has only to offer x = x0* when z = z0, and x = x1* when z = z1. Therefore, undersymmetric information regarding z, the bidder who initially holds the shares of the target firm
can succeed in value-increasing takeovers. In other words, the free-rider problem in corporate
takeovers can be solved by the bidder’s initial holdings.
However, under the more realistic assumption of information asymmetry between a bidder
and shareholders, the story is not as simple. When z is private information for a bidder, thebidder has an incentive to pretend that her z is low, to make a lower bid x, and to extract larger
profits. For example, in Figure 1-B, a z0-bidder (a bidder whose z is z0) may dishonestly say that
his z is z1, and offer x1* instead of x0*. If the shareholders believed that this bidder’s statement(z = z1) was true and accepted a lower offer x1*, they would lose profits of (x0* - x1*) per share.
Therefore, when shareholders do not know the bidder’s z, they have to predict the true value ofz by themselves, compare its expectation with x, and decide whether to accept the offer. How doshareholders formulate expectations for the unknown z in this case?
The answer to this question from economic theory is that rational shareholders predict z byobserving the bid price x offered by a bidder; shareholders use the bid price as a signal which
reveals the bidder’s private information about z. This logic is employed in the following two
papers.
First, Shleifer and Vishny (1986) claim that shareholders predict z by using the bidderprofitability condition (2). They argue that rational shareholders would recognize that the bidder
must make a profitable bid and hence the bid satisfies (2). Then after observing the bid x,
shareholders would rationally expect that z > [(0.5-α)/0.5] x from (2). Given this expectation
formation, Shleifer and Vishny (1986) show that when the bid x is greater than a critical value xc,
x becomes larger than the shareholders’ expected value of z.10 Thus, with a bid greater than xc,
10

Let us develop this point in more detail. For expositional simplicity, assume that z’s priordistribution is uniform on [0, zmax]. Then, from (2), the shareholders’ conditional expected value of z,E(z | x), isE(z | x) = [ [(0.5-α)/0.5]x + zmax ]/2.

(N-1)

For the shareholder to accept an offer, the bid x must be larger than this expected value of z. Hence,
we can state the shareholder’s acceptability condition asx >[ [(0.5-α)/0.5]x + zmax ]/2.

(N-2)

Notice that as a bidder makes the bid x (the left-hand side) higher, shareholders’ expectation of z
(the right-hand side) becomes higher, but the latter increase is not as large as the former (dE(z | x)/dx
is positive but less than one). Therefore, we know that there exists an x which satisfies (N-2).
11

shareholders accept offers and takeovers are successful. That is, Shleifer and Vishny’s (1986)
model suggests that takeovers by an initial shareholder may be successful and that there is apositive relationship between a bid price and the probability of takeover success (more precisely,
the probability of success is an increasing step function of the bid price). These results are in
sharp contrast with Proposition 1 presented earlier.
Hirshleifer and Titman (1990) obtain similar results by using the same setting as Shleifer and
Vishny (1986), but employing a more sophisticated equilibrium concept, the perfect Bayesianequilibrium. They show that in a perfect Bayesian equilibrium of the takeover game, thetakeover succeeds probabilistically and the probability of takeover success P(x) is continuously
increasing in the bid price x (i.e., P’(x) > 0). They obtain these results by introducing theassumption that shareholders have some personal costs of tendering, c, which are unknown tothe bidder.
To understand their model, suppose that shareholders predict the post-takeover value z
correctly. Then, the shareholder tenders her shares if x-c > z. The bidder, however, does notknow c, and hence is uncertain whether or not shareholders will accept the bid. Consequently,
takeovers succeed probabilistically. The bidder, however, knows that the larger x she offers, thegreater the likelihood that x-c > z (shareholders accept the bid), and hence the probability ofsuccess increases with the bid x (P’(x) > 0). On the other hand, perceiving P’(x) > 0, a high z
bidder, who has more to gain from a successful takeover, is willing to bid higher (i.e., dx/dz > 0)
to increase the probability of success. This bidding behavior, however, fully reveals the bidder’sprivate information on z to shareholders. That is, shareholders perfectly infer z by observing abid x, which is consistent with the initial supposition of the shareholder’s correct prediction of z.
Thus, we confirm here that the above story is consistent with the perfect Bayesian equilibrium.11
Hirshleifer and Titman’s (1990) paper makes two important contributions. One is to present

Rearranging (N-2), we getx >[zmax / (1+2α)] ≡ xc .

(N-3)(N-3) says that shareholders accept an offer if the bid x is greater than the critical value xc. A bidder
whose z is greater than [(1–2α) zmax / (1+2α)] can obtain positive profits with these bids. That is,
takeovers succeed when a high-z-bidder makes a high bid.
11

In their paper, Hirshleifer and Titman (1990) also show another perfect Bayesian equilibrium
where the bidder sets the optimal bid x* exactly equal to z. In this equilibrium, shareholders are
indifferent about whether or not to tender, so that any mixed strategies are optimal for shareholders.
Therefore, shareholders can choose the mixed tendering strategy such that the probability of success(P(x)) is strictly increasing in x and also supports the proposed bid x* = z. Hirshleifer and Titman(1990) claim that this mixed-strategy equilibrium may be viewed as a metaphor for the equilibrium
shown in the text; when shareholders’ unknown tendering costs c are arbitrary small, from thebidder’s perspective, shareholders seem to randomly choose whether or not to tender, i.e., they seem
to use mixed tendering strategies (see, Harsanyi (1973)).

12

an equilibrium in which takeovers succeed probabilistically. This stochastic success of takeovers
coincides with our casual observations. The other is to indicate that a high level of a bidder’sinitial shareholdings (α) increases the probability of takeover success in two ways. One is thatwith a higher α a bidder can make a greater bid x and consequently shareholders are more likely
to tender. We call this the tendering effect. The other is that a high α reduces the number ofshares needed to complete takeovers (0.5-α) and hence the probability of takeover success rises
given shareholders’ tendering decisions.12 We call this latter effect the pure number effect.
To summarize, from Shleifer and Vishny (1986) and Hirshleifer and Titman (1990), we canderive the following proposition about the possibility of takeover success under atomistic
shareholder markets when the bidder has some initial shareholdings.
Proposition 2 (Shleifer and Vishny (1986), Hirshleifer and Titman (1990))
When the post-takeover value z is unknown to the atomistic shareholders and the bidder
initially holds the shares of the target firm,
2-1. takeovers succeed with positive probability, and2-2. a positive relation exists between the bid price x and the probability of success.
Proposition 2-1 indicates that initial shareholdings by a bidder can produce successful takeovers,
and that such shareholdings thus improve social efficiency. This outcome stems from the bidderinternalizing a part of the benefits from successful takeovers. On the other hand, Proposition 2-2
tells us that takeovers are more likely to succeed under high bids than low ones. This relation
stems from either the method used by shareholders to predict z (Shleifer and Vishny (1986)) orfrom shareholders’ personal tendering costs or benefits (Hirshleifer and Titman (1990)). In
addition, we should note that these two theoretical predictions (Proposition 2-1, 2-2) are notobserved when a bidder has no initial shareholdings as we saw in section II-A.
III. Experimental Design and Procedures
To test these theoretical propositions (Propositions 1 and 2), we construct takeover markets in alaboratory and conduct some experiments. In this section, we discuss our experimental design
and procedure.
Our experiments were conducted in January and May 1998 using undergraduate students at
Osaka University who volunteered to participate in a “decision-making game”. In order tomitigate any value biases, we (the experimenters) did not use any terms that would indicate that

12This is true as long as shareholders have some personal costs of tendering that are unknown to thebidder or they use some mixed tendering strategy.

13the experiment was about takeovers.13 We told participants that they were buying and sellingcommodities in the experiment. Thus, during the experiments, words about takeovers used inthis paper (e.g. “bidder”, “shareholder”, “share”) were replaced by those about commodity
trading (e.g. “buyer”, “seller”, “commodity”).14
In the experiments, a group consists of one bidder and twenty shareholders. Before theexperiment, the experimenter assigns roles to each participant by lottery. These roles are fixedduring the experiment. The experiment consists of 20 rounds for each group. One round of theexperiment proceeds as follows.
1) The experimenter lets the bidder know the post-takeover value z. z varies from 0 to 200 atintervals of every 10 (0, 10, 20, … 180, 190, 200), and z may be different in each round. z
is revealed only to the bidder, but not to the shareholders (asymmetric information).
2) Looking at the value of z revealed by the experimenter, the bidder offers a bid price x.
3) Observing the bid price x, shareholders choose either “to tender” (accept the offer) or “notto tender” (reject the offer).
4) Finally, the experimenter announces to all of the participants the number of shareholders
who have accepted the offer, and the value of z for this round.
This is one round of the experiment. It is repeated 20 times. The 20-round length is common
knowledge to all participants. Also, no communication is allowed throughout the experiment.
Each participant sits at her desk with side-board blinders to ensure as much privacy andanonymity as possible.
We conducted two kinds of experiments, [Experiment A] and [Experiment B]. These twodiffer according to whether or not the bidder initially holds the shares of the target firm. In[Experiment A], a bidder initially has no shares, and each shareholder owns one share (i.e.,shareholders as a whole have 20 shares). We call this case the no shareholdings case or the
Grossman and Hart case. In this case, when the bidder can purchase the shares from 10
shareholders or more, she succeeds in the takeover. Then the bidder’s payoff is 10 (z – x), andthe shareholders who have accepted the offer (tendered) obtain the offer price x while theshareholders who have rejected the offer (not tendered) obtain the post-takeover value z.15 16

13

In this respect, we follow the previous experiments of Kale and Noe (1997) and Cadsby andMaynes (1998).

14

For details, see the instruction sheet in the appendix.

15

In fact, in determining each shareholder’s payoff, we judge the takeover outcome by the numbersof shareholders to accept the offer other than her. We will explain this point later.

16

This shareholder payoff structure assumes that shareholders, having decided to tender, can sell
their shares with certainty in successful takeovers. Although this “certainty assumption” isintroduced to make shareholders’ decisions easier, it contradicts the bidder’s behavior in our settingin that she never buys more than 10 shares in successful takeovers. For consistency of the14

When 9 shareholders or less accept the offer, the takeover fails. Then, no transaction occurs,17and both the bidder’s and shareholders payoffs are zero.18
In [Experiment B], the bidder initially holds 5 shares, while each shareholder holds one
share as in [Experiment A]. That is, the bidder’s initial holdings are 20% (5/25) of the shares(α=0.2 in section II-B). We call this case the initial shareholdings case. In this case, when thebidder can purchase the shares from 8 shareholders or more, she obtains more than half of theshares ((5+8)/25) and succeeds in the takeover. Then, the bidder’ payoff is 5z + 8(z – x), while
the shareholders’ payoffs are the same as in [Experiment A]. When 7 shareholders or less accept
the offer, the takeover fails, and all the participants’ payoffs are zero.
In our experimental procedure, we must tackle the problem of how to reproduce atomistic
markets in the laboratory. As we stated earlier, we wish to test the propositions for corporate
takeovers developed by Grossman and Hart (1980), Shleifer and Vishny (1986), and Hirshleifer
and Titman (1990) which were discussed in the last section. We should note that these
propositions hold under the atomistic shareholder assumption; there are many small
shareholders, none of whom can affect the outcome of a takeover. Under this assumption, eachshareholder makes her tendering decision viewing the probability of takeover success as given.
On the other hand, as Bagnoli and Lipman (1988) point out, when there are only limited numberof shareholders, some shareholders must be pivotal in the sense that they may affect theoutcome of a takeover. In this case, each shareholder determines her tendering decision byrecognizing its impact on the probability of success, and consequently she may have more
incentive to tender. Under this non-atomistic shareholders assumption, Bagnoli and Lipman(1988) and Holmstrom and Nalebuff (1992) show that Grossman and Hart (1980)’s classicalproposition does not hold and successful takeovers are possible even in the no initialshareholding case. From the results of these theoretical models, we know that the takeover
outcome with non-atomistic shareholders is quite different from that with atomistic
shareholders.
Kale and Noe (1997) and Cadsby and Maynes (1998) test non-atomistic shareholder models

experimental procedures, we would have to drop this certainty assumption and adopt the“uncertainty assumption”, determining by lottery which shareholders could sell the shares when thenumber of tendering shareholders is more than 10 in successful takeovers. We can show, however,that the optimal tendering strategy of shareholders under the uncertainty assumption is the same asthat under the certainty assumption (‘not tendering’ is the weakly dominant strategy for shareholders
under both assumptions). Therefore, we adopt the certainty assumption for simplicity in our
experiments.
17

We consider conditional offers. See footnote 7.

18

Monetary rewards for participants are related to payoffs in the experiment. For details, see theinstruction sheet in the appendix.

15

in laboratory takeover markets. In contrast to their experiments, we test atomistic shareholders
models such as Grossman and Hart (1980), Shleifer and Vishny (1986), and Hirshleifer andTitman (1990). However, we cannot gather a huge number of participants for experiments andhence it is not easy to create the atomistic shareholder setting in the laboratory. One may argue
that 20, the number of shareholders in our experiment, is large enough to ensure atomistic
shareholder markets. However, this intuitive argument is false. The results of the non-atomistic
shareholder models indicate that even when the number of shareholders is 20, eachshareholder’s decision and the takeover outcome differ considerably from those under atomistic
shareholder markets. For example, let us suppose that the post-takeover value z is 100 and abidder with no initial shares offers a bid price (x) of 75. Then, using equation 2 of Kale andNoe’s (1997) paper, we obtain the theoretical results that (i) each of the 20 shareholders chooses
the mixed strategy where she tenders her share with probability of 0.506 (she does not tenderwith probability of 0.494); (ii) the probability of takeover success is 60.94%. These results arefar from Grossman and Hart’s results (no shareholders tender and no takeovers are successful).
Judging from this numerical example, in the usual laboratory setting we cannot expect that 20
shareholders behave as atomistic shareholders would.
Therefore, to test the atomistic shareholder model, we need to construct some experimental
device that makes each shareholder choose her decision as if she were an atomistic shareholder,i.e., she determines her tendering decision without considering its effect on the probability of
takeover success. Our solution to this problem is that we additionally define a takeover outcome
for each shareholder which is not affected by her own tendering decision. That is, we judge thetakeover outcome (success or failure) for each shareholder by the number of shareholders totender other than herself, and determine each shareholder’s payoff according to this definition.
To be specific, in [Experiment A] ([Experiment B]), if 10 (8) or more shareholders other thanher tender, we say that the takeover is successful for her, and she obtains the payoff in the caseof takeover success (gets x if she has tendered, z if she has not). In this setting, eachshareholder’s tendering decision does not affect the outcome of takeovers for that shareholder
to determine her payoff. Thus, she is expected to decide whether to tender without considering
the effect of her choice on the probability of takeover success. On the other hand, for the bidder(and for us, experimenters), we follow the usual rule, i.e., takeovers succeed if 10 (8) or moreshareholders accept the offer in [Experiment A] ([Experiment B]).
We expect that our experimental device will create an atomistic shareholder market in thelaboratory. At the same time, however, we recognize some limitations of our device inreplicating real atomistic markets. First, in our laboratory markets, if some shareholders arealtruistic or kind enough to others, their decisions may be biased toward more tendering
compared to those in real atomistic markets. In our markets, each shareholder’s decision does16

not affect the outcome of takeovers for herself, but it does affect the outcome of takeovers forthe bidder and for other shareholders. Thus, an altruistic shareholder may be willing to tender
her share for others in our markets,19 while she would not do so in real atomistic markets where
her decision does not affect any takeover outcome.20 Second, under our experimental device,different takeover outcomes among the participants may occur in the same round. For example,
suppose that just 10 shareholders accept the offer in [Experiment A]. Then a takeover issuccessful for a bidder and non-tendering shareholders, but it is unsuccessful for tendering
shareholders because the number of tendering shareholders other than each tendering
shareholder is 9. These different outcomes among the participants seem odd, but we consider
that this possibility does not significantly affect the behavior of each participant.
In spite of these limitations, we believe that our experimental device does create an
atomistic world in a finite participant laboratory and is an innovation of our paper. It is worth
noting that our device may be useful in other experiments where atomistic agents makedecisions facing some threshold for the aggregate outcome. For example, we can conduct
experiments on the provision of step-level public goods21 under atomistic agents, while thisissue has already been explored in the laboratory under non-atomistic agents by Offerman,
Sonnemans, and Schram (1996). Another application of our device might be in experiments on
the majority voting behavior of atomistic agents.
For more details about our experimental procedures, see the players instruction sheets usedin our experiments that are shown in the Appendix. We conducted [Experiment A] and[Experiment B] for four groups each. As one group consists of 21 persons (one bidder and 20
shareholders), 168 students participated the experiments. All students were inexperienced in thesense that they had not participated in such an experiment before. We paid the participantsmonetary rewards related to the payoffs they gained in the experiment. Average monetary
rewards of participants were $ 25.31 (3,290 yen if $1.00 = 130 yen) for sellers and $ 29.35(3,816 yen) for bidders. It took about 110 minutes to conduct one experiment.
IV. Hypotheses

19

We cannot ignore the effects of altruistic behavior. For example, Andreoni (1995) reports thatkindness or altruism can induce voluntary contributions in public goods experiments.

20

Note that, in real atomistic markets, each shareholder’s decision does not affect the takeover
outcome for others as well as for her, since both definitions of the takeover outcome are the same.

21

Step-level public goods are specific kinds of public goods that are only provided if a certain
minimum level of money (contribution) is raised. This minimum-contribution requirement(threshold) is also called a provision point (see Issac, Schmidtz, and Walker (1989)). Offerman,
Sonnemans, and Schram (1996) provide as examples of step-level public goods, bridges, lighthouses,
dikes, laws in parliament, and restoration of a public building.
17

Using this experimental setting, we test the theoretical predictions of the atomistic takeovermodels outlined in section II. We present six hypotheses derived from Propositions 1 and 2.
Hypothesis 1: Takeovers never succeed when a bidder has no initial shares of the target firm.
This hypothesis is a restatement of Proposition 1-1. This is a strong hypothesis in the sense thatit predicts that takeovers never succeed when a bidder initially has no shareholdings([Experiment A] in our laboratory). We would observe this result if shareholders are always as
rational as economic theorists assume, i.e., if shareholders know that they can gain the posttakeover value z by rejecting the offer and also rationally predict that z is larger than a bid x.
Hypothesis 2: Takeovers succeed with positive probability when a bidder initially has shares of
the target firm.
As Proposition 2-1 says, when a bidder has initial shareholdings ([Experiment B] in ourlaboratory), she may overcome the free-rider problem and succeed in takeovers since she caninternalize a part of post-takeover benefits z. Furthermore, comparing this Hypothesis 2 with
Hypothesis 1, we also predict that
Hypothesis 3: The probability of takeover success is lower in the no shareholdings case than in
the initial shareholdings case.
This Hypothesis is a weak version of Hypothesis 1. Even if Hypothesis 1 is not supported (i.e.,takeovers are sometimes successful in the no shareholdings case), we expect from the theory
that a takeover is less likely to succeed in the no shareholdings case (Grossman and Hart’s case)compared to the initial shareholdings case because of the severity of the free-rider problem.
Next, we measure the economic efficiency of takeovers for each group. As we mentioned in
section II, the takeovers we examine in the present paper are all value-increasing because theyrealize the positive post-takeover value z if they are successful. Hence, from a social point ofview, it is desirable that all takeovers succeed, but they may not, due to the free-rider problem ofshareholders. In order to find to what degree these post-takeover values z are realized bysuccessful takeovers, we define the efficiency of each group as
efficiency= (the sum of z realized by successful takeovers over the 20 rounds/ the sum of z over the 20 rounds)

Thus, efficiency represents the percentage of the post-takeover values actually realized bysuccessful takeovers compared to post-takeover values given by the experimenter for one group.
When takeovers succeed in fewer rounds, efficiency decreases. Hence, considering Hypothesis
3, we predict that18

Hypothesis 4: Efficiency is lower in the no shareholdings case than in the initial shareholdings
case.
Finally, the following two hypotheses are restatements of Propositions 1-2 and 2-2 whichindicate the relation between the bid price x and the probability of takeover success.
Hypothesis 5: The probability of takeover success is not related to the bid price x in the noshareholdings case.
Hypothesis 6: The probability of takeover success is increasing in the bid price x in the initialshareholdings case.
Grossman and Hart’s (1980) proposition predicts that when a bidder has no initial shares([Experiment A] in our laboratory), rational shareholders would expect that a bid x must be
lower than a post-takeover value z, so that a high bid would not induce shareholders to tendertheir shares. On the other hand, theoretical predictions by Shleifer and Vishny (1986) and
Hirshleifer and Titman (1990) suggest that when a bidder initially hold shares ([Experiment B]
in our laboratory), a high bid induces shareholders to accept the offer, and raises the probabilityof takeover success.
V. Experimental Results
A. Overview
We present the experimental results in Table 2-A ([Experiment A]) and Table 2-B ([ExperimentB]). These tables indicate information about the value of z presented by the experimenter22, thebid price x offered by the bidder, and the numbers of shareholders who accepted the offer foreach round. In the bottom three rows of the tables, we can also observe the average bid price,
the acceptance rate (the sum of the number of shareholders who accept the offer / total numberof shareholders (20×20)), the number of rounds of successful takeovers, and efficiency (definedin the last section) for each group.
These two tables show the main results that the formal analysis will confirm. First, theprobability of successful takeovers is lower in the no shareholdings case (Grossman and Hart’s
case, [Experiment A]) than in the initial shareholdings case ([Experiment B]). The numbers ofsuccessful takeovers are 3, 4, 1, 8 for groups of [Experiment A], whereas they are 13, 17, 14, 13
for groups of [Experiment B]. Second, as a result of this, the efficiency is also lower in the noshareholdings case than in the initial shareholdings case. In [Experiment A], the efficiency
22

The value of z was determined by the experimenter with dice. To make comparisons easily, we use
the same stream of z for all the groups.

19remains at a low level (2.19% - 41.67%), while in [Experiment B], it is fairly high (66.67% 92.54%). These results seem to support Hypothesis 3 and Hypothesis 4 in the last section. This
indicates that a severer free-rider problem occurs in the no shareholdings case (Grossman andHart’s case) than in the initial shareholdings case. In addition, we also observe that the averagebid is larger in the initial shareholdings case than in the no shareholdings case. This reflects thefact that a bidder can afford to make a higher bid in the initial shareholdings case because she
can obtain more profits by internalizing part of post takeover gain in successful takeovers (see,the bidder’s profitability condition in Figure 1-B).
Next, let us look at Figure 2-A and Figure 2-B. These two figures show the relationships
among the post-takeover value z, the bid price x, and the probability of takeover success. The
height of each bar shows the probability of takeover success for a specific z and x range. For
example, in Figure 2-A, the probability of success is 0.364 (36.4%) in the 130-160 z and 90-120
x range. This probability of success is calculated from Table 2-A where we find that 4 out of 11
takeovers succeeded in this z and x range. An empty square indicates no offers are made in thatcell (e.g. in the 130-160 z and 50-80 x range) and a bar with no depth indicates offers weremade but no takeovers were successful (e.g. in the 90-120 z and 50-80 x range). In addition, in
the figures, to exclude extreme probability values due to small samples, we consider a cell with
only one offer (where the probability of success must be either 0 or 1) as that with no offers.
Figures 2-A and 2-B highlight the relations between a bid price x and the probability of
takeover success for each experiment. In Figure 2-A ([Experiment A], the no shareholdingscase), we do not find an obvious relationship between the bid price x and the probability ofsuccess. If anything, there may be a positive relation because cells with zero probability ofsuccess (a bar with no depth) can be seen in only the lower x range (0-40, 50-80, 90-120), but
this positive relationship seems to be very weak. On the other hand, in Figure 2-B ([ExperimentB], the initial shareholdings case), there seems to be a fairly clear positive relationship between
the bid x and the probability of success. There, we observe a higher probability of takeoversuccess in higher ranges of x, although we do see a conspicuous exception in that the probabilityof success is high (0.8) in the cell of the 0-40 z and 0-40 x range (we know that 4 out of 5
takeovers succeeded in this cell from Table 2-B).
The above observations seem to be consistent with Hypotheses 5 and 6. We will later
confirm whether our impression is right by conducting formal statistical analyses. A further
finding in Figures 2-A and 2-B is that there is a positive relation between z and x in both figures.
This positive relation presumably reflects the bidder’s profitability condition illustrated in
Figures 1-A and 1-B.

20

B Tests of Hypotheses
In this subsection, we test the hypotheses listed in Section IV. We discuss to what degree ourexperimental data support the hypotheses and examine the appropriateness of the takeovermodels such as Grossman and Hart (1980), Shleifer and Vishny (1986), and Hirshleifer andTitman (1990). Results 1-6 shown below correspond to the results of tests on Hypotheses 1-6, inorder.
Result 1: The probability of takeover success is 0.2 (20%) in the no shareholdings case.
Table 3 summarizes the results of the probability of takeover success, acceptance rates, andefficiency for each experiment. From the first column of Panel A, we find that in [ExperimentA] (the no shareholdings case), takeovers are successful in 16 out of 80 rounds. Thus theprobability of success is 0.2 (20%). This result does not support Hypothesis 1, the strong
hypothesis that takeovers never succeed when a bidder has no initial shareholdings. In Panel B,
we also observe the acceptance rate, i.e., the proportion of shareholders who accepted the offer.
The first column shows that in [Experiment A], 639/1600 shareholders choose to accept theoffer and hence the acceptance rate is 0.399 (39.9%) Thus, we recognize that the two-fifths ofthe participants who play shareholders’ roles decide to tender their shares, while Grossman andHart (1980) predict that no shareholders tender at all. In Section VI, we examine the possible
reasons why these participants did not behave as the theory predicted.
Thus, our experimental evidence contradicts Hypothesis 1 which is originally derived from
Grossman and Hart’s (1980) classical proposition. We should not, however, dismiss the basic
insight of Grossman and Hart that corporate takeovers fail due to the free-rider problem amongshareholders. Our evidence indicates that in the no shareholdings case, only 20% of takeovers
succeed (80% of takeovers fail), which means that most of the post-takeover values which
would be realized by successful takeovers (z) disappear. In fact, in Panel C of Table 3, we
observe that average efficiency over groups of [Experiment A] is only 21.38%, that is, about
80% of social values are lost in [Experiment A]. These results suggest that the optimistic storyof corporate takeovers is doubtful. We observed fairly severe free-rider problems in ourlaboratory and consequently takeovers tended to be unsuccessful. In this sense, we can say that
Grossman and Hart (1980)’s classical proposition contains a valuable message to help us
understand the nature of takeover markets.
Result 2: The probability of takeover success is about 0.7 (70%) in the initial holdings case.
This result can be seen in the middle column ([Experiment B]) of Panel A of Table 3. We
find that in [Experiment B] (the initial shareholdings case), 57 out of 80 takeovers are
successful, and thus the probability of success is 0.713 (71.3 %). This result supports
Hypothesis 2 that takeovers succeed with positive probabilities when a bidder initially has
21shares. In Panel C of Table 3, we also notice that the average efficiency over groups of[Experiment B] is 76.54%. From these results, we conclude that the initial shareholdings of abidder can substantially mitigate the free-rider problem in corporate takeovers and greatly
improve social welfare.
Result 3: The probability of takeover success is significantly lower in the no shareholdings casethan in the initial shareholdings case.
Result 4: The efficiency is significantly lower in the no shareholdings case than in the initialshareholdings case.
Result 3 can be easily deduced from Results 1 and 2. As the lowest row of Panel A of Table
3 shows, the difference in the probability of success between [Experiment A] and [ExperimentB] is 0.513, and this difference is statistically significant (p-value <0.001) by Fisher’s exact test.
Therefore, our experimental data support Hypothesis 3. Also, as predicted from Result 3,
Hypothesis 4 is supported as well. Panel C of Table 3 shows that the average efficiency in[Experiment A] (21.38%) is much lower than that in [Experiment B] (76.54%). The difference
between the two amounts to 55.16% and this difference is statistically significant at 0.3% levelby Welch’s t-test. Results 3 and 4 indicate that the free-rider problem is more serious in the noshareholdings case (Grossman and Hart’s case) than in the initial shareholdings case.
The approximately 50% (51.3%) point increase in the probability of success in the initialshareholdings case compared to the no shareholdings case may stem from two effects, according
to the theoretical arguments in Section II-B. One is the tendering effect which states that in theinitial shareholdings case, the bidder can offer a bid x higher than z so that shareholders tend totender their shares. Another is the pure number effect such that initial shareholdings by a bidder
reduce the number of shares needed to succeed in takeovers. To make a takeover successful, abidder has to purchase only 8 shares or more in [Experiment B], whereas she has to purchase 10
shares or more in [Experiment A]. To grasp the magnitude of each effect, we calculate theprobability of takeover success in [Experiment B] assuming that takeovers succeed when abidder purchases 10 (not 8) shares or more. This hypothetically calculated probability of successin [Experiment B] can be interpreted as the probability of success in the initial shareholdings
case without the pure number effect, since the number of the shares required (10) is the same asthat in the no shareholdings case. We find that this calculated probability of success is equal to0.375 (37.5%). Thus, we can say that out of the 51.3% point rise in the probability of successgained by the initial shareholdings, 17.5% (37.5% minus 20%) comes from the tendering
effect23 and 33.8% (71.3% minus 37.5%) stems from the pure number effect.

23

Panel B of Table 3 shows that shareholders are more likely to tender in the initial shareholdings22

It is worth noting that Walking’s (1985) empirical study also finds a positive relationshipbetween the bidder’s initial shareholdings and the probability of takeover success, using datafrom the U.S. capital markets over 1972-76. It is not clear from his study, however, what factor
gives rise to this positive relation, although he did present some hypotheses concerning thisissue.24 This may be partly because in empirical studies (in general) it is not necessarily easy toisolate one specific factor from naturally occurring phenomena in a complex reality. In contrast,
our experimental research has made it clear why the bidder’s initial shareholdings increase theprobability of success by testing the takeover models directly in the laboratory. This positive
relation comes from the tendering effect and the pure number effect.
Result 5: The probability of takeover success is not related to the bid price x in the noshareholdings case.
Result 6: The probability of takeover success is increasing in the bid price x in the initialshareholdings case.
Results 5 and 6 support Hypotheses 5 and 6, respectively. To obtain Results 5 and 6, weconducted the following logit analyses for both experiments.
Model 1: Prob = F ( a + b x )(3)Model 2: Prob = F ( a + b x + c1 ROUND + c2 GROUP2 + c3 GROUP3 + c4 GROUP4)(4)

where Prob equals 1 if the takeover is successful and equals 0 otherwise. F(k) = 1/(1 + e -k) is
the logit function, and x is the bid price offered by a bidder. To control for the group effect andmonotonic trends in the probability of success over time, we add in Model 2 group dummies(GROUP2-GROUP4) and the variable ROUND which equals 1 for the 1st round, equals 2 forthe 2nd round, and so on25. From Hypotheses 5 and 6, we expect b = 0 for the groups in the noshareholdings case ([Experiment A]), and b > 0 for the groups in the initial shareholdings case([Experiment B]).
Table 4 reports the regression results for each experiment. In [Experiment A], thecoefficients of the bid price x are positive but they are not statistically significant in bothcase ([Experiment B]) than in the no shareholdings case ([Experiment A]); the acceptance rate in[Experiment B] is 0.4575 while that in [Experiment A] is 0.3994, and its difference (0.058) is
statistically significant at 0.1% level by Fisher’s exact test.
24

Walking (1985) discusses two hypotheses on why the bidder’s initial shareholdings raise theprobability of takeover success. One is the strong influence of the bidder on the target management,
and the other is the increased shareholder fear of becoming inactive minorities.

25

We also used the round dummies (RDQ2 takes the value of 1 for the 6th – 10th rounds, RDQ3 takes
the value of 1 for the 11th – 15th rounds, and RDQ4 takes the value of 1 for the 16th – 20th rounds)
instead of ROUND to control the round effect. However, the results did not change.

23Models 1 and 2. This result is in line with Hypothesis 5; the probability of takeover success is
not related to the bid price in the no shareholdings case. On the other hand, in [Experiment B],
we observe statistically significant positive coefficients on the bid price x in both models (pvalues are less than 1% in both models). This suggests that Hypothesis 6 is also supported; theprobability of takeover success is increasing in the bid price x in the initial shareholdings case.
In addition, we do not find any group effects or round effects on takeover success, since theestimated coefficients of group dummies and round variables are not statistically significant.
In Figure 3, we predict the probability of takeover success for each bid price x by theestimation results of Model 2 in Table 4.26 To compare the predicted values to the observed ones,
the figure includes the actual probability of success for each x range depicted in Figures 2-A and
2-B. First, in the no shareholdings case, the predicted probability of takeover success does notseem to increase significantly with a bid price x (the dotted line). The predicted probability ofsuccess is 0.10 (10%) for a bid of 20, and it is only 0.25 (25%) for a bid of 180. That is, theprobability of takeover success remains low at a higher bid price. This evidence is consistent
with Grossman and Hart’s (1980) theoretical prediction that shareholders rationally expect that abid price x is lower than z and they are not induced to accept the offer at any bid level.
On the other hand, in the initial shareholdings case (the solid line), the graph obviously
shows that the probability of success increases with the bid price x. For example, while thepredicted probability of takeover success is only 0.26 (26%) when the bid x is 20, it rises to 0.94
(94%) when the bid x is 180. Thus the difference between two predicted probabilities amounts
to 0.68 (68% points).27 This suggests that the positive effect of the bid price x on the probabilityof success in the initial shareholdings case is economically significant.
These results give us an insight into the importance of the bid premium in influencing theoutcomes of takeovers, an issue that some researchers have empirically investigated.
Hoffmeister and Dyl (1981) report that the bid premium has no effect on success or failure of atakeover, using a U.S. sample from 1976-77. Walking’s (1985) study, however, shows that thebid premium has a positive effect on the probability of takeover success during 1972-76.
Compared to these empirical studies, our experimental evidence suggests more general results;
the bid does not affect the takeover outcome in the no shareholdings case, but it does affect theoutcome in the initial shareholdings case. In other words, we have shown that the effect of thebid premium on the takeover success is different, depending upon whether the bidder initially26

Figure 3 assumes that ROUND equals 10 and the intercept term is at the mean of four groups.

27

In Figure 3, it may seem odd that the actual probability of success in the initial shareholdings case(‘Initial Shareholdings: Actual’, depicted as a circle) for 0-40 x range (0.67) is not in theneighborhood of the predicted probability line (the solid line). But this can be understood once werecognize that the number of rounds for the 0-40 x range is only 6, which is a relatively small
number compared to the number of total rounds 80.
24holds the shares of the target firm or not.
To summarize our observations, (i) the free-rider problem is severe in Grossman and Hart’s
world, but (ii) initial shareholdings by a bidder significantly mitigate the free-rider problem. On
the whole, our experimental evidence supports the messages from takeover models such as
Grossman and Hart (1990), Shleifer and Vishny (1986), and Hirshleifer and Titman (1990).
From these results, we conjecture that the free-rider problem potentially exists in real takeovermarkets as well, and that the bidder’s initial shareholdings may make takeovers successful inreality.
VI.

Discussion
In this section, we present two kinds of analyses. First, we analyze the individual bidders’and shareholders’ behavior in our laboratories. Does each participant (bidder or shareholder)
behave as the theory suggests? In experimental research, just as in other empirical research, wesometimes observe some evidence that is not consistent with the theoretical prediction. In thissense, our experiment is no exception. We point out some anomalies in participants’ decisions in
our laboratory and explore how to interpret them. Second, we focus on the results for the laterrounds in each session in order to examine the robustness of our conclusions.
A. Bidders’ Behavior
It is important to examine bidders’ behavior because it could affect shareholders’ behavior
and takeover outcomes. The theory suggests that a bidder determines a bid price x so as to gain
positive profits from a successful takeover. Thus, a bid is expected to satisfy the bidderprofitability conditions that are shown in Figure 1-A and 1-B. Is this the case in our
experiments?
Using the data on bid prices shown in Table 2-A and 2-B, we confirm that a bidder usuallyoffers a bid satisfying the bidder-profitability condition. At the same time, however, we also
notice that there are some rounds in which a bidder overpays, that is, a bidder offers too high abid to gain profits even if a takeover succeeds. In [Experiment A], for example, in the 8th roundof Group A-1, the bidder offers 60 which is higher than the post-takeover value z of 50. In thisround, the bidder would incur losses of 10 per share if the takeover succeeded. Excessively highbids of this kind occur in four rounds in Group A-1, one round in Group A-3, and seven rounds
in Group A-4, as can be seen in Table 2-A. We also find bidder overpayments in [Experiment B],
violating the bidder-profitable condition (2), in two rounds (the 2nd and 18th rounds) in Group B2 and in three rounds (8th, 10th, and 18th rounds) in Group B-4.
Why did some bidders overpay in our experiments? We consider two possibilities. The first25

one is confusion; a bidder misunderstood or could not calculate her payoffs and unconsciously
offered too high a bid. To explore this possibility, we checked the bidder’s (buyer’s) record
sheets, and examined whether bidders made any mistakes in calculating their payoffs. However,no mistakes were found on the bidder’s record sheets throughout our experiments. We therefore
conjecture that overpaying bidders did not confuse their payoffs, rather they consciously
overpaid.
Another possibility is that bidders overpay to establish a reputation for offering higher bids
and induce shareholders to tender in later rounds. If this were the case, the bidder’s overpaying
behavior would be observed less in later rounds than in earlier rounds; in our experimental
setting with a finite number of rounds (20 rounds), the value of reputation must decrease as thesession approaches its end. To examine whether this reputation effect motivates bidders to
overpay, we run regressions on the bid price x. We use as explanatory variables, z (posttakeover value), ROUND (which equals 1 for the 1st round, equals 2 for the 2nd round, and soon) or round dummies (RDQ2 takes the value of 1 for the 6th – 10th rounds, RDQ3 takes thevalue of 1 for the 11th – 15th rounds, and RDQ4 takes the value of 1 for the 16th – 20th rounds),
and group dummies (GROUP2, GROUP3, and GROUP4). If a bidder decides her bid based on
the reputation effect, ROUND or the round dummies (RDQ2, RDQ3, and RDQ4) should havenegative effects on a bid price.
Table 5 reports regression results using Ordinary Least Squares. Model 1 represents theestimation results of the equations using the variable ROUND, whereas Model 2 shows results
using the round dummies (RDQ2, RDQ3, and RDQ4) instead of ROUND. First, we notice thatthe post-takeover values z have significant positive effects on the bid prices in both experiments([Experiment A] and [Experiment B]). This is a natural result emanating from the bidderprofitability condition; a higher-z-bidder can afford to offer a higher bid.28 Next, let us examine
the reputation effect. The results of Model 1 show that ROUND is not significant in either
experiment. The results of Model 2 also indicate that the round dummies are not significant ineither experiment, except that RDQ2 is significant but positive in [Experiment A]. In addition,
in Model 2, we also confirm (not reported in the table) that neither the difference between thecoefficient of RDQ2 and that of RDQ3, nor the difference between the coefficient of RDQ3 andthat of RDQ4, was significant in either experiment. Therefore, we do not find any evidence
suggesting that the bid level becomes lower as the session approaches its end. This result
contradicts the hypothesis that bidders consider their reputation for later rounds, and suggests

28

Walking and Edmister (1985) report that the bid premium is a positive function of potential
acquisition-related benefits using the data from 158 cash tender offers for 1972-1977. This empiricalresult is consistent with our experimental result that a bid price (x) is positively related to potential
post-takeover benefits (z).
26that overpayment is not due to reputation concerns.
Thus overpayment remains an anomaly and seems to represent irrational behavior by abidder. However, it is worth noting that although we sometimes observed bidders overpaying in
our laboratory, the messages of the theoretical takeover models are supported by ourexperimental results as shown in the last section. This suggests that the takeover models areappropriate for predicting the phenomena of takeover markets even if there exist some irrational
bidders.
B. Shareholders’ Behavior
In Section V-B, we observed that about 40% of shareholders sell their shares in [Experiment A],
while Grossman and Hart (1980)’s classical proposition predicts that no shareholders tender at
all in the no shareholdings case. How can we interpret this gap between the experimental result
and the theoretical prediction? In this sub-section, we examine three possible reasons why aconsiderable proportion of shareholders sell their shares in [Experiment A]: pivotal confusion,
implicit cooperation among shareholders, and response to a bidder’s excessive bid.
1. Pivotal Confusion
Pivotal confusion may be one reason for some shareholders to tender. As we explained in
Section III, in our experimental setting each shareholder’s tendering decision does not affect theoutcome of a takeover for her. However, if a participant (a shareholder) does not understand thisrule, she may incorrectly perceive that she may be a pivotal shareholder to affect a takeover
outcome that determines her payoff. In this case, as the non-atomistic shareholder models(Bagnoli and Lipman (1988) and Holmstrom and Nabeluff (1992)) suggest, the shareholder ismore likely to tender the share expecting that her tendering raises the probability of a takeoversuccess. We call this confused shareholder behavior pivotal confusion.
To explore to what degree such pivotal confusion occurs, we checked the shareholders’(sellers’) record sheets. On this sheet, each shareholder enters her decision (sell or not sell), thenumber of shareholders who agree to sell their shares, the number of shareholders other than her
who sell their shares, and her payoff. By inspecting the mistakes on these items in eachshareholder’s record sheet, we can specify for whom and in what round the pivotal confusion
occurs. Suppose, for example, that in one round on one shareholder’s record sheet, we find thather decision = ‘sell’, the number of the shareholders who agreed to sell their shares’ = ‘8’, andthe number of the shareholders other than her who sold their shares = ‘8’. This shareholder
clearly makes a mistake in this round; since her decision is ‘sell’, ‘the number of shareholders
other than her who sold their shares’ must be ‘7’ (8 minus 1). Then, we judge that pivotal
confusion occurs in this round for this shareholder.
27

In Group A-1, we find 5 pivotal confusions out of a total of 400 selling opportunities (20shareholders times 20 rounds). We also find 2, 2, and 10 pivotal confusions in Group A-2, A-3,
and A-4, respectively. Therefore, for four groups in [Experiment A], the number of pivotal
confusions is 19 out of a total of 1600 selling opportunities (20 shareholders × 20 rounds × 4
groups), and the proportion of pivotal confusion is thus only 1.19% (19/1600). This suggeststhat pivotal confusion hardly occurs throughout [Experiment A]29, judging from shareholders’(sellers’) record sheets. For reference, we re-calculate the acceptance rate (the proportion ofshareholders who tendered their shares) shown in Panel B of Table 3, assuming that theshareholders with pivotal confusion do not tender in those rounds. Then, the acceptance rate in[Experiment A] declines to 0.3875, which is only slightly lower than the 0.3994 figure in Table
3.30
This suggests that pivotal confusion cannot be a major reason that about 40% of
shareholders tender their shares in [Experiment A]. At the same time, the above observation oflittle pivotal confusion also means that almost all shareholders (participants) understand ourexperimental setting and thus know that each shareholder’s decision does not affect a takeover
outcome for her. In this sense, we can say that our original device is fairly successful in making
the finite participant laboratory close to the atomistic shareholder world.
2. Implicit cooperation among shareholders
The second possible reason for shareholder tendering is that some shareholders implicitly
may cooperate with one another. That is, even without communication, they may accept theoffer jointly to realize social gains from a takeover success, rather than attempting to free rideby rejecting the offer. Does this cooperative behavior occur in our experiments?
From game theory, the standard answer to this question would be ‘No’. In the finite repeatedgame framework, based upon a backwards induction argument, a subgame perfect equilibrium
strategy is that everyone takes a one-shot Nash equilibrium strategy (‘reject the offer’ in ourgame) in every round, rather than taking the cooperative strategy (‘accept the offer’ in ourgame).31 Thus, there is no possibility that shareholders implicitly cooperate and tender their

29

Throughout [Experiment B], the number of pivotal confusions is 42 out of 1600. Thus, the fractionof the pivotal confusion is 2.63% (42/1600), which is also at a fairly low level.

30

On the assumption that the shareholders with pivotal confusion do not tender, the probability ofsuccess and the average efficiency in [Experiment A] decline to 0.1750 (17.5%) and 17.98%,
respectively. These figures, however, are only slightly lower than those in Table 3 and hence do notbasically change our results.

31

On the other hand, it is also well known that cooperation among agents can be an equilibrium in
an infinitely repeated game through the use of threats. A typical example of this is the infinitely
repeated Prisoners’ Dilemma. There cooperation is a subgame perfect equilibrium using the Tit-for28

shares jointly, as long as the number of rounds is finite (20 in our experiment).
However, there is also an alternative to this standard view in game theory. Kreps, Milgrom,
Roberts, and Wilson (1982) present a reputation model showing that cooperation can occur evenin a finitely repeated Prisoners’ Dilemma. They suggest that when the players are uncertain
about their rivals’ rationality, each player chooses to cooperate to establish a reputation for an
irrational (cooperative) behavior, and doing so results in higher payoffs to her. In addition,
Kreps, et al. (1982) also predict that the degree of cooperation decreases over time because thereputation value becomes lower in later periods.
A considerable number of public goods experiments with a finite number of rounds typicallyshow that cooperation (contributions to public goods) occurs and that the cooperation rate (thecontribution rate) declines as the session approaches close to its end.32 This evidence isconsistent with the above prediction of Kreps, et al. (1982). Thus, with the Kreps, et al. (1982)
story, our evidence of shareholders’ tendering may also be considered as cooperative behavior
among shareholders.
To explore this possibility, we examine whether the degree of shareholder tendering declines
over time as Kreps, et al. (1982) suggest. To put it more concretely, in the logit regression oftendering probability we run later, we see whether the round number (ROUND) or the rounddummies (RDQ2, RDQ3, and RDQ4) have negative effects on the probability of tendering.33

3. Response to the bidder’s excessive bids
In Section VI-A, we saw that bidders sometimes overpay in our experiment. We could not
specify the reason for this behavior. However, whatever the reason may be, it is possible thatshareholders are induced to tender their shares by the bidders’ excessive bids. Suppose that ashareholder observes that bidders overpay (i.e., x > z in [Experiment A]) in one round. Then,
she may expect that the bidder will overpay again for some reason and choose to sell the shareto gain a bid price x (that may be larger than z). Therefore, the shareholder tendering observed
in [Experiment A] may be a response to bidders overpaying in previous rounds.
To examine this effect, we employ a logit regression of shareholders’ probabilities oftendering, adding one of two variables representing overbidding, OPAYAVG or OPAYDUM.
OPAYAVG is the average of overpayments (x-z) from the 1st round to the previous round.
OPAYDUM is a dummy variable that takes a value of 1 if overpayment has occurred at least
once prior to the previous round, and 0 otherwise. If shareholders’ tendering stems from bidders
Tat strategy.
32

See, for example, Dawes and Thaler (1988) and Davis and Holt (1993, Chapter 6).

33

For the variable ROUND and the round dummies, see Section VI-A.

29

historical overpayments, the coefficient of OPAYAVG or OPAYDUM must be positive.
4. Logit regression analysis
We perform the following logit regression of shareholders’ probabilities of tendering for[Experiment A].
Model 1: Prob (tender) = F ( a + b x + c1 ROUND + c2 OPAYAVG+ c3 PIVOTAL + group dummies)(5)

where Prob (tender) equals 1 if a shareholder tenders the share (accepts the offer) and equals 0 if
she does not tender (rejects the offer). F is the logit function as before (see eqs. (3) and (4) in
Section V-B), and x is the bid price offered by a bidder. ROUND and OPAYAVG are the roundnumber and the average of overpayments, respectively, as defined above. PIVOTAL is a dummy
variable that takes a value of 1 if pivotal confusion is observed for that shareholder in that round.
If pivotal confusion induces shareholders to be more likely to tender, PIVOTAL has positiveeffects on tendering probability. Model 2 differs from the above Model 1 in that the former uses
the round dummy (RDQ2, RDQ3, and RDQ4) instead of ROUND. Model 3 and Model 4 aredifferent from Model 1 and Model 2, respectively, in that the former models include
OPAYDUM instead of OPAYAVG.
The logit regression results are presented in Table 6. We first notice that the round number(ROUND) and the round dummies (RD2, RD3, and RD4) are not significant in any of theregressions. In addition, in Model 2 and Model 4, we also confirmed (not reported in the table)that neither the difference between the coefficient of RDQ2 and that of RDQ3, nor thedifference between the coefficient of RDQ3 and that of RDQ4, was significant. That is, we do
not find that the tendering probability declines over time in our experiments. This contradicts
the prediction of Kreps et al. (1992). Therefore, the shareholder tendering observed in our
experiment cannot be interpreted as implicit cooperation among shareholders as in Kreps, et al’s
(1982) story. Second, OPAYAVG and OPAYDUM, the variables for historical overpayments, do
not have significant effects on tendering probability either.34 Hence, a bidder’s overpayment
does not seem to induce shareholders to tender their shares, that is, the bidder’s overpayment
cannot be a reason for the shareholder tendering observed in our experiments. Third, PIVOTAL
has a significant positive effect on tendering probability in all regressions.35 This suggests that34

We also use as independent variables the average of overpayments during the previous 5 (and 3)
rounds, the overpayment in the previous round, and the number of the overpayment rounds prior to
the previous round instead of OPAYAVG or OPAYDUM. None of these variables are significant.

35

This marginal effect (not reported in the table) equals 0.23. Thus, the tendering probability of ashareholder with this confusion is 23 percentage points higher than those without this confusion,
ceteris paribus.

30

shareholders with pivotal confusion are more likely to sell their shares, as expected.36 However,since pivotal confusion occurs so rarely, it cannot play a major part in determining tendering
decisions.
Overall, although we presented three possible reasons for shareholders to tender in[Experiment A] (pivotal confusion, implicit cooperation among shareholders, and response tobidders’excessive bids), none of them were supported by our results. Thus, the observation ofless than perfect free-riding still remains an anomaly. We now point out some other hypotheses
which may explain this anomaly.
One possibility is shareholder misperception; perhaps some shareholders did not notice theadvantage of free-riding behavior. As we mentioned earlier, our experiments were conductedunder asymmetric information settings, which is more realistic than the symmetric information
settings of Grossman and Hart’s original paper. In addition, our experiment is not a simple
repetition of the same game since the values of z differ from round to round. Therefore, it waspossible that some shareholders could not rationally predict that z is larger than x, and hence
they chose to tender their shares. Another possibility is shareholder altruism. In our experiments,
as we explained earlier, each shareholder’s decision affects the takeover outcome for the bidder
and for other shareholders while it does not affect her own takeover outcome. Thus, if ashareholder was sufficiently altruistic, she might choose to tender in order to contribute to a
takeover success for others. We cannot ignore this possibility because we recognize that in
public goods experiments voluntary contributions can be induced by kindness or altruism.
To explore these possibilities, it seems useful to conduct additional experiments. First, toexamine whether tendering arises from shareholder misperception, we could conduct ourexperiments under symmetric information settings and/or use experienced participants, andcompare the results with those we obtained. Second, to figure out whether altruism motivates
tendering decisions, we could run an experiment where the takeover outcome is determined bysome completely random process.37 In this setting, a shareholder could not affect others’ payoffs
by her actions, and therefore there would be no scope for altruism. If we observe less tendering
behavior in this setting than in our experiments, we could conclude that altruism or kindness is
one reason for shareholder tendering in our experiments. We leave these additional experiments

36

We also use the variable, PIVOTAL-ALL, which equals 1 for all of her rounds if a shareholder
experiences pivotal confusion in at least one round during the experiment, and equals 0 otherwise.
We find that PIVOTAL-ALL also has a significant positive sign on shareholder tendering
probabilities in all regressions. Thus, the shareholders who experience pivotal confusion are more
likely to tender during the whole session. In addition, we recalculate the acceptance rate (panel B of
Table 3) in [Experiment A], dropping these shareholders. It equals 35.91%, which is only slightly
lower than that of Table 3.

37This idea was suggested by Bram Cadsby and Elizabeth Maynes.

31for future research.
Also, it should be added that non-free-riding behavior is typically observed in public goods
experiments (Dawes and Thaler (1988) and Davis and Holt (1993, Chapter 6)). The reason whysome people do not free ride in the provision of public goods has been the subject ofcontroversy over the last few decades, however, it still remains an anomaly. Explaining thisanomaly would help understand the non-free-riding behavior observed in our takeover
experiments.
Before ending this sub-section, we note in Table 6 that the bid price x has a significant
positive effect on tendering probability, that is, a high bid induces shareholders to tender. This
result seems to contradict the result in Section V-B which suggested that a high bid does not
significantly increase the probability of takeover success in [Experiment A]. Calculating themarginal effects from the logit regressions in Table 6, however, we find that the effect of x on
tendering probability is relatively small. The average of the marginal effects for Model 1 Model 4 is 0.000763 (not reported in the table), which indicates that when a bid price x
increases from 0 to 200, the tendering probability increases by only 15.26%. This isconsiderably smaller than the 45.96% which we obtain for [Experiment B]38. In addition, as we
will show later, the effect of a bid x on tendering probability is no more significant in theanalyses for the final 10 or 15 rounds. That is, in the no shareholdings case (i.e., [ExperimentA]), shareholders are not induced to tender by a high bid price after experiencing several roundsof the experiment. This result seems to suggest that shareholders’ behavior approaches thetheoretical prediction of Grossman and Hart (1980) (Proposition 1-2 in Section II-A) as
participants learn more about our takeover game.
C. Analyses for Later Rounds
Finally, we report the results of our analyses for the final 15 and 10 rounds of each session.
If there is some learning process taking place, the results for the final rounds may be different
from those for the whole session. To explore this possibility, we conduct the same analyses forthe final 15 (6th – 20th) and final 10 (11th – 20th) rounds. As shown below, we find that our basic
conclusions remain largely unchanged.
Table 7 summarizes the probability of takeover success, the acceptance rates, and theaverage efficiency for the final 15 and 10 rounds. We notice that the results are very similar to
those for the whole session reported in Table 3. First, in [Experiment A], the probability ofsuccess and average efficiency is low; the probability of success is 0.1833 for the last 15 rounds
38

We run the same regressions (Model 1 – Model 4) for [Experiment B], obtain the average of themarginal effects of x on the tendering probability for Model 1 – Model 4, and calculate the increasein tendering probability when x rises from 0 to 200.
32

and 0.1500 for the 10 rounds, and the average efficiency is 19.08% for the 15 rounds and16.49% for the 10 rounds. Therefore, our result for the whole session that a valuable takeovertends to fail due to the free-rider problem in the no shareholdings case is also supported in the
final rounds. Second, in [Experiment B], the probability of success and the average efficiency
are high for both the final 15 and 10 rounds (for example, for the final 15 rounds, the probabilityof success is 0.700 and the average efficiency is 77.08%). Thus, we confirm our result that
initial shareholdings held by the bidder mitigate the free-rider problem also holds for the final
rounds. Third, the acceptance rates are lower in [Experiment A] than in [Experiment B] for boththe final 15 and 10 rounds. This result is the same as that for the whole session (in Table 3)
although the difference is not highly significant (the p-value is 0.075 for the 15 rounds and0.093 for the 10 rounds).
Next, we examine the relation between the bid price x and the probability of takeoversuccess. We run the same regressions for the final 15 and 10 rounds as those for the wholesession presented in Table 4 (the detailed results are not reported to save space). In the[Experiment A] regressions, we obtain exactly the same results for both the final 15 and 10
rounds as those in Table 4; a bid price x does not significantly affect the probability of success.
In the [Experiment B] regressions for the final 15 and 10 rounds, we observe the positive effectsof x on the probability of success, as we did for the whole session in Table 4, although thiseffect is significant only for the final 15 rounds (for the final 10 rounds, the p-values for the x
coefficients are 0.25 in Model 1 and 0.21 in Model 2). Thus, we can say that the results on therelation between the bid price and the probability of success for the final rounds are almost thesame as those for whole session.
In addition, as for the individual participants’ (the bidder’s and shareholders’) behavior,
most of the findings observed for the whole session are robust for the final 15 and 10 rounds.
We run the same regressions for the final 15 and 10 rounds as those in Table 5 (the bidder’sbehavior) and Table 6 (the shareholders’ behavior). The results are very similar to those for thewhole session (the detailed results are not reported to save space); in the regressions on bidder
behavior, ROUND and the round dummies are not significant; in the regressions on theshareholder tendering decision, the variables for the round number and the variables foroverpayments do not seem to affect the probability of tendering. Therefore, conducting theanalyses for the later rounds, we still cannot explain the anomalies pointed out earlier (why abidder sometimes overpays and why some shareholders tender their shares in [Experiment A]).
Finally, we find that a bid price does not significantly affect the shareholders’ probability oftendering in [Experiment A] in both the final 15 and 10 rounds. This result is different from thatfor the whole session (in Table 6) and consistent with the theoretical prediction by Grossman
and Hart (1980), as we stated in the previous sub-section.

33

VII. Concluding Remarks
Our research started with the observation of the gap between the well-known proposition by
Grossman and Hart (1980) and the practical evidence from real takeover markets. While
Grossman and Hart’s classical proposition states that corporate takeovers fail due to the freerider problem, such a problem is not readily apparent in real capital markets. This conflict gave
rise to our question, “Does the free-rider problem actually occur in corporate takeovermarkets?”
To answer this question, we conducted an experimental study by constructing laboratory
takeover markets comparable to Grossman and Hart’s model. In contrast to earlier experimentson corporate takeovers by Kale and Noe (1997) and Cadsby and Maynes (1998), we attempted
to create a world of atomistic shareholders in the laboratory. To realize this, we developed an
original experimental device such that the takeover outcome for each shareholder was to be
judged by the number of tendering shareholders other than herself. We believe that this device isan innovation of our paper and can be easily applied to other experiments with atomistic agents
such as those on step-level public goods and majority voting.
In our laboratory, free-rider problems did occur; only 20% of takeovers were successful andconsequently most (80%) of the potential social value from takeover success disappeared. This
result suggests that Grossman and Hart’s (1980) classical proposition provides valuable insight
into the nature of takeover markets. Their proposition denies the ‘optimistic story’ of takeovers
and argues that takeovers should fail even if they were socially valuable. This is what we
actually observed in our laboratory.
From our laboratory evidence, we naturally conjecture that the free-rider problem
potentially exits in real takeover markets as well. If this conjecture is true, why do we often
observe successful takeovers in reality? One possible answer from financial economics would
be that “(bidders) find ways to get around the free-rider problem” (Grinblatt and Titman (1998),
pp.696). Subsequent takeover models show that under some conditions, Grossman and Hart’s
classical proposition does not hold and takeovers may be successful. In particular, Shleifer and
Vishny (1986) and Hirshleifer and Titman (1990) predict that initial shareholdings by a biddermitigate the free-rider problem and may allow a takeover to succeed. This prediction was
supported in our laboratory; when a bidder initially holds shares of the target firm, about 70% of
takeovers are successful. This experimental result indicates that the bidder’s initialshareholdings may overcome the free-rider problem in real takeover markets and can beconsidered one reason for the successful takeovers observed in reality.
While we demonstrated the importance of Grossman and Hart’s classical proposition, we

34should also note that their proposition does not perfectly explain our evidence. Specifically, theobserved probabilities of takeover success (20%) and that of shareholder tendering (40%) in ourlaboratory were far in excess of the 0% predicted by Grossman and Hart. We examined several
possible reasons why some shareholders did not free ride, but this finding remains an anomaly.
To explain this anomaly, we need to conduct experiments in slightly different settings. Also, thefuture development of research exploring the provision of public goods would help us to better
understand our anomaly, since non-free-riding behavior is also observed in public goods
experiments.39
Overall, our experimental evidence supports economists’ views of real takeover markets;
the free-rider problem exists, but it can be mitigated by factors such as a bidder’s initialshareholdings. This result has important implications for capital markets, public policy, andfinancial economics. First, we should not believe the “optimistic story of takeovers”. Takeovermechanisms do not necessarily work well. Thus, shareholders have to care about how todiscipline bad management, and bidders need to find ways to get around the free-rider problem.
Second, institutional environments that limit bidders’ initial shareholdings may prevent takeoversuccess and lower social welfare. For example, under U.S. regulations, potential bidders cannot
freely accumulate initial shares in the target firm, because they are required to file schedule 13D with SEC disclosing holdings and intentions after purchasing 5% of target shares. This
regulatory environment may discourage valuable takeovers. Third, a considerable number of
takeover models may be useful in explaining reality. We showed that Grossman and Hart’s(1980) model, the starting point for various takeover models, and two subsequent models
regarding the bidder’s initial stakes (Shleifer and Vishny (1986) and Hirshleifer and Titman(1990)) were supported in our laboratory. Therefore, it is also possible that other takeovermodels based on Grossman and Hart (1980) show us remedies for the free-rider problem andexplain successful takeovers in reality. In exploring this possibility, experimental research seems
particularly effective.40

39

Dawes and Thaler (1988, pp.196) summarizes the general result of public goods experiments, “Itis certainly true that there is a free-rider problem. . . . On the other hand, the strong free-rider
prediction is clearly wrong  not everyone free-rides all of the time”.

40

Kale and Noe’s (1997) and Cadsby and Maynes’ (1998) experiments are two examples of this.
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36

Hirshleifer, D. and S. Titman (1990), Share Tendering Strategies and the Success of Hostile
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37

Table 1 Shareholders’ Payoffs

The Outcome of a Takeover

Successful

Not Successful

Tender (Accept)x0

Not Tender (Reject)z0

Shareholder’s Decision38

Table 2-A The Results of [Experiment A](The no shareholdings case)Group A-1
Round
NumberThe Valueof Z

1Group A-2

Group A-3

Group A-4

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

150

110

12

110

9

90

6

110

9

2

100

40

6

80

6

80

3

90

9

3

190

120

4

130

6

130

4

100

6

4

170

110

6

150

13

150

9

180

11

5

150

90

9

120

12

130

8

150

12

6

140

130

9

120

9

120

6

130

8

7

180

160

9

130

7

170

9

150

13

8

50

60

5

30

10

50

10

70

14

9

150

100

10

130

9

130

9

150

8

10

30

40

8

30

6

10

5

40

9

11

70

50

6

50

7

50

7

70

12

12

90

90

7

60

7

70

9

80

5

13

160

130

10

120

7

140

8

100

10

14

120

120

6

110

10

110

7

130

11

15

120

100

6

100

9

110

7

120

5

16

50

80

9

40

9

40

8

60

11

17

90

80

6

70

6

80

8

100

7

18

30

60

7

20

6

40

8

40

7

19

180

190

7

140

9

170

9

80

8

20

60

50

7

50

5

60

8

40

5

95.50

0.373

89.50

0.405

96.50

0.370

99.50

0.450

Average Acceptance
Rate
Bid# of Rounds ofSuccessful Takeovers
Efficiency

3

4

1

8

20.18 %

21.49 %

2.19 %

41.67 %

39

Table 2-B The Results of [Experiment B](The initial shareholdings case)Group B-1
Round
NumberThe Valueof Z

1Group B-2

Group B-3

Group B-4

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

Bid
Price

# of sellers
to accept

150

120

13

160

15

130

12

140

12

2

100

100

8

180

17

70

5

110

7

3

190

120

8

140

11

170

12

140

8

4

170

90

5

160

17

140

6

150

15

5

150

160

8

140

14

140

7

140

9

6

140

160

9

120

11

160

8

140

7

7

180

150

11

130

9

190

15

150

8

8

50

10

4

70

10

80

6

100

7

9

150

170

17

120

10

140

12

130

9

10

30

40

4

40

8

40

10

110

9

11

70

90

7

50

8

70

6

100

6

12

90

110

8

60

9

110

8

100

8

13

160

160

12

120

8

150

11

130

5

14

120

130

8

120

10

130

10

100

13

15

120

130

6

100

12

130

6

100

14

16

50

80

6

50

3

60

11

80

10

17

90

110

11

90

7

100

9

90

8

18

30

40

8

50

5

40

8

80

8

19

180

150

9

130

14

180

13

90

7

20

60

60

7

70

8

60

8

70

4

Average
Bid

Acceptance
Rate

100.900.423

105.000.515

114.500.458

112.500.435# of Rounds ofSuccessful Takeovers

13

17

14

13

Efficiency

75.88 %

92.54 %

71.05 %

66.67 %

40

Table 3
The Probability of Takeover Success, Acceptance Rates, and the Efficiency

Panel A. The Probability of Success[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings# of Total Rounds

80

80# of Success Rounds

16

57# of Failure Rounds

64

23

Difference

The Probability of
Success0.20000.71250.5125*** (0.000)
Note: ***, **, * indicates p<0.001, p<0.01, p<0.05. p-values are shown in parentheses.

Panel B.

Acceptance Rates[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings# of Total Shareholders

1600

1600

Shareholders who accepted

639

732

Shareholders who rejected

961

868

Acceptance Rate

0.39940.4575

Panel C.

Average Efficiency

Difference

0.0581** (0.001)

The Efficiency[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings

21.38 %

76.54 %

41

Difference

55.16% **(0.003)

Table 4
Logit Regression Results: The Probability of Takeover Success[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings

Model 1Model 2Model 1Model 2

Intercept- 2.2437** (0.004)- 1.8220(0.152)- 1.0904

X (Bid Price)

0.00860.0068(0.402)0.0191** (0.005)

ROUND- 0.0600(0.285)0.0321(0.541)GROUP20.3750(0.660)1.3668(0.110)

GROUP3- 1.2649(0.297)0.1854(0.805)

GROUP4

1.3395(0.090)- 0.1656(0.817)(0.214)(0.135)- 2.2167(0.091)0.0240** (0.004)# of observations

80

80

80

80

Log Likelihood-39.24-34.50-43.60-41.30Note: ***, **, * indicates p<0.001, p<0.01, p<0.05. p-values are shown in parentheses.

42

Table 5
OLS Regression Results: Bid Price Offered by the Bidder[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings

Model 1
Intercept
Z
ROUND

3.1481(0.742)0.7420***(0.000)
0.7399Model 2Model 1Model 2(0.889)46.845***(0.000)

40.573***(0.001)

0.7570***(0.000)

0.6052***(0.000)

0.6130***(0.000)- 1.3212(0.088)- 0.6509(0.200)RDQ215.796* (0.019)

3.2463(0.682)RDQ312.282(0.065)- 0.9797(0.901)RDQ4

13.993(0.053)- 8.0895(0.347)

GROUP2- 6.0000(0.344)- 6.0000(0.340)- 4.0000(0.591)- 4.0000(0.595)

GROUP31.0000(0.874)1.0000(0.873)5.5000(0.461)5.5000(0.734)

GROUP44.0000(0.528)4.0000(0.524)3.5000(0.639)3.5000(0.642)# of observations

80

80

80

80

Adjusted R2

0.771

0.776

0.661

0.655

Note: ***, **, * indicates p<0.001, p<0.01, p<0.05. p-values are shown in parentheses.

43

Table 6
Logit Regression Results: Shareholders’ Probabilities of Tendering[Experiment A]
Model 1
Intercept- 0.7199

X (bid)0.0033* (0.013)

ROUND- 0.0065(0.206)

Model 2

No Shareholdings

Model 3Model 4(0.077)- 0.9041***(0.000)- 1.0283***(0.000)

0.0034* (0.011)

0.0030* (0.021)

0.0032* (0.017)- 0.9686(0.715)- 0.0116(0.356)RDQ2

0.2083(0.254)0.1563(0.346)RDQ30.0404(0.866)- 0.0360(0.841)RDQ4

0.0374(0.892)- 0.0600(0.761)0.0004(0.965)0.1877(0.328)OPAYAVG

0.0029(0.774)

OPAYDUM0.2432(0.210)PIVOTAL

0.9699* (0.044)

0.9783* (0.043)

0.9864* (0.041)

0.9905* (0.041)

GROUP2

0.1980(0.235)0.2172(0.195)0.3706(0.055)0.3373(0.079)

GROUP30.0342(0.842)0.0542(0.753)0.1848(0.311)0.1560(0.390)

GROUP40.3200(0.162)0.3625(0.116)0.3192* (0.039)

0.3308* (0.032)# of observations

1520

1520

1520

1520

Log Likelihood-1012.51-1011.40-1011.77-1010.92

Note: ***, **, * indicates p<0.001, p<0.01, p<0.05. p-values are shown in parentheses.

44

Table 7
Results for Later Rounds[Experiment A][Experiment B]

No Shareholdings

Initial Shareholdings

Difference

Panel A. The Final 15 Rounds (6th – 20th rounds)
The Probability of Success

0.18330.70000.5167*** (0.000)

Acceptance Rates

0.39920.43580.0366

Average Efficiency

19.08%

77.08%

58.00%** (0.002)(0.075)

Panel B. The Final 10 Rounds (11th – 20th rounds)
The Probability of Success0.15000.67500.5250*** (0.000)

Acceptance Rates

0.38250.42380.0413

Average Efficiency

16.49%

69.07%

52.58%** (0.005)(0.093)

Note: ***, **, * indicates p<0.001, p<0.01, p<0.05. p-values are shown in parentheses.

45

Figure 1-A

The Free-rider Problem in Corporate Takeoversxx=z

Shareholder Acceptable

Bidder Profitable
x0

z

z0

Figure 1-B

The Bidder’s Initial Holdings and Takeover Success
x =[0.5/(0.5-α)]zx

Bidder Profitable
Shareholder Acceptable
x0

*

x1*

z

z1

z0
46

47

48

Appendix: Players Instructions for [Experiment B]41

(Exact Transcript)

Overview of this Experiment
1. We will begin the explanation of this experiment with a recorded tape. The experimenter will
operate the tape. After the explanation, you may ask questions.
2. You will draw an envelope. A piece of paper in the envelope assigns your role in thisexperiment.
3. If you are assigned to the Buyer, move to the seats to which the experimenter will guide you,with everything on your desk.
4. There are both the sheets for the Buyer and the sheets for Sellers on your desk. Make surethat you have the sheets you will use in this experiment. Summary and Explanation, Individual
Card, and Overview of this Experiment are on white papers. They are common to both the
Buyer and Sellers. Except for these white papers, the sheets for the Buyer are YELLOW, andthe sheets for Sellers are BLUE. Make sure that you have the appropriate sheets for you. The
experimenter will distribute the Desired Purchasing Price Cards (yellow) to the Buyer, and the
Selling Decision Cards (blue) to Sellers.
Make sure that you have the following:
Buyer-

Summary and Instructions (white)-

Individual Card (white) *Fill in your card before the experiment begins.

-

Overview of this Experiment (white)-

Buyer’s Record Sheet (yellow)-

Desired Purchasing Price Cards (yellow)-

Buyer’s Payoff Sheet 1 (yellow)-

Buyer’s Payoff Sheet 2 (yellow)-

Receipt (white) *Enter your name and address, and impress your seal before the experiment
begins.

-Ballpoint pen.

41

Player instructions for [Experiment A] are similar except for the bidder’s initial holdings andthings related to them.

iSellers-

Summary and Instructions (white)-

Individual Card (white) *Please fill in your card before the experiment begins.

-

Overview of this Experiment (white)-

Sellers’ Record Sheet (blue)-

Selling Decision Cards (blue)-

Sellers’ Payoff Sheets (blue)-

Receipt (white) *Enter your name and address, and impress your seal before the experiment
begins.

-Ballpoint pen.

* Even if you are the Buyer (a Seller), you may refer to the sheets for Sellers (the Buyer).
5. Before this experiment begins, you may ask questions. If you have any questions during thisexperiment, raise your hand without saying a word. The experimenter will come to your seat.
6. We will start the first experiment. Do not communicate with any other participant during
the experiment.

i.

The experimenter will let the Buyer know the value (Z) of a commodity. If you are theBuyer, record the value on your Record Sheet. You are not to read the value aloud.

ii.

If you are the Buyer, enter your desired purchasing price of the commodity in your Desired
Purchasing Card for the said round, remove and hand it to the experimenter. You may
consider slowly. If you are a Seller, please wait for a while.

iii.

The experimenter will announce the commodity’s desired purchasing price that each Buyer
will have decided. If you are a Seller, decide whether to sell your commodity or not. Enterthe Selling Decision Card for the said round according to your decision, remove and place it
face down on the right edge of your desk in such a way that the face of the card will not beseen by any other participant. The experimenter will collect your card.

iv.

The experimenter will announce to all of the participants the value of Z and how many
Sellers have sold the commodities. Record the announced value in your Record Sheet.

v.

Record also your payoff according to your Payoff Sheet(s).

*The experiment will be repeated twenty times.

7. When the twentieth round of the experiment has finished, the experimenter will say “We havefinished this experiment.” and this experiment will finish. Your Record Sheets will be collected.

iiWhile the experimenter calculates your monetary reward, fill in our questionnaire.
8. Your reward of this experiment will be paid. Wait until your Individual Number is called.
9. If your Individual Number is called, come to the experimenter’s desk with your Individual
Card, Receipt and the questionnaire.
10. You will receive your reward. Enter the amount of money that the experimenter will tell youin the price column of your Receipt. Make sure that you have entered your name and address in
the Receipt. Impress your seal if not, and receive your reward. Then the whole experiment will
finish.

Summary and Instructions(Read the following while listening to the tape)
We will begin the instructions of this experiment from now. See Summary and Instructions on
your desk.
SummaryThis is an experiment in economic decision making. The instructions are simple, and if you
follow them carefully and make good decisions, you would earn a considerable amount ofmoney. The experiment will be repeated twenty times. In each repetition, or “round”, yourpayoff will be calculated and the sum of your payoffs in the all of the rounds will determine
your actual payoff which will be paid in cash at the end of this experiment. Later we will
explain how to calculate your payoff.
The experiment will be conducted between one Buyer and twenty Sellers of a commodity.
Who is going to be the Buyer and who are going to be Sellers will be decided by lottery.
If you are the Buyer, you will offer the price at which you would like to buy the commodity,or your “desired purchasing price” to twenty Sellers. Each Seller possesses the commodity. Heor she will choose “Sell” or “Not Sell”, referring to the “desired purchasing price” offered by
the Buyer.
During this experiment, neither the Buyer nor the Sellers are allowed to talk to any otherparticipant. If somebody should talk, the experiment will be suspended. Also, you are asked tofollow the various instructions given by the experimenter.

iii

Instructions
When you sit down, make sure that there are the follows on your desk.
-Summary and Instructions (this sheet)-Buyer’s Record Sheet-Individual Card

-Record Sheets (for Sellers)-Desired Purchasing Price Card and Selling Decision Card (on pieces of yellow and papers)-Overview of this Experiment-Buyer’s Payoff Sheet 1-Buyer’s Payoff Sheet 2-Sellers’ Payoff Sheet-Receipt-Ballpoint pen

Fill in your Individual Card, and enter your name and address and impress your seal before theexperiment begins.
Sellers’ Record Sheet is for recording your information on this experiment, if you are a Seller.
Buyer’s Record Sheet is for recording your information on this experiment, if you are a Buyer.
Desired Purchasing Cards are for entering the price at which you would like to buy thecommodity (desired purchasing price), when you are a Buyer. Now you have only one Desired
Purchasing Card. It makes a pair with the Selling Decision Card. For the experiment you will begiven twenty cards. You will use one of them in each round. Remove and hand it to theexperimenter.
Selling Decision Cards will be used if you are a Seller. You will enter your decision, “Sell”, or“Not Sell” the commodity you have, in the cards considering the Desired Purchasing Price theBuyer will offer. Now you have only one Selling Decision Card. It makes a pair with theDesired Purchasing Card. For the experiment you will have twenty cards. For each round you
will fill in one of them, remove and turn it over on the right hand side of your desk. The
experimenter will collect it.
Overview of this Experiment is the summary of what the participants are to do in thisexperiment. Refer to it when necessary.
From now on we will give you the instructions of this experiment.
Before we begin this experiment, we assign one of the participants to the Buyer and twenty toSellers by lottery. In this experiment, whether you will be the Buyer or a Seller does not matterfor the opportunity of earning money. The amount of the reward depends only on your decisionand luck.

Buyer (one person)iv

Let us give the instructions to the Buyer. To begin with, put on your desk Buyer’s Record Sheet,
Buyer’s Payoff Sheet 2, and the Desired Purchasing Card (The yellow one in a pair of small
pieces of paper). The Buyer will use the yellow sheets.
Now you have 5 units of a commodity, and you are thinking of purchasing 8 more units. The
value (Z) of the commodity per 1 unit varies from 0 to 200, at intervals of every 10 (0, 10, 20,
30, …, 180, 190, 200). From among these values, Z will be determined completely at random.
At the beginning of each round, the experimenter will let you know the value of Z with a pieceof paper. The value of Z will be revealed only to you, the Buyer, and you are not to show it toanyone. The value of Z may be different in each round.
The value (Z) of the commodity is realized, however, only when you can purchase 8 more units,that is, only when you can get the offers of “Sell” from 8 Sellers or more out of 20. If you can
get the offers only from 7 Sellers or less, the commodity has no value for you, and you are tostop purchasing it. And in that case, the value of 5 units of the commodity you originally havewill also be zero.
Looking at the value of Z revealed by the experimenter, you will enter your “desired purchasing
price” or the price at which you would like to purchase one unit of the commodity, in yourDesired Purchasing Price Card. Then you will show the card to the experimenter. You can offer
the value from 0 to 300, at intervals of every 10 (0, 10, 20, 30, …, 280, 290, 300). Referring to
your offer, each Seller will choose either “Sell” or “Not Sell”. And your payoff will depend onwhether 8 Sellers or more would choose “Sell” or “Not Sell”.
The way the Buyer’s (your) payoff will be determined is summarized in Buyer’s Payoff Sheeton your desk. Let us explain how to use it. Suppose that more than 8 Sellers agreed to “sell”,
and let this case be “Case 1”. Then your payoff will be:
Z×5( Z – desired purchasing price) × 8.

+

For example, if Z is 150 and the desired purchasing price you offer is 100, then your payoff willbe:
150 × 5+( 150 – 100 ) × 8 = 1150.

Your payoff in this “Case 1” is shown in Buyer’s Payoff Sheet 2 as well. Looking at Buyer’s
Payoff Sheet 2, you will find your payoff 1150 at the box where the column of Z 150 and therow of the desired purchasing price 100 intersect.
On the other hand, suppose only 7 Sellers or less agreed to “sell”, and let this case be “Case 2”.
In this case, the commodity will have no value for you. Therefore you will stop purchasing thecommodity and the value of 5 units of the commodity you originally have will also be zero, sovthat as you can see in Buyer’s Payoff Sheet 1, your payoff will be 0.
We will explain the Buyer’s payoff patterns with some simple examples.
Example 1 Suppose that the value of Z you were shown (the value of the commodity for you)was 130, that then you offered 90 as your desired purchasing price, and that 12 Sellers agreed to“sell” referring to your offer. This case is “Case 1”, since 8 Sellers or more agreed to sell thecommodity. Therefore your payoff would be, according to Sellers’ Payoff Sheet 1,
130 × 5+

( 130 – 90 ) × 8 = 970.

This can also be confirmed with Buyer’s Payoff Sheet 2. On Buyer’s Payoff Sheet 2, you willfind your payoff 970 at the box where the column of Z 130 and the row of the desired
purchasing price 90 intersect.
Example 2 Similarly, suppose that the value of Z was 130 and that you offered 90 as yourdesired purchasing price. Then, suppose also that 8 Sellers agreed to “sell”. This case is “Case1” as well, since 8 Sellers or more agreed to sell the commodity. Therefore your payoff would
be 970, as in Example 1. The result is recorded at Example 2 on Sellers’ Record Sheet.
Example 3 Next, suppose that the value of Z was 80, that your desired purchasing price was
90 and that 10 Sellers agreed to “sell”. This case is also “Case 1”, since 8 Sellers or more agreed
to sell. Then your payoff would be, according to Buyer’s Payoff Sheet 1,
80 × 5+( 80 – 140 ) × 8 = -80,

so that you would lose 80. This can be confirmed with Buyer’s Payoff Sheet 2. On the Payoff
Sheet of Buyer 2, you will find your payoff – 80 at the box where the column of Z 80 and therow of the desired purchasing price 140 intersect. The result is recorded at Example 3 on
Sellers’ Record Sheet.
Example 4 Suppose that the value of Z was 190, that your desired purchasing price was 100
and that 5 Sellers agreed to “sell”. This case is “Case 2”, since 7 Sellers or less agreed to sell.
Therefore, according to Buyer’s Payoff Sheet 1, your payoff would be 0. As an exercise, record
the result of Example 4 in Sellers’ Record Sheet.
Taking these things in to account, in each round you will decide at what price you would like topurchase the commodity or your “desired purchasing price”. Then you will enter it into theDesired Purchasing Card, and hand the card to the experimenter.
The above is the instructions for the Buyer in one round. You may see the sheets for the Sellers
as well. However, make sure that you will not confuse the sheets for you with those for the
Sellers.

vi

Sellers (20 persons)
Now let us give the instructions to the Sellers. To begin with, put on your desk Sellers’ Record
Sheet, Sellers’ Payoff Sheet, and the Selling Decision Card (the blue one in a pair of small pieceof paper). The Sellers will use the blue sheets.
If you are a Seller, you have one unit of a commodity. You will choose either “Sell” or “NotSell”, referring to the “desired purchasing price” offered by the Buyer.
Your payoff depends not only on your decision as to “Sell” or “Not Sell”, but also on those of
the other Sellers. However, you will not know the other Sellers’ decisions when you make yourown decision.
As for how your payoff will be determined, see Sellers’ Payoff Sheet. Now we will explain how
to use this sheet. If 8 Sellers or more other than you agreed to “sell” ([Case A] in Sellers’ Payoff
Sheet), your payoff will be determined as follows. If you choose “Sell”, your payoff will be the“desired purchasing price” offered by the Buyer. Instead, if you choose “Not Sell”, your payoff
will be “the value of Z for the Buyer”. At the beginning of this experiment, the experimenter
will reveal the value of Z to the Buyer, but not to you. At the end of each round, however, theexperimenter will announce the value of Z to all of the participants.
Next, if 7 Sellers or less other than you agreed to “sell” ([Case B] in Sellers’ Payoff Sheet), yourpayoff will be 0, regardless of your choice of “Sell” or “Not Sell”.
In order to make sure, we will explain the payoff patterns of Sellers with three simple examples.
Example 5 Suppose that you chose “Sell” at the desired purchasing price 130 offered by the
Buyer, and that 14 Sellers agreed to “sell” at the same time. In this case, the number of Sellers
other than you who sold the commodity is 13. This is [Case A], since 8 Sellers or more otherthan you agreed to “sell”. Since you chose “Sell”, according to Sellers’ Payoff Sheet, yourpayoff would be the “desired purchasing price offered by the Buyer”, that is, 130. The result isrecorded at Example 5 of Sellers’ Record Sheet. There “the value of Z announced by theexperimenter” is 80, but it has nothing to do with your payoff in the case of Example 5.
Example 6 Suppose that you chose “Not Sell” at the desired purchasing price 120 offered by
the Buyer, and that 12 Sellers agreed to “sell”. In this case, the number of Sellers other than you
who sold the commodity is 12. This is [Case A], since 8 Sellers or more other than you agreed
to “sell”. However, your payoff would be, according to Sellers’ Payoff Sheet, Z (the value of thecommodity for the Buyer), because you chose “Not Sell”. The value of Z will be announced at
the end of each round. If Z is 100 then your payoff would be 100, and if Z is 150 then yourpayoff would be 150. The result is written at Example 6 of Sellers’ Record Sheet.

vii

Example 7 Suppose that you chose “Sell” at the desired purchasing price180 offered by the
Buyer, and that 6 Sellers agreed to “sell”. In this case, the number of Sellers other than you whosold the commodity is 5. This is [Case B], since 7 Sellers or less other than you agreed to “sell”.
Therefore, according to Sellers’ Payoff Sheet, your payoff would be 0. Suppose the value of Z
announced at the end of the round was 140. However, in this Example, the value of Z has
nothing to do with your payoff. As an exercise, record the result of Example 7 in Sellers’
Record Sheet.
Taking into account the instructions mentioned so far, in each round the Sellers will choose
either “Sell” or “Not Sell”, referring to the desired purchasing price offered by the Buyer thatthe experimenter will announce, and fill in the Selling Decision Card with a circle.
The above is the instructions for the Sellers in one round. You may see the sheets for the Buyer
as well. However, make sure that you will not confuse the sheets for you with those for the
Buyer.
These are the instructions for one round. At the end of each round, the experimenter will
announce to all the participants the value of Z and the number of the Sellers who agreed to“sell” the commodity. Based on the announcement, confirm your payoff and record it in the
Record Sheet.
How to fill in Record Sheet
Buyer
i.

Enter the value of Z revealed by the experimenter in Buyer’s Record Sheet.

ii.

Choose your desired purchasing price from 0 to 300 at the intervals of every 10 (0,10,20, …, 280, 290, 300).

iii.

Enter the desired purchasing price in the Desired Purchasing Price Card, remove, andhand it to the experimenter.

iv.

Enter the desired purchasing price also in Buyer’s Record Sheet.

v.

Enter the number of the Sellers who agree to “sell” the commodity, which will beannounced by the experimenter, in Buyer’s Record Sheet.

vi.

Enter your payoff in Buyer’s Record Sheet (see Buyer’s Payoff Sheet 1 and Buyer’s
Payoff Sheet 2).

Sellersi.

Enter the Buyer’s desired purchasing price announced by the experimenter in Sellers’
Record Sheet.

ii.

Choose either ”Sell” or “Not Sell” and enter it in Sellers’ Record Sheet and the Sellingviii

Decision Card.
iii.

Remove the entered Selling Decision Card, and hand it to the experimenter

iv.

Enter the value of Z and the number of the Sellers who agree to sell the commodity,
which will be announced by the experimenter, in Sellers’ Record Sheet.

v.

Enter the number of the Sellers other than you who sold the commodity in Sellers’
Record Sheet.

vi.

Enter your payoff in Sellers’ Record Sheet (see Sellers’ Payoff Sheet).

*In Sellers’ Record Sheet, how your payoff will be determined is mentioned on the right handside of the column in which you will fill in each round. This is the same as Sellers’ Payoff Sheet.
Refer to it when you record your payoff.
Finally, we will explain how the amount of money you receive is determined. The amount ofmoney depends on “Your Payoff” in each round. It is calculated as follows.
The Buyer’s monetary reward is:
1,000 + 0.5 × ( the sum of “Your Payoff” ) yen.
For example, if the sum of “Your Payoff” in all of the rounds is 4,000 you will receive:
1,000 + 0.5 × 4,000 = 3,000 yen.
Next, a Seller’s monetary reward is:
1,000 + 2 × ( the sum of “Your Payoff” ) yen.
For example, if the sum of “Your Payoff” in all of the rounds is 1,000 you will receive:
1,000 + 2 × 1,000 = 3,000 yen.
This is the end of the instructions of this experiment. If you have questions, raise your handquietly. The experimenter will come to your desk.

ix

Buyer’s Record SheetYour Individual Number
Example 1
The value of Z
(enter the value of Z
revealed by theexperimenter)

Your desired
purchasing price( a value from 0 to 300
at the interval of every
10)

The number of
The way your payoff is determined(see Buyer’s Payoff Sheet 1 and 2)
Sellers announced
by the experimenter“Case 1”130

90

The number of Sellers
announced is 8 or more

12

See Buyer’s Payoff
Sheet 2

970

“Case 2”0

The number of Sellers
announced is 7 or lessExample 2
The value of Z
(enter the value of Z
revealed by theexperimenter)

Your desired
purchasing price( a value from 0 to 300
at the interval of every
10)

The number of
The way your payoff is determined(see Buyer’s Payoff Sheet 1 and 2)
Sellers announced
by the experimenter“Case 1”130

90

The number of Sellers
announced is 8 or more

8(enter the value of Z
revealed by theexperimenter)

Your desired
purchasing price( a value from 0 to 300
at the interval of every
10)

970

“Case 2”0

The number of
The way your payoff is determined(see Buyer’s Payoff Sheet 1 and 2)
Sellers announced
by the experimenter“Case 1”80

140

The number of Sellers
announced is 8 or more

10

revealed by theexperimenter)( a value from 0 to 300
at the interval of every
10)Your Payoff

See Buyer’s Payoff
Sheet 2−80

“Case 2”0

The number of Sellers
announced is 7 or lessExample 4 (Record the result by yourself)
Your desired
The value of Z
(enter the value of Z purchasing priceYour Payoff

See Buyer’s Payoff
Sheet 2The number of Sellers
announced is 7 or lessExample 3
The value of Z

Your Payoff

The way your payoff is determined
The number of(see Buyer’s Payoff Sheet 1 and 2)
Sellers announced
by the experimenter“Case 1”
The number of Sellers
announced is 8 or moreYour Payoff

See Buyer’s Payoff
Sheet 2

“Case 2”The number of Sellers
announced is 7 or lessx0

Sellers’ Record Sheet
Example 5
The desired
purchasing
priceoffered by
the BuyerYour choice(put a circle
around either ofthem)Your Individual Number
The numberof Sellers
announced

The number ofSellers other than
you who sold thecommodity

The way your payoff is determined (see Seller’s Payoff
Sheet)The number of Sellers other than you
who chose “Sell”[Case A]
[Case B]
8 or More

7 or less

Sell

130

14

13

Not Sell

The value of Z announced
by the experimenter

Example 6
The desired
purchasing
priceoffered by
the BuyerYour choice(put a circle
around either of
them)

130

The numberof Sellers
announced

The desired
purchasing priceoffered by the Buyer

0

Not
Sell

Z

0

Your
ChoiceYour payoff

80

Sell

The number ofSellers other than
you who sold thecommodity

The way your payoff is determined (see Seller’s Payoff
Sheet)The number of Sellers other than you
who chose “Sell”[Case A]
[Case B]
8 or More

120

Sell

12

12

Not Sell
The value of Z announced
by the experimenter

100 (150)
Example 7
The desired
purchasing
priceoffered by
the BuyerYour choice(put a circle
around either of
them)

Your
ChoiceYour payoff

100 (150)

The numberof Sellers
announced

The number ofSellers other than
you who sold thecommodity

7 or less

Sell

The desired
purchasing priceoffered by the Buyer

0

Not
Sell

Z

0

The way your payoff is determined (see Seller’s Payoff
Sheet)The number of Sellers other than you
who chose “Sell”[Case A]
[Case B]
8 or More

7 or less

Sell
Not Sell
The value of Z announced
by the experimenter

Your
ChoiceYour payoff

xi

Sell

The desired
purchasing priceoffered by the Buyer

0

Not
Sell

Z

0

Buyer’s Payoff Sheet 1

The number of Sellers who agreed to sell

“Case 1”“Case 2”

8 or More

7 or Less

Z × 5 + ( Z – your desired purchasing price) × 8

0Sellers’ Payoff Sheet
The number of Sellers other than you who chose“Sell”[Case A]
8 or More[Case B]
7 or Less

Sell

The desired purchasing
price offered by the
Buyer

0

Not Sell

The value of Z

0Your
Choicexii

Buyer's Payoff Sheet 2Your desired
purchasing price

The value of Z revealed by the experimenter
0
10
20
30
40
50
60
0
0
130
260
390
520
650
780
10
-80
50
180
310
440
570
700
20 -160
-30
100
230
360
490
620
30 -240 -110
20
150
280
410
540
40 -320 -190
-60
70
200
330
460
50 -400 -270 -140
-10
120
250
380
60 -480 -350 -220
-90
40
170
300
70 -560 -430 -300 -170
-40
90
220
80 -640 -510 -380 -250 -120
10
140
90 -720 -590 -460 -330 -200
-70
60
100 -800 -670 -540 -410 -280 -150
-20
110 -880 -750 -620 -490 -360 -230 -100
120 -960 -830 -700 -570 -440 -310 -180
130 -1040 -910 -780 -650 -520 -390 -260
140 -1120 -990 -860 -730 -600 -470 -340
150 -1200 -1070 -940 -810 -680 -550 -420
160 -1280 -1150 -1020 -890 -760 -630 -500
170 -1360 -1230 -1100 -970 -840 -710 -580
180 -1440 -1310 -1180 -1050 -920 -790 -660
190 -1520 -1390 -1260 -1130 -1000 -870 -740
200 -1600 -1470 -1340 -1210 -1080 -950 -820
210 -1680 -1550 -1420 -1290 -1160 -1030 -900
220 -1760 -1630 -1500 -1370 -1240 -1110 -980
230 -1840 -1710 -1580 -1450 -1320 -1190 -1060
240 -1920 -1790 -1660 -1530 -1400 -1270 -1140
250 -2000 -1870 -1740 -1610 -1480 -1350 -1220
260 -2080 -1950 -1820 -1690 -1560 -1430 -1300
270 -2160 -2030 -1900 -1770 -1640 -1510 -1380
280 -2240 -2110 -1980 -1850 -1720 -1590 -1460
290 -2320 -2190 -2060 -1930 -1800 -1670 -1540
300 -2400 -2270 -2140 -2010 -1880 -1750 -1620

70
910
830
750
670
590
510
430
350
270
190
110
30
-50
-130
-210
-290
-370
-450
-530
-610
-690
-770
-850
-930
-1010
-1090
-1170
-1250
-1330
-1410
-1490

80
90
100
1040 1170 1300
960 1090 1220
880 1010 1140
800
930 1060
720
850
980
640
770
900
560
690
820
480
610
740
400
530
660
320
450
580
240
370
500
160
290
420
80
210
340
0
130
260
-80
50
180
-160
-30
100
-240 -110
20-320 -190-60-400 -270 -140-480 -350 -220-560 -430 -300
-640 -510 -380
-720 -590 -460
-800 -670 -540
-880 -750 -620
-960 -830 -700
-1040 -910 -780
-1120 -990 -860
-1200 -1070 -940
-1280 -1150 -1020-1360 -1230 -1100

xiii

110
1430
1350
1270
1190
1110
1030
950
870
790
710
630
550
470
390
310
230
150
70
-10
-90
-170
-250
-330
-410
-490
-570
-650
-730
-810
-890
-970

120
1560
1480
1400
1320
1240
1160
1080
1000
920
840
760
680
600
520
440
360
280
200
120
40
-40
-120
-200
-280
-360
-440
-520
-600
-680
-760
-840

130
1690
1610
1530
1450
1370
1290
1210
1130
1050
970
890
810
730
650
570
490
410
330
250
170
90
10
-70
-150
-230
-310
-390
-470
-550
-630
-710

140
1820
1740
1660
1580
1500
1420
1340
1260
1180
1100
1020
940
860
780
700
620
540
460
380
300
220
140
60
-20
-100
-180
-260
-340
-420
-500
-580

150
1950
1870
1790
1710
1630
1550
1470
1390
1310
1230
1150
1070
990
910
830
750
670
590
510
430
350
270
190
110
30
-50
-130
-210
-290
-370
-450

160
2080
2000
1920
1840
1760
1680
1600
1520
1440
1360
1280
1200
1120
1040
960
880
800
720
640
560
480
400
320
240
160
80
0
-80
-160
-240
-320

170
2210
2130
2050
1970
1890
1810
1730
1650
1570
1490
1410
1330
1250
1170
1090
1010
930
850
770
690
610
530
450
370
290
210
130
50
-30
-110
-190

180
2340
2260
2180
2100
2020
1940
1860
1780
1700
1620
1540
1460
1380
1300
1220
1140
1060
980
900
820
740
660
580
500
420
340
260
180
100
20
-60

190
2470
2390
2310
2230
2150
2070
1990
1910
1830
1750
1670
1590
1510
1430
1350
1270
1190
1110
1030
950
870
790
710
630
550
470
390
310
230
150
70

200
2600
2520
2440
2360
2280
2200
2120
2040
1960
1880
1800
1720
1640
1560
1480
1400
1320
1240
1160
1080
1000
920
840
760
680
600
520
440
360
280
200

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

1st round

11th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

2nd round

12th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

3rd round

13th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

4th round

14th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

5th round

15th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

6th round

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

16th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

xivYour Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

7th round

17th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

8th round

18th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

9th round

19th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

You are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

Your Individual Number
Desired Purchasing Price CardYour Individual Number
Desired Purchasing Price Card

10th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

20th roundYou are the Buyer. Put a circle around one of thevalues below.
0 10 20 30 40 50 60 70 80 90 100 110
120 130 140 150 160 170 180 190 200
210 220 230 240 250 260 270 280 290 300

xv

QuestionnaireYour Individual NumberYour role in this experiment (put a circle around the appropriate one) Seller Buyer

The experiment has finished. Finally, please answer the questions below.
This questionnaire is used in order for us to understand how the participants of this experiment madedecisions. You have plenty of time to answer the questions. Whenever you have anything unclear,
ask the experimenter. When you have finished answering these questions, wait quietly until the otherparticipants finish.

This questionnaire is anonymous, so that you do not have to enter your name. Please answer all thequestions below. If you do not answer any one of these questions, we cannot use your questionnaire
sheets as proper data. How to answer the questions is as follows. Put a × mark according to youranswer.

Example Question:
Was this experiment easy, or difficult?
Very Easy

Very Difficult

If you feel the experiment was very easy,
Very Easy ×Very Difficult

put × in the most left box. If you feel the experiment was very difficult,
× Very Difficult

Very Easy
put × in the most right box. If you feel the experiment was easy,
Very Easy

×Very Difficult

put × as above. If you feel the experiment was somewhat easy,
Very Easy

×Very Difficult

put × as above. If you feel the experiment was difficult,
×Very Easy

Very Difficult

put × as above. If you feel the experiment was somewhat difficult,
×Very Easy

Very Difficult

put × as above. If you feel the experiment was neither easy nor difficult,
Very Easy

×xvi

Very Difficult

put × in the center box as above.
Thank you in advance for your assistance.

Questions on the Instructions of this ExperimentFirst, we will ask questions about the instructions of this experiment given at the beginning of thisexperiment. Check (×) one box that applies.
We distributed Summary, Overview of this Experiment and payoff sheets (Buyer’s Payoff Sheet 1,
Buyer’s Payoff Sheet 2, Sellers’ Payoff Sheet). Did you refer to them during this experiment?
Never

Very Frequently

Did you have anything unclear in the instructions of this experiment?
YesNo

If your answer is Yes, please specify where in the instructions were unclear.

If you have any idea to improve the instructions of this experiment, please write it down below.

Did anything out of the instructions occur in this experiment?
YesNo

If your answer is Yes, what was out of the instructions?

Did you understand the procedure of this experiment before it actually started?
Yes

No

If No, at which round did you come to understand the procedure?

Questions on Your Decision Making
When you make decisions (your desired purchasing price if you were the Buyer, or whether you
would sell or would not sell if you were a Seller), what did you take into account? Explain briefly.

xvii

Did your decision making change as this experiment proceeded?
YesNo

If Yes, how did your decision making change?

・In general, was your decision making difficult, or easy?
Very Easy

Very Difficult

・As this experiment proceeded, did your decision making become easier, or more difficult?
Decision making:Became Much EasierBecame much more Difficult

・To what degree do you think your decision influenced your payoff?
Very Much

Never・ To what degree do you think your decision influenced the other participants’ payoffs?
Very Much

Never・ To what degree do you think the other participants’ decisions influenced your payoff?
Very Much

Never・ If this experiment had been such that your decision would be known to the other participants,
how do you think your decision making would have changed?
Your decision making would have been:Completely the Same

Completely Different

・What would your decision making have been like?

・ To what degree did you consider the influence that your decision would give to the otherparticipants’ payoffs?
Never

Very Much

・ To what degree do you think the other participants’ consider the influence that their decisions
would give to your payoff?
Never

Very Much

・ Did the past results influence your next decision making?
Very Much

Never・ If the results in the past rounds influenced your decision making, please specify what.

xviii

General Questions on this Experiment・ Next, we will ask general questions about this experiment. To what degree do the following
sentences fit the impressions you have.

*This experiment was boring.
Completely False

Very True*My purpose in this experiment was to earn money as much as possible.
Completely False

Very True*I came to think about my decision making less, as the experiment proceeded.
Completely False

Very True*I am satisfied with my payoff.
Completely False

Very True*My purpose in this experiment was to earn more money than other participants.
Completely False

Very True*The experiment was carried out smoothly.
Completely False

Very True*The value of Z was chosen at random.
Completely False

Very True*This experiment was enjoyable.
Completely False

Very True*I did not fully understand the procedure of this experiment until the experiment actually started.
Completely False

Very True*My purpose in this experiment was to earn money as much as possible, together with the otherparticipants.
Completely False

Very True*(Sellers) I did not find it worthwhile to sell the commodity, because not many Sellers were willingto sell the commodity.
Completely False

Very True*I was looking forward to the result in each round.
Completely False

Very True*I thought the experiment was too long.
Completely False

Very True*I did not take this experiment as a whole seriously.

xixVery True

Completely False
・ Had you heard of this experiment before the experiment began?
YesNo・ If Yes, what did you hear.
・ If you have any comments or opinions for future experiments, please write them down below.

xx