Does manager voluntarily disclose private information?
−A test of the basic model of full disclosureusing experimental approach
Masayuki Ueeda
Discussion Paper 01-10
June 2001
この研究は「大学院経済学研究科・経済学部記念事業」
基金より援助を受けた、記して感謝する。
Graduate School of Economics andOsaka School of International Public Policy (OSIPP)
Osaka University, Toyonaka, Osaka 560-0043, Japan

Does manager voluntarily disclose private information?
−A test of the basic model of full disclosure using experimental approach*

Masayuki Ueeda**
Graduate School of Economics, Osaka University
June 2001

Abstract
Theoretical models have shown that full disclosure of private information will be induced whendisclosures are credible and costless. Managers/sellers are predicted to disclose so as not tothought as holding the worst possible information. The objective of this paper is to test the basicmodel of full disclosure by using experimental methods. In this paper, I conducted 16 laboratory
markets, manipulated two treatments and produced a 2×2 factorial cell design: (1) the numberof possible states and (2) the existence of an antifraud rule. The former is due to question marks
derived from the review of prior experimental researches. The latter is due to the concern for an
antifraud rule posited as a critical condition in the model. The results support the theoreticaland behavioral predictions generally, and provide some interesting findings.

JEL Classification: M41, C92
Key Words: Voluntary disclosure; Accounting regulation; Experimental Economics*

I gratefully acknowledge insightful comments from Tatsuyoshi Saijo, and the participants at theExperimental Economics Workshop 98 on 26th December 1998. Also, I really appreciate helpful comments
and assistances from Takayuki Asada, Hiroji Takao, and the accounting seminar members. Of course any
remaining errors are the author's responsibility.
**

Graduate School of Economics, Osaka University, Machikaneyama1-7, Toyonaka, Osaka 560-0043,

JAPAN
Phone: +081-6-850-5234, Fax: +81-6-850-5277
E-mail: mueeda@compsrv.econ.osaka-u.ac.jp

1. Introduction
In this paper I report some results of experimental markets designed to test the basicmodel of full disclosure 1 based on the theoretical model that was introduced from the‘persuasion game’ of Milgrom (1981) and extended by Milgrom and Roberts (1986). Theirresearches shows that the senders of information will fully disclose their information so as
not to be assumed to interpret non-disclosure as implying the worst possible news by thereceivers of information when disclosures are both credible and costless.
The research of voluntary disclosures is of big importance because much issue has to dowith the fundamental question of whether accounting regulation is necessary to enforce
managerial disclosure or not (for example, King 1991a, 1991b, Choi and Muller 1992, Suda
1992, Okabe 1994, Fujii 1998, and Oishi 2000). According to the results of theoreticalanalyses above, there is no need to force firms to disclose any information, because market
mechanism alone would induce managers to disclose their private informations voluntarily.
Obviously, disclosure or accounting regulations will be led from a lot of political, social, andof course economic factors and conditions, most of which are not included in the basic modelof full disclosure. Therefore, for setting up some regulation it is not sufficient only tounderstand how market forces exercise some influence on voluntary disclosures, but that is1

The term ‘the basic model of full disclosure’, of course, is my representation in this paper, andwas not used in their papers.

１essential to the setting process of accounting regulation2 (Chow 1996, footnote 3, p.134).
As one of the realms that experimental approach can be exercise its intrinsic ability, thebasic model of full disclosure has been already tested experimentally in Forsythe et al.
(1989), King and Wallin (1990, 1991a, 1991b) and Chow et al. (1996). In additional to these
papers, King (1995) has conducted experimental tests for the modified versions of the basicmodel of full disclosure too, which were motivated by many empirical results of discrepancy
between the theoretical prediction and the real world (that is, full disclosure did not havealways occurred). Except for Chow et al. (1996), it has been reported that the experimental
results supported the theoretical predictions generally.
Accepting these findings of prior researches solely, I might be called for conducting
experiments to investigate one revised model that has not been conducted yet. However,reviewing the prior disclosure experiments in greater detail, it seems to me that they havesome question marks here and there about their operations, designs, and interpretations of
the results. One of major puzzles is that, for example, not to speak of Chow et al. (1996)
concluded that full disclosure of private informations had not been arisen, there are somewhich are difficult to admit myself the occurrences of full disclosures among papers
obtaining positive conclusions. Added to those question marks, it must be pointed out, theprior researches that had been intended to conduct the straight experimental tests of the2

For copious discussions about accounting regulations, see Fujii (1998) and Oishi (2000).

２

basic model of full disclosure are few for the number of both designs and markets, which is
the main focus of the tests of the modified versions.
On those accounts, I find it remained meaningful to test the basic model experimentally atthis moment.
In this paper, 16 multiperiod experimental markets are conducted. In each market there
were a single seller and three buyers. In each period, each seller was endowed with one
commodity to offer for sale to the buyers. The distribution of commodity’s value is assumed
to be common knowledge. At the beginning of each trading period, the seller was informedof the realization of commodity ’s value, and decided its message whether to reveal it
truthfully to the buyers or not. Receiving the seller’s message, the buyers bade to purchasethe commodity. The trading mechanism used was a first-price, sealed-bid auction
institution. A 2×2 factorial design was created by manipulating (1) the number of possible
commodity’s values nature selects and (2) the existence of an antifraud rule 3 .The
manipulation (1) is relied mainly on the review of prior researches. There is no solid
theoretical prediction in the cell without an antifraud rule (by the manipulation (2)), but

3 According to King (1990), “an antifraud rule is a mechanism that requires that the disclosure set must

include as one of its elements the true (known) quality level. The rule permits vagueness but not lying(Ibid., p.860).” Non-disclosure is permitted because of not lying under this rule. While it might to bethought as a very strict assumption when applying to the real world, this setting may take on somerealistic tinct if I assume both the existence of huge penalty and the positive probability that the fact of３

the rule is an essential condition for the basic model of full disclosure. So, the cell without
an antifraud rule was set up in order to examine the influence of excluding it on the results.
The results from this experiment, in general, supported the theoretical prediction of full
disclosure, while sellers (i.e., manages in accounting context) were not indifferent between
disclosures of the worst informations and non-disclosures of those, they usually disclosed
their informations completely. The number of possible states (i.e., liquidating dividends)
had little influence on the results. This is inconsistent with the results of prior papers. In
the cells without an antifraud rule, overdisclosures occurred in general, but buyers (i.e.,
investors) saw through them and discounted fairly the commodity’s (liquidating dividend’s)values disclosed by sellers (managers).
The paper proceeds as follows. The next section 2 explains the basic model of full
disclosure briefly, and describes how the model has been applied and modified inaccounting context. In section 3, I indicate the reason why direct tests of the model has
been conducted using experimental approach, review some prior researches, points out
problems and question marks for the prior researches, and demonstrates the features ofthis paper. The experimental procedures and cell design are presented in the 4th section.
Section 5 develops the hypotheses and some behavioral prediction and reports theexperimental results. Summary and concluding remarks are given in section 6.

lying comes to light.

４

2. Theory – The basic model of full disclosure and its application and extension
2-1. The basic model of full disclosure
The basic model of full disclosure (hereafter, ‘the basic model’) is based on a theoreticalmodel that was introduced from the ‘persuasion game’ of Milgrom (1981) and extended byMilgrom and Roberts (1986). In this section, I borrow heavily from their papers and explain‘the basic model’ briefly 4.
The persuasion game can be represented as a game of an extension form as follows.
Players consist of one seller and buyers and the transaction of a commodity is put into
practice. First, Nature determines a certain point x i from a finite set X . This represents
the seller’s private information at once5. Here, i = 1,2,..., n and 0 < x1 < x 2 < ... < x n . x i
is a number which is directly connected with the value of the traded commodity. Buyers
know the probability that any x i is selected, P (xi ) > 0 . The seller observes x i and sends
some message M to the buyers. This message M is required to be truthful ( M = xi ).
That is, as far as the seller sends a message, he/she can’t lie to the buyers. He/ She only can

4 Here, the chief object in view is the ease of understanding. For the strict mathematical formation, seeMilgrom (1981) particularly.
5 The fact that nature determinesx i has an important implication. While x i is the numerical valuethat determines the final allocation of resource, it is given and the seller can’t influence its value. In short,
it is assumed that what is called ‘moral hazard problem’ is out of question.

５

either send the true value of xi ( M = x i ) or send no message ( M = ∅ ). In King (1990),
the mechanism that gives reliability to the message is referred to an antifraud rule. All thebuyers receive same message. So the seller can’t take a selective action that he/she sends
the message to only some of the buyers. Observing the message M from the seller, buyers
evaluate its commodities. At the last, the final allocation is decided according to sometransaction mechanism. The time line 6 above is as follows.

① Nature decides thecommodities’ valuexi .

② Seller selects③ Buyers evaluate the④ The

allocation

the Message M .

commodities’ value.

wealth is decided.

of

The payoff of a seller is equal to the amount received from a purchased buyer, and that ofa purchased buyer is equal to the commodities’ value minus the amount he/she paid and 0
for buyers who lost in bid. So utilities of both a seller and buyers are supposed to be
increasing functions of their payoffs, they have tried to maximize their payoffs.
In this dynamic game of incomplete information, there are many Bayesian-Nashequilibria. Each of them are composed two stages, i) being selected one message by a seller,buyers forms their belief about why that message are sended, and they decide bidding
strategies aimed to maximize their expected payoffs, ii) given such buyers’ strategies, aseller decides his/her message-sending strategy to maximize its expected utility (For moredetails, see the 4th chapter of Gibbons (1992)).

6 The term ‘time line’ is used in Berg et al. (1990).

６

Bayesian-Nash equilibrium of this game has two extreme cases, classified into the
proportion that a seller sends a message about its truthful value of the commodity. One
extreme is a case where a seller sends no message when any x i ’s determined by nature,buyers take it at face value and their prior beliefs are never changed, and they value its
commodity at the average of the distribution ( µ ). This means that, p (xi ) = 1 andnx s +1 − x s = x1 , assumed a discrete uniform distribution7, given no message, buyers continue
to think that p( xi M = ∅ ) = 1 and evaluate its commodity’s value at µ = (n + 1) x 1 . Milgromn2

and Roberts (1986) express these buyers as ‘unsophisticated’ or ‘naively credulous’. Other
extreme is the equilibrium that Milgrom and Roberts (1986) express sophisticated or‘assume-the-worst’, and in that equilibrium, perhaps except when i = 1 , a seller always
announces its commodity’s value x i . When i = 1 , for a seller, it is indifferent between
sending a truthful message and no message. Being sended a message, the buyer value thecommodity at x i , and he/she acts upon the belief that commodity ’s value is the lowest
possibility x1 in the case of no message.
There are many Bayesian-Nash equilibria between these two extreme proportions
messages are sended, of 0 % or 100%. All of these equilibria are that the seller only reveals

7 Theoretical literatures don’t specify one established distribution form. So in the analysis on and after

and the following experiment, for the ease of understanding and handling, I use the discrete uniform
distribution.

７

a specific level of the commodity’s value. Corresponding to such seller’s behavior, buyers
build up their beliefs and bid zero for the seller ’s behavior deviated those equilibria.
However, all these equilibria have undesirable properties, because buyers’ beliefs are notrational and these information sets are off the equilibrium path. In particular, for example,
when a seller reveals the truthful quality, it is not rational intuitively that buyers bid zeroon the ground the behavior is out of their beliefs.
Excluded all implausible equilibria by using the solution concept of perfect Bayesian-Nashequilibrium8, all of the equilibrium are removed except for that of buyers assuming worst 9.

8 In Milgrom (1981) and Milgrom and Roberts (1986), the solution concept of sequential equilibrium isused. However, in Gibbons (1992, p.179), as stated (1) there’s no difference between the perfect Bayesianequilibrium and the sequential equilibrium in many economic applications, and (2) for the complexity of adefinition and the way of application, almost anther use the former, so I denote ‘perfect Bayesianequilibrium’ here.
9 By reference to Verrecchia (1983, p.185), being transformed and abbreviated, this is demonstrated

following numerical expression. The payoff of a seller is equal to (1)(2) the buyers’ expectation given no message from him/her, i.e.

x i when he/she send a message, andE (xi M = ∅ ) in the case of no message.

Under the condition of no message, rational buyers assume that x i is equal to some cutoff of disclosure(for example,

x̂ ) or fall below it. That is to say, they value the commodity at E(xi xi ≤ xˆ ). A rational seller

who aims to maximize its payoff recognized this, (1) if
given

xi ≥ E( xi x i ≤ xˆ ) , he/she sends a message, and (2)xi < E (xi xi ≤ xˆ ) , he/she send no message. Therefore, for a seller the cutoff of disclosure isxi = E (xi xi ≤ xˆ ) . At equilibrium, the cutoffs of both a seller and buyers are got to be equal. So it isxi = E (xi xi ≤ xˆ ) . Based on the assumption here that the commodity follows a discrete uniform
distribution, the last equation is x i = 1 x i and this means all of the messages except for the case of2

lowest commodity’s value are sended.

８

The explanation is as follows.
If a seller selects to send no message, therefore M = ∅ , at the first step, a rational buyer
might recognize that the seller prefer selecting M = ∅ and being valued at the average ofdistribution µ such as the former extreme case to selecting M = xi and being valued at

x i . If nature selects the commodity’s value beyond the mean (i.e., prior expectation of the
distribution), a seller could get more payoff when he/she reveals it to buyers. So, under thecondition of no message, the buyer gives zero to the percentage that the commodity’s value
is above the mean.
After this period, given these buyers’ beliefs and strategies, a seller decides its messagesending strategy. At the second step, if a seller doesn’t send any messages and reveal thecommodity’s value, it is recognized to below the mean by buyers and the commodity isvalued at the average of zero and the mean of distribution µ ( ( 0 + µ ) = µ ) from the22assumption of the discrete uniform distribution. Therefore, if the commodity ’s value isbeyond µ , a seller prefers to send a message.
2

These unraveling processes are continued same as above, and at last, the range of acommodity’s value a seller can select when he/she doesn’t send an informative message 10 isvanished, and he/ she reveals all of the commodity ’s value perhaps except for only the

10 King et al. (1990) demonstrates that an informative message is thatE (~x M ) ≠ E(~x ) . Being send one

message are not synonymous with being send no message, it demands to revise one’s prior expectation.

９lowest value. Fig. A depicts this process, using numerical lines and numerical values. It is
assumed here that the commodity’s value is distributed [0,1,2,...,100] .
100

1st
2nd

50

3rd
Last

Fig. A: Unraveling process

250

The average of distribution is 50 . Then, at the 1st step, if nature selects the commodity’svalue more than 50 , a seller will be able to get more payoff to reveal it and evaluate its
face value (for example, 70 ). For the buyers, so, both not to being revealed the commodity’svalue and that the commodity’s value is from zero up to 50 are the same thing. At the 2nd
step, if the commodity’s value is more than 25 , a seller gets more payoff to reveal it.
Accordingly, when the commodity’s value is not revealed, a rational buyer values it under

25 . Hereafter, these downward unraveling process are repeated, finally at the perfect
Bayesian equilibrium, a seller prefer to sending all of the message of commodity’s value
except of zero, and buyers take this into consideration and recognize that the commodity’svalue is the lowest possibility given no message11.

11 Showing here is the process of thinking to reach equilibrium, and it never means how many times needs

to reach there or the space when a seller send no message have become 1

2

trial by trials. The important

thing is a process that, given no message, a rational buyer renewals his/her belief.

１０

In short, though there are a lot of perfect Bayesian-Nash equilibria in this dynamic gameof incomplete information, it reaches out perfect Bayesian-Nash equilibrium by excluding
implausible equilibria that are off the equilibrium path. Consequently, except for the lowest
value of the commodity, a seller discloses all of its values to buyers.

2-2. Applications and extensions of the basic model to accounting
For the basic model of perfect (or full) disclosure discussed in the section 2-1, though
Milgrom (1981) and Milgrom and Roberts (1986) suggest the applicabilities to various
economic instance, they don’t deal with the accounting issues directly. However, it is clear
that, this basic model has very important implications to accounting reports andregulations and is easily applicable. In that place, a ‘seller’ and ‘buyers’ are changed into a‘manager’ and ‘investors’ respectively, the setting has changed that a manager transacts
the asset (equity) that are paid the liquidation dividend at the end of a term with investors.
In the first place, nature reveals to a manager some signal, concerned with the real
liquidation value of its risky asset 12 . It is not necessary to change the basic model’s

12

More easily, it is possible to think it as just the information about liquidation value of the asset (equity).

Personally speaking, however, I think this signal as ‘a critical information on one’s decision making’. It’s amain issue that the critical information is either disclosed or not by a manager and is recognized exactly or
not by investors, but adding these, I think there is another stage that the investors make decision using
the information.

１１

assumption that only a manager is endowed with the signal and the distribution of thesignal is common knowledge between the interested parties. Upon received the signal, thealternatives for a manager are disclosing its exact value or making no disclosure (under anantifraud rule). Receiving the disclosure or nondisclosure from a manager, investors value
the firm in order to purchased the asset. It is the same as the former model that sometransaction mechanism is used to decide the allocation13. The time line of the application ofbasic model to the accounting disclosure is as follows.

① Nature reveals the②A manager makes③ Investors value the④ The

allocation

firm’s condition (liquidated

a disclosure of its

firm.

wealth is determined.

value) of this period.

firm’s state.

The result of analysis is just the same. If communication between the parties (① and ②,② and ③) has no cost and there is an antifraud rule in ②, at the equilibrium a manager
makes full disclosure about its firm’s state (perhaps, except for the worst). Thisconsequence that occurs voluntary disclosures of information is called, ‘disclosure principle’

13 It is assumed that a manager has to transfer its asset to the winning investor. The asset is of no value

to the manager. This setting is referred in King (1990), and it is assumed a non-owner/manager. Jensen
and Murphy (1990) carries on investigate the relation between accounting profits and rewards of CEOs.
They obtain an interesting result, which shows the management reward increased by ￠17.7 as theaccounting profit increased by $1,000. This finding may give some validity to the setting here that thepayoff of a manager is influenced its firm’s situation decided by nature. Still more, though the model
assumes a firm liquidates period by period, the result of analysis holds true for going concerns too.

１２ofin Dye (1985) or ‘market-induced information disclosure’ in King (1991).
These results of analysis have a great interest in arguing accounting regulation14. By
working some market mechanism, any information could be disclosed voluntarily by amanager. Therefore, it implies that there’s no need to force firms to disclose publicly any
information. Thinking out both the costs of accounting regulation15 and the propriety offorcing all of the firms to obey a same regulation 16, this result casts a pall of gloom over theargument about accounting regulation on the assumption that more and more regulations
must be needed.
The results in the basic model, however, have been revised and expanding by taking costly
disclosure (Verrecchia 1983), costly obtainment of disclosure (Matthews and Postlewaite1985), uncertainty of seller’s disclosure endowment (Dye 1985, Jung and Kwon 1988), and

14 Definition of accounting regulation lies in Nakamura (1992) or Oishi (2000) for example. Here, I grasp itis ‘what forces to disclose the critical information for making decisions’ in a quite broad sense. It might bethought that the presence of an antifraud rule itself is an accounting regulation, but the problem is solved
to some extent, adding that an antifraud rule provides to punishes a manager who makes a fictious
disclosure with a very severe penalty, assuming that there is a positive probability of being detected
his/her fraud disclosure, and a manager imposes himself/herself an antifraud rule.
15 In Nakamura (1992, Ibid., p.30), they are ‘the costs related consumption of the resources resulting fromthe establishment of the accounting laws or principles, observance and lookout, and lawsuit. In the
opposite direction, the government will impose taxes on the people.
16 Fujii (1998) points out, standing a point of view that any regulations are unnecessary, because of thediversity of firms’ managerial environment, optimal disclosure levels can be different between firms.

１３

the presence of proprietary information (Dye 1985, Wagenhofer 1990) and so on. All of themattempt to address some situation where a manager has an incentive to withhold disclosurein some range among the state nature selected on the assumption of an antifraud rule. For
example, Jung and Kwon (1988) analyze the settings there is positive probability that amanager doesn’t know its firm’s state of one period. Then, investors can’t distinguish nondisclosure from either the seller’s lack of information or the unfavorableness of his/her
information same as the basic model. Under such situation, it might be the case that the
information is threshold and is not disclosed voluntarily.
These expansions of the basic model focus on some discrepancy between the theoreticalprediction for voluntary disclosures and the real world. First, there are lots of empiricalevidences which prove voluntary disclosures don’t always occur. Some of them are including
papers such as, the earnings prediction of a manager and its reaction of the capital market(Patel 1976, Waymire 1984, 1985, and Lev and Penman 1990), the practice of blind bidding
behavior in the motion picture industry in the U.S.A., and gas-octane reporting (Jovanovic
1982). For example, Lev and Penman (1990) argued that, managers tend to disclose goodnews rather than bad news and the firm not to disclose doesn’t experience the drastic fallin its stock price. And second, the evolutions of the basic model are originated from theaccounting regulations in the real world. As pointed out, accounting regulation in many
countries a r e heading the way of tightening, and there is some empirical researches,

１４stating that the public and the quasi-public accounting principle setting institutions pass a
judgment that market force is not enough to enforce managers to make sufficient
disclosures (A series of movement in the U.S.A. is detailed in Chow et al. (1996)).
However, is it possible to do direct tests of the model by the empirical researches using
datas from naturally occurring markets17? In the next section, I’ll give a negative view on
this question and explain why experimental approach has used.

3. Experimental approach
3-1. The limitation of empirical research18―why the experiment is fit?
As noted in the former section, the tests of the model using data from naturally occurring
markets are problematic. Chow et al. (1998, Ibid. p.135) remarks that, touching this point
at issue, “in addiction to problems of potential model misspecifications and omitted
variables, a key difficulty is measurement error in variables, which is an especiallysignificant obstacle because of the researcher’s lack of access to the complete information
set of managers.” Showing along time line of the model, that is, it is impossible for
empirical researches using data from naturally occurring markets to recognize the critical

17 They are also called ‘archival data’. To compare the data generating in the laboratory, this term is used.
18 It’s true that the experimental approach is one of the methods of empirical research. So, the title of thissection may be needed to add an objective verb ‘previous’.

１５matters for analysis, for example ① what states that nature selects can be arisen (priordistribution) or ② what means (actions) a manager can select. Since it is necessary toprovide some assumptions and comparisons, it demands some interpretations for thefindings of these empirical researches and it makes unclear the result itself (For similarviews, see the section 6 of Waymire (1985)).
Contrary to above problems, in the experiment, both the states of its firm which are
selected by nature at ① and the means which a manager can select at ② can be
determined as a rules in a laboratory, and we can have control over them perfectly.
Therefore, we can do the direct test of models.
Both methods of empirical researches using datas from naturally occurring markets andexperimental datas are not alternative or exclusive each other. It is true that, taking theformer researches opportunities, theoretical models have been revised, and the newexperiments have been stimulated to conduct (For more details, see the chapter 1 of Kageland Roth (1995)). However, for the tests of the basic model and the models
revised/expanded it, it is not appropriate using the data from naturally occurring markets,
experimental approaches become powerful means.

3-2. Prior experimental researches
There are some prior experimental researches. Some of them had already incorporated the

１６extension of the basic model as above, and the issues to confirm by experiments havedeveloped from “Can the private disclosure suggested by the basic model occur inlaboratory actually?” into “Under what conditions does a manager have an incentive tothreshold his/her information disclosure?”
Forsythe et al. (1989) is one early experimental literature addressing this issue. Taking
into account the institution of blind bidding in the motion picture industry of the U.S.A.,
and the actual cases such that entering protects from exhibitors (i.e., owners and operatorsof movie theaters) and laws prohibiting its practice by some states, they conducted tests ofthe basic model. Numbers of the possible states which nature selects were 125 in one cell
( [1,2,...,125 ] ) and 8 in another cell ( [TypeⅠ,Ⅱ,..., Ⅷ] + ([1,2,...,15 ]) )19. In Forsythe et al. (1989),
their experimental markets consisted of four sellers and four buyers, differing widely inthat there were a single seller and three (or four) buyers in other prior experiments. They
explain “the purpose of having multiple sellers was simply so that buyers could have more
rapidly gain experience with the trading rules (Ibid., p.221).” This factor does not affect thepredictions of the theory in a significant way as they describe, but it was not the directtests of the model. Each four buyer made decisions to purchase four items from four

19

In this latter cell, the value of an asset was determined by both its common value [TypeⅠ,Ⅱ,..., Ⅷ] (typenumber were multiplied by fifteen) and the private value([1,2,...,15]) . The common value was same among

all subjects acting as buyers in the markets, but the private value was different for each subject. And its
total represented the asset value for one buyer.

１７distinct sellers each period, and taking both this setting and competitions with other rivals
into consideration, each four seller decided its disclosure. Forsythe et al. (1989) conclude
that “it is clear that the sequential equilibrium model is a good predictor of behavior inthese simple markets (Ibid., p.230)”, revealing a support of full disclosure model.
R. R. King and D. E. Wallin are researchers who have conducted the most extensive
experimental researches in this realm. In King and Wallin (1990), the thesis was effect of
antifraud rules and ex post verifiability on theoretical predictions of the model, and someexperiments were conducted in a 2×2 cell setting. An asset of an object for transaction was,differing critically from other experiments, a $1 lottery ticket. The ticket could have one ofthree realization levels that nature selected (10, 50, and 90 percent), specifying theprobability that it would pay $1 or zero. For example, in the cell with an antifraud rule,
when a seller revealed that the realization level was 90 percent, each buyer valued thelottery ticket which was pay out $1 by the probability of 90 percent20. Same transactions
were repeated fifty times, and for each period one unit was traded. The exchange
institution used was a first-price sealed bid auction. Their results supported the predictionof the basic model strongly, in the cells with an antifraud rule, and the equilibrium of full
disclosure occurred generally regardless of export verifiability.
King and Wallin (1991b) investigated the prediction of the basic model and the effect of

１８

the number of disclosure options available to a seller. It was assumed that there was an
asset which was paid a liquidating dividend chosen from one uniform discrete distribution[15,25,...,85] , while a seller was restrained by an antifraud rule, he/she had some disclosure
options. The last setting was that, for example, when nature had selected 55 from above
distribution, a seller was able to make four forms of disclosure options such as; (1) a point
disclosure of {55}, (2) a consecutive pair of {45,55} ordividendvaluesof{55,65,75,85} ,

and

(4)

{55,65}, (3) the latter half of possible
non-disclosure

which

would

be

{15,25,35,45,55,65,75,85} . Their intention was to investigate the effect of the disclosure
options on the arrival at equilibrium, because given the theoretical prediction that therational buyer put a lower and lower estimation on the value of an asset when no disclosure
is made, the number of disclosure options may weaken the buyer’s ability to reach someequilibrium. Also, a double auction (DA) was adopted as the trading institution because of
its favorableness to converge to competitive equilibrium, and eight assets were endowedwith a seller and were traded each period. These settings are characteristic of this paper.
The result is that, the seller moved toward full disclosure (in their paper, referred to‘market-induced information disclosure: MID), though the theoretical predictions were
weakened as the number of disclosure options increased, ceteris paribus.
In King and Wallin (1991a), the asset value of one particular period was drawn out of the

20

They also have introduced two different distributions of realization levels, but it is not interest here.

１９

uniform discrete distribution identical with King and Wallin (1991b). It was characteristicof this paper to report experimental results in the case that there was positive priorprobability both a seller and buyers were given no information about the asset value of that
period, based on the model in Dye (1985) and Jung and Kwon (1988). The prior probability
a manager was endowed with no information was 0 , 0.1 , or 0.3 . Then, it was notdifferent from the basic model in the case of 0 , but, for example if it was set at 0.3 in one
setting, a manager was not informed of its period’s asset value at the probability of thirty
percent of all trading periods (= 50 in their setting), so a manager didn’t know the asset
value either. Though coincidence with a point prediction from the theoretical calculations
were not found out, they concluded that their results were consistent with the general
proposition of the model stating that the range of no disclosure had came to large as theprior probability increased.
King and Wallin (1995) presented the results of experimental test based on Wagenhofer’s(1990) model. In Wagenhofer (1990), it was assumed that there was an opponent who
entered the market and reduced the terminal value of the asset by certain fixed amount
only if the opponent believed the firm’s expected value was more than one exogenously
specified threshold. In this case, a buyer can ’t know the reason why a seller makes nodisclosure either due to unfavorableness of his information about the firm’s value (similar
to the basic model) or due to the avoidance of loss from entering an opponent. Wagenhofer

２０(1990) proved the existence of three sequential equilibria, then King and Wallin (1995)
investigate which equilibrium would have reached in the laboratory. The uniform
distribution of the asset’s value here was [0,1,...400 ] . Mixed with above complex settings,
although they concluded that the experimental results supported the theoretical predictionof Wagenhofer’s (1990) disclosure model, but the results were somewhat unclear tointerpret 21.
Chow et al. (1996) is the only article argued “this findings fails to support the(equilibrium) prediction of analytical research that when disclosure is costless, managers
voluntarily disclose all news (Ibid., p.149).” In this experiment, the number of possible
values of asset was 201 which was drawn from the uniform discrete distribution such as[0,1,...,200] , and added to the basic model, they investigated the Verrecchia’s (1983)
disclosure model which proved that､ full disclosures might not have occurred in the certain
situation when disclosure was costly. Even in the cells with no cost of disclosure, however,among four test periods out of all 13 periods (from period 9 to 12) of 39 markets conducted,
no disclosures were occurred by the proportion of 41.7 percent, failing to support thetheoretical predictions. Chow et al. (1996) point out as the main reasons, sparing the21

To add to this, King (1996) researches the effect of allowing a seller discretionary disclosures on theparties’ actions. However, I don’t refer to it here because buyers’ payoffs were influenced directly by aseller’s action in his setting.

２１

number of pages about why such results were achieved, there existed some buyers who
didn’t price-protected themselves (that is, didn’t assume the worst), continued to bid thehigher prices, hold the seller ’s payoff at higher levels, and didn’t give sellers incentives todisclose 22.
In summary, except for Chow et al. (1996), the prior researches have obtained theaffirmative conclusions about the theoretical predictions of both the basic model and its
modified models.

3-3. Problems and question marks for the prior researches
Accepting these findings of prior researches solely, it might be necessary to conduct
experiments to investigate one revised model that has not been conducted yet. However,reviewing the prior disclosure experiments minutely, it is true to find some question marks
here and there about their operations, designs, and interpretations of results. In thissection, I will point out some problems in the prior researches and explain this paper ’s
standpoint positing an emphasis on the experiments of the basic model.
One major puzzle is that, not to speak of Chow et al. (1996) concluded full disclosures of22

It has not been given a clear explanation about why right then such buyers existed. However, theysuggested that the realized pay for subjects acting as buyers was admittedly low. I will touch this problem
of reward in the experiment later.

２２

private informations had not been arisen, there are some papers which are difficult tointerpret as the occurrences of full disclosures among papers obtaining positive conclusions.
For instance, in King and Wallin (1991b), no disclosure occurred in the proportion of 40
percent (in cell A: a manager was endowed with the firm’s value and it was common
knowledge among all subjects, that is similar to the basic model) even in the latter half of
their fifty trading periods. Also, in King and Wallin (1991a), no disclosure occurred in the
proportion of 8 to 34 (=23.5 percent) in the situation which was predicted theoretically theoccurrence of full disclosures. In Forsythe et al. (1990), these problem is somewhat
moderated, but no disclosure occurred in the ratio of about one to five.
Having reviewed the prior researches in detail above, one can notice that King and Wallin(1990) is the only paper that is able to accept the occurrences of full disclosures without
reservation. In King and Wallin (1990), disclosures occurred in the proportion of both 95.5
percent (=128/134, in the setting of cell A, which had an antifraud rule and all the buyers
were informed of what had happened in its period trial by trial) and 89.6 percent (120/134,
in the cell B, which also had an antifraud rule but the buyers were not informed of theconsequence of one period). As pointed out in the section 3-2, however, in this experiment, it
was a lottery ticket, which took only one of three probabilities to come up. So, it turns outthat the equilibrium was able to be reached without reservation when the number ofpossible states selected by nature was three, but the experimental results became

２３somewhat ambiguous as the number increased to 8, and it put obvious obstacles to reachthe analytical equilibrium as the possibilities numbered in 125 or 201. This matter is ofimportance, I think. That is to say, it can be interpreted that, only in the case where it is acommon knowledge that the firm’s value (or the liquidating dividend of one period) could
take one form from only three forms, for example, that is ‘high’, ‘neutral’ and ‘low’, amanager discloses its value except for ‘low’ and investors can find it to be ‘low’ when no
disclosure is made. Consequently, the applicability of the results to real world that the
distribution of firm’s value must be continuous and not a common knowledge may beconstrained severely. Also, though employing last one or a few from dozens of trials for its
test period and arriving at some decision, it means that it needs to take considerable trials
to reach an equilibrium.
Relatively low monetary rewards to subjects may be one of the problems. For example, in
Chow et al. (1996), the average monetary reward for their three hours experimental session
was $13.84 (s=$0.85) to subjects participated as sellers and $7.76 (s=$10.53) to ones
participated as buyers, it might have not been enough to motivate subject students 23.

23

There always exists criticisms for the experimental method itself that whether certain theory is

supported or not depends on the level of monetary rewards. I don’t deliberate this here, but generally
speaking, it doesn’t give a great influence upon experimental results insofar an experimenter pays its
experimental reward s according to induced-value theory of Smith (1976). However, it seems that when
student subjects are involved in the experiment, it is necessary for an experimenter to design his/her

２４In addition to the monetary motivation for subject’s level of interest and involvement,
there is an intrinsic problem in the method of determining subject’s reward of disclosure
experiment, which indicated in Berg et al. (1990) as “a trading institution that gives all
gains to trade to one side of the market (Ibid., p831)”24. In other words, it is a zero profit
condition whose expected trading profits are zero for subjects acting as buyers (investors).
In some equilibrium predicted theoretically, a seller (manager) makes full disclosures ofhis/her private informations. Being no disclosures, investors (buyers) can detect that the
manager (seller) has the worst possible information. Then investors (buyers) are confronted
with making decisions on which how they valued the asset whose terminal value(liquidating dividend) is known, and competitions among investors (buyers) drive buyers’
expected profit to zero. That is, a winning investor (buyer) expects to value at 100 andreceive 100 when a manager (seller) disclosed the firm’s state is 100, for example, As theamount received become equal to the amount paid, investors’ (buyers’) trading profits
expect to equal to zero in the equilibrium25. How do the subjects acting as buyers think thatthe consequences of their rational decisions are not quite connected with their monetary

experimental settings taking their due reward levels for the part-time jobs into consideration.
24 King and Wallin (1991, p.176) point out the similar problem.
25 As denoted above, my awareness of problem is whether one critical information for decision making is

disclosed or not, and I assume to be a next stage in which investors (buyers) make decisions themselves
taking the manager’s (seller’s) behavior into consideration. They are assumed to gain in this next stage, so

２５rewards?
The number of trials in one experimental session, too, may be problematic. In priorresearches, there is major difference between King and Wallin (1990) which was used thecomputer system (AEMLS: the Arizona Experimental Markets Laboratory System) inexperimentation and was able to report 50 times, and Forsythe et al. (1989) and Chow et al.
(1996) which manually conducted their experiments and could duplicate only 20 and 13
times, respectively. Chow et al. (1996, p.149) reveals that, by referring this issue
particularly, their primary obstacles to the number of trading periods was the tight time
demand of manually conducting their experiment. In contrast, many trading periods suchas 50 trials and more may arise another problem of slowness to reach the equilibrium.
Because of easier learning and favorableness to reach the equilibrium, in some priorresearches, the experimental designs such as the double auction (DA) institution withmultiple assets (King, 1991b) and the competitions among four sellers has been introduced
to test the basic model. Though the theory itself does not stipulate one particular tradingmechanism, the DA institution is not appropriate for the test of basic model because it
would have admit some additional information flow from a manager (seller) to investors(buyers) by way of the offer made and the bids accepted 26. Introduction of competitions

it is not a wonder their inferences given no or full disclosure don’t make profits.
26 This is just what themselves point out in King and Wallin (1990, p.870).

２６

among plural managers (sellers) imports a new factor into the basic model, although
Forsythe et al. (1989, p.221) expresses the factor does not affect the predictions of theory ina significant way. The buyers have bid to purchase plural assets from the distinct sellers at
the same time.
Finally, I want to point out too, it should also be stressed that the prior researches that
had been intended to conduct the straight experimental tests of the basic model are few for
the number of both designs and markets.
In summary, I find it remained meaningful to test again the basic model experimentally.
On the other hand, it is the case that there is ample scope leaving its design to theexperimenter’s discretion even if one experiment is directed toward the test of the basicmodel. For that reason, in this paper, according to the findings of prior researches and myquestion marks above, it should be very significant to conduct experiments to test theprediction of the basic model using as refined design as possible.

4. Experimental methods
4-1. Market environment
The terms such as, ‘a manager’, ‘investors’, and ‘the firm’s state (liquidating dividend)’,and ‘disclosures’, may give subjects some psychological biases. So, I use more general terms
such as, ‘a seller’, ‘buyers’, ‘the commodity’s value’, and ‘sending messages’ as a substitute２７

for such words as ‘a manager’, ‘investors’, and ‘the firm’s state (liquidating dividend)’, and‘disclosures’, respectively 27 . Therefore, although I have more passionate concern foraccounting settings, the general terms are in principle used in this and next sections whilein part both are used compatibly.
In each market, there were a single seller and three buyers. This group consisted of four
subjects has been maintained throughout the periods of one experimental session 28. The
tasks of subjects in this experiment were transactions of fictious commodities 29. In each27

In consequence, the experiments have been conducted in consonance with the models of Milgrom (1980)

and others. This transformation into more general words may be interpreted to be an obstacle in case of
the application of experimental results to the real world. However, the more realistic the objects that wewant to test in the experiments are, the further the experiments part from the empirical inspections oftheories without removing the factors which the subjects may act based on outside of their monetary
incentives. For example, it is physically impossible to believe that, informing the subjects that theexperiment researches about bribery, tax evasion, or swindle, gives no psychological bias.
28 It can be thought the experimental design, which changes the matching of seller with buyers in eachperiod of one session, or what more, which changes to assign even the subject’s role in one experiment
randomly. But it was not employed because the adoption of such setting would have got the control ofexperiment very intricate. So, the influences of these designs to the results are remained unknown. If it istrue for the theoretical prediction that the reasonable buyer revises his/her beliefs graduatelly and reachthe equilibrium over time, the results might be deteriorated when such settings were adopted.
29 Informally, I received an indication from a practioner that some prior image against the

tangible/intangible goods/service is essential to a transaction of commodity (that is, the commodity of this‘widget’ is like this). Though I intended to get over this by the setting of distribution of possible values of
the commodity, the indication was thought to be convincing. The complement ‘fictious’, therefore, wasinterpolated in the instruction.

２８

period, each seller had only one commodity to offer for sale to the buyers. At the beginningof each trading period, each seller was informed of the realization of the commodity’s value
for sale in that period, and buyers were conscious that the seller had that knowledge. In
each period and for each commodity, this value was drawn with replacement from thediscrete uniform distribution described after, where all integers in that interval wereequally likely. Both the seller and the buyers knew the distribution of the commodity
values. Also, the seller and the buyers were told that the commodity was sold in each period
without reserve. If no transaction occurred, any unsold commodities were worthless to theseller, but all the market participants were not informed of this 30.
The trading mechanism was a first-price sealed-bid auction institution. As the theory
itself does not stipulate a specific institution, other trading mechanism can be selected. But
I selected this institution because the double auction (DA) institution was somewhat
problematic as argued in the section3-3 and other institution such as the second-pricesealed-bid auction institution was thought to be difficult to understand for subjects, while
the second-price sealed-bid auction institution had an advantage to reveal buyers’
evaluation of the commodity completely 31. And one reason why the first-price, sealed-bid

30 As denoted in the next section 5, some subjects took advantage of the characteristic in this experimental

design.
31 Under the second-price sealed-bid auction institution, the dominant strategy for each buyer is to bid

his/her true reservation price.

２９

auction was implemented is to relax a zero profit condition, which was mentioned above.
In a main issue of this experiment is to investigate whether the theoretical prediction offull disclosures of private informations takes place in the laboratory, and if not, where thecauses on the equilibrium path are. Based on such a concern, it is problematic to set a newstage that reveals the buyers’ evaluation of the commodity using this trading mechanism,
the first-price, sealed-bid auction (the model doesn’t consider this stage). The prediction of
the theory may be influenced by this new stage. However, in the theoretical model it isassumed that there is an antifraud rule, so the value of commodity reveals itself when not
only a message is sended, but also in equilibrium no message is sended. Competition
among the buyers drives their evaluations to be nearly equal to the price. Therefore, using
the first-price, sealed-bid auction institution in the experiment does not generateinconsistency with the theory (for detailed arguments of using the sealed-bid auction in
more complex settings, see the section 2 of Forsythe et al. (1989, p.219)).

4-2 Experimental designs
Two manipulations32 were conducted. One of them was the distribution of commodity’svalue from which nature selected. The commodity’s value was randomly drawn from the32

It is also called ‘treatment’.

３０discrete uniform distribution either of [25, 50, 75,100,125,150,175] or of [25, 26,..., 175 ] 33. These
two were equal in ranges and means of one hundred, but differ widely in that the numbersof possible commodity’s value were 7 in one cell and 151 in the other. These reflect theargument in the section 3-3, in which the number of possible states nature select may
influence on the experimental results, and will discuss particularly in the next section of
the Hypotheses.
Another manipulation was related to the existence and inexistence of an antifraud rule.
The existence of an antifraud rule is a critical factor for the basic model and its
modification. So, given no antifraud rule, the theory losses its predictable power. Whilesome forecasts are possible and I will dispute over that issue, experiments of the cellwithout an antifraud rule were conducted not to test the solid theoretical prediction but toobtain some findings about influences of no antifraud rule.
According to these two manipulations, cells design of this experiment is represented asfollows.

Cells design of the experiment
The number of possible states
7151
An antifraud
Exist
Cell ①cell ②rule
Not exist
Cell ③cell ④33 These number settings were arbitrary.

３１

4-3. Conduct of experiments
Experimental markets were run at the Toyonaka campus, Osaka University on the 26th
and next 27th of November in 1998. Subjects were students of Osaka University recruitedfrom graduate and undergraduate courses, and they were manifold in their academic
background34. All four cells had four independent markets, and each market had one sellerof a commodity and three buyers, figuring up 64 subjects.
Each market consisted of a number of repetitions of same events. Upon arrival at aclassroom, subjects drew lots35 at the entrance and were ushered their numbers’ seatsguided by assistants. A written instruction and experimental materials 36 within an
envelope were prepared for in advance on each seat, and the subjects were cautioned not toopen and look at them before indicated. There placed kitchen guards37 on their desks toprevent one subject from seeing others’ informations and decisions. After all the subjects

34

For example, they were majoring economics, law, literature, science, medicine, and so on. In the priorpapers, Forsythe et al. (1989) denoted to use undergraduate students at three different location (CarnegieMellon University, the University of Arizona, and the University of Iowa), and in Chow et al. (1996) there
were 156 students recruited from upper level and graduate finance course, and in King and Wallin (1991a,
1995) and King (1996), Washington University business students were involved as subjects. Upon
recruiting subjects, I did not ask any academic backgrounds, grades, and knowledge.
35 The lots were used to assign randomly the subjects to their tasks in a particular markets.
36 The instruction and the main experimental materials are available upon request from the author.
37 The kitchen guard is an oil-guarding steel board using generally in the kitchen. Three directions areintercepted from other subjects by about thirty centimeters in height.

３２

took their seats, the experimental sessions were started. At first, I took considerable time
for the instruction to inform the subjects about their tasks and the rules governing tradeand how their cash reward would be determined. Written instruction was given each andplaybacked by a cassette recorder with a radio. At the end of the instruction, two examples
were given to confirm the actual transaction flow and payoffs. A transaction in each period
was as follows (the parenthetic numbers (1)-(4) correspond to the time line of the basicmodel in the section 2-1).
(1) The value of its period’s commodity was determined by nature from the distribution
described above 38 , and was informed only to the subject acting as a seller. The
preselected value sequences differed for each market in the same session, but they weresame in the cell ① and the cell ③, and in the cell ② and the cell ④ 39.
(2) The seller decided whether to reveal this information to buyers (i.e., message). In thiscase, it meant that all three subjects acting as buyers received the same message from aseller (so, some different treatment across the buyers was not allowed). In the cell ①

38 The sequence of commodity’s values over all twenty periods had been preselected using random number

generating tool of the software. See DeJong et al. (1985) for a discussion of this presequencing.
39 Given the same distribution is used, it has been found that the actual value flows drowned from its

distribution had some influence on the experimental results (for example, King 1996). So I changed thesequences market by market although the subjects were not able to know anything about the other market
in which they were not participated. The reason why the cells with and without an antifraud rule had thesame sequence was to facilitate the comparison of the results.

３３and the cell ②, the disclosure options available to the seller was either ‘disclosing theinformed value truthfully’ or ‘making no disclosure’, but in the cell ③ and the cell ④
without antifraud rules, the former option was changed to ‘selecting one possible value
and disclosing it’ and the antifraud rule was excluded according to the cell designs inthis way.
(3) Receiving the seller ’s message, the buyers valued the commodity to purchase in that
period and tendered written bids.
(4) The highest bid among the three wined in the auction, and the winning buyer paid theamount equal to his/her bid. If plural buyers tied for the highest bid, then a dice
determined who purchased its commodity.
It is the payoff of that period for a winning buyer to be the trading profit (or loss) that
equaled to the commodity’s value minus the amount paid was. The payoff of a seller was
equal to the bid amount received from the buyer and those of the losing buyers were
zero in that period.
All three bid prices, the winning bid, the commodity’s value, and the identification of
the winning buyer in that period were told to all the participants in the market at theend of each period40.

40 There are some design choices such as, the only winning buyer and (of course) the seller can know thehighest bid, or not all three bid prices but only the highest bid is revealed publicly. The design used in this３４All necessary informations, for example that period’s commodity value and bids submitted
etc., were informed and transmitted using B8 cards by assistants.
The transaction of commodity was repeated 20 times, which was prescribed and informed
to all subjects in the instruction 41. The total payoff for twenty periods (= rewards) was fixedaccording to the following expressions (in: ¥).
The seller: the sum of the amount received from buyers+ the number of period conducted (=20) × 40
The buyers: the sum of his/her trading profit × 2 + 1,000+ the number of period conducted (=20) × 80
In consonance to the theory, I asked the subjects for acting to maximize the first term, but
the other terms were added in. 1,000 was the initial endowment (referred to the ‘budget’ inthe experiment due to the facility of comprehension), and it was given to the buyer because
he/she was not endowed with a commodity in each period and there was positive
probability to suffer the loss in the transaction. The payoffs that were related to thenumber of periods conducted were added in because of a zero profit condition for the buyers

experiment might have functioned to fasten the subjects’ learning.
41 Letting the subjects know the terminal trading period may have an effect on the outcome of the game.

Chow et al. (1996, p.140), for example, consider the potential biases of end-of-game strategic behavior.
However, actually such an effect has been found. I, therefore, do not touch this problem hereafter.

３５

as mentioned above42. The same reasoning applies to the treatment that the sum of thebuyer’s trading profit was doubled43.
After the actual trading session ended, the subjects completed an evaluation forms andthen questionnaires, were paid and left. Throughout the instruction and actual experiment,
all participants were monitored to prevent communication with each other. Eachexperimental market lasted about two hours and twenty minutes. Average cash pay was¥2,721.86, the maximum was ¥3,384 and the minimum was ¥2,24944.

5. Hypotheses and experimental results
5-1. Hypotheses and behavioral forecasts
Hypotheses of the cells with an antifraud rule (i.e., the cell ① and ②)
The first hypothesis is directly linked with the main theme of this paper. As being positedan antifraud rule, a seller must inform the realization of its commodity’s value as far as

42 Although the intention was quite different, Forsythe et al. (1989) gave the similar payoffs to only thebuyers as commission values.
43 According to these expressions, the prior expected payoffs for the subjects were, ¥2,800 for the sellerand ¥2,600 for the buyer, respectively. A slight higher expected payoff for the seller was due to the result ofa non-cash payment pretest, which had been conducted using undergraduate students majoring
accounting on the 9 th of November. Being priced very low by the subjects acting as buyers, the seller had
been taken away much of its payoff. Also, for the seller, the expected pay is equal to the maximum too.
44 Because of its design, there were not large differences among the subjects. To give incentives to involve

hardly for them, it might be desirable to come out perceptive differences due to their decision-makings. In
this respect, I might have to say that this is one of the intrinsic problems of these disclosure experiments.

３６

he/she send a message. Then, the theory in the section 2-1 predicts the disclosure patternin equilibrium as follows.

Hypothesis 1: In the cells with an antifraud rule, a seller reveals all the commodity’s value.
So, M = x i . When the commodity’s value is the lowest, namely 25 in thesetting here, the seller is indifferent between disclosing it and withholdingit.

As the somewhat plausible alternative hypotheses, this paper attempts to research theconvergences to other representative Bayesian Nash equilibria such as, the naive expectedvalue model in King and Wallin (1991b), the goods news hypothesis in King and Wallin(1991a), and the naive model in Miller and Plott (1985)., and so on. Concretely speaking,there are: (1) no disclosure always occurs, (2) the values more than the mean of the
distribution (i.e., here 100) are only revealed by sellers, (3) disclosures of some specificvalues (or value) and (4) random disclosures occur.
In order to examine whether the perfect Bayesian equilibrium could be reached or not,including the relevant actions on the side of subjects acting buyers, some conditions arenecessary to set. Unlike Forsythe et al. (1989), these conditions are not set as formal
hypotheses. However, I will investigate properly whether the subjects acted as suggested to

３７

the theoretical prediction or not, as argued in Forsythe et al. (1989) and Chow et al. (1996).
The second hypothesis is built on the indication of the section 3-3, implying the question
marks from the reviews of prior researches. There was one of the question marks as to ‘therelationship between the number of possible states and the experimental result’. It
mentioned that, the results had been weakened as the numbers were increased to 8, 125,and 201, respectively, although full disclosure occurred undoubtedly when the number ofpossible states is three. The unraveling process predicts that the buyer narrows the set ofcommodity’s value graduatelly given no disclosure. Therefore, it could be understood that it
does not imply that the number of possible states influences the experimental results, but
this dysfunction in the case of 8 suggests that the experimental results are less applicableto the real world. In this paper, I examine this issue to judge the possibility for future
developments of these experiments by changing the number of possible commodity’s values
into 7 (= cell ①) and 151 (cell ②).
According to the theory, the number of possible states does not have any influences.

Hypothesis 2: About sellers’ disclosure patterns, there is no difference between the cell ①
and the cell ②.

３８Behavioral forecasts of the cells without an antifraud rule (i.e., the cell ③and ④)
As stated in the section 4-2 of experimental design, the creation of cells without anantifraud rule is not based on any theoretical prediction. And, the argument of the basicmodel explained in the section 2 and its modified versions were all premised on this rule. In
contrast, there seems no solid theoretical prediction about what the equilibrium of the cells
without an antifraud rule is, while it is one of the hot topics in the researches of truthtelling and reputation formation. Because at present it has not been analyzed and resolved
completely, given positive probability of seller’s fraud reporting, how the buyer actuallyvalues the commodity after receiving the seller ’s report, and given the buyers’ beliefs andstrategies grounded on their beliefs, how a seller in fact decides a message-sending strategy.
That is the reason why I made this section’s title not ‘hypotheses’ but ‘behavioral forecasts’.
However, “in practice, antifraud rules are imperfect due to the cost and complexities ofenforcement (King, 1996, Ibid., p.375).” So, although I realize the integrity of theoreticalmodels whose critical bases of functioning are the existences of antifraud rules, the cells
without an antifraud rule have been set up for this experiment. Thus, these cells are just
exploratory cells and only designed to obtain some preliminary evidence.
The experimental researches, which was supposed that there was no antifraud rule andexamined its influences are, for example, the cell B of King and Wallin (1990) which was
the test of the basic model with no antifraud rule and the NC session in King (1996) which

３９investigated in the setting with no antifraud rule and no cost telling lies. The former was
the setting that the number of possible values was three and the traded asset was a lottery
ticket as denoted earlier and the latter was that experimenter paid for precisions in theprediction itself of subjects., so both settings are different from that of this experiment.
Regarding a taste of the behavioral predictions, they explained as follows. The buyer
anticipates, in the single period game, a seller sends a false message about commodity’svalue because the buyer is not able to impose a penalty on lying itself. Since the message is
not informative, the buyers will ignore the seller’s message and value the commodity at themean of the distribution µ , i.e., 100 here, because of competition among buyers. Given
that the buyers are expected to ignore the message, the seller’s best response is uncertain.
But if there is positive probability which the buyer might believe a seller’s message, theseller might overstate the value nature selected 45. In the finitely repeated game, this result
is regarded as one of plausible ones using backward induction. For more detailed
discussions about the seller ’s incentive to deviate from truthful reporting and themechanism that caused to occur the equilibrium of seller’s truthful disclosure by positingsome additional assumptions when there is no antifraud rule, see King and Wallin (1990)

45 On the contrary, in this situation, it may not be advantageous to a seller to under-state, that is, to senda message that the commodity value is below the value nature selected. Because it is not reasonable forthe buyer to bid above 100 when the commodity value is revealed just 100, even if the buyer ignores theseller’s message.

４０and King (1996).

5-2. Results and data analyses
In this section, I analyze the experimental data and report the results. In carrying out
statistical tests, plural (more than one) observations from each experiment will be used.
Therefore, there may be serial correlation, and conclusions should be deliberated with thisin mind. Also, I must point out there are only a little data of 80 (= each cell had four market
and each market had 20 periods)46.
In the analyses of cells with an antifraud rule, the data from the latter half mentioned
frequently, as well as the data of all 20 periods. The reason why I will deal with such an
additional data is that the subjects are assumed to establish their consistent messagesending/bidding behavioral rules in the course of repeated trials. In this experiment, thequestion 3 and 7 of the post-experiment questionnaire asked all subjects acting as either
sellers or buyers: ‘How many periods did you take to establish the way of reacting to
opponents’ behaviors approximately?’ Their answers to the post-experiment questionnairesuggested that the almost all subjects had established their consistent approaches by theend of period 10. Thus, I write the data from the latter half in a separate with the intentionof the analysis based on results that were arisen after all market participants fixed their

４１

behavioral rules. Whereas the subjects acting as buyer decided how to react by five period
at latest (some already had decided it at the 2nd period!), the subjects acting as sellers wereclearly slow at deciding, although these results might not be surprising.

Results from the cells with an antifraud rule (i.e., the cell ① and ②)

Table 1: Proportions of disclosures
All 20 periods
Cell ①（７)*68.8%(＝55/80)
Cell ②（151）*
67.5%(＝54/80)

The latter half (Period 11〜）
77.5%(＝31/40)
75.0%(＝30/40)* Parentheses represent the number of possible value.

Table 1 represents the proportions of disclosures in each cell (calculations are given inparentheses). On average, in the cell ① and ② sellers sended messages on 68.8 percent
and 67.5 percent for all 20 periods, and the proportions of the cell ① and ② has increased
to 77.5 percent and 75.0 percent for the latter half, respectively. However, these differences
between all the periods and the latter half are not statistically significant ( z = 1.216 ,p > 0.1 for the cell ① , and z = 1.026 , p > 0.15 for the cell ② ). Using a test of
proportions, even if the data from the latter half are employed, these proportion are
significantly below 1.0 ( z = 3.41 for the cell ① and z = 3.65 for the cell ② , bothp < 0.01 ). Therefore, it would be impossible to conclude that full disclosures were occurred.
However, it is here necessary to demonstrate the limitation on statistical test, which isderived from both the small samples of 40 and the fact that a single non-disclosure when

46 Experimental datas are available upon request from the author.

４２

disclosure is theoretically predicted causes rejection of a 0 or 100 percent base-rate
hypothesis 47.
The basic model of disclosure does not always predict the occurrence of full disclosure. For
sellers, the worst information (the lowest commodity ’s value) is indifferent between todisclose and not to disclose. To argue the Hypothesis 1, I examined the proportions of
disclosures both in each possible value of commodity (the cell ①) and in each range of thecommodity’s values (the cell ②). The results are presented in Figure 1-1 (the cell ①) and
Figure 1-2 (the cell ②). Also, in Figure 1-2 of the cell ②, as the number of possible values
were 151, I divided them into 5 equal ranges arbitrarily. That is, the five range are, ‘theneutral news’ which is from 85 to 115 and includes the mean of distribution 100, ‘the goodnews’ and ‘the very good news’ which are beyond ‘the neutral news’ and from 115 to 145 andfrom 145 to 175, respectively and ‘the bad news’ and ‘the very bad news’ which are below‘the neutral news’ and is from 55 to 85 and from 25 to 55, respectively. Three values thatjust dropped on the border are not depicted in the Figure 1-2. These two figures seem toprovide the obvious support for Hypothesis. Except for both the realizations of 25 when thenumber of possible value was 7 and the range [25,...,55] (i.e., ‘the very bad news’) when it

47 For example, in order not to reject the null hypothesis that the proportion of disclosures is 100 percent

at significant level of 0.05 , that is, to show that it is impossible to conclude that full disclosures are notoccurred, more than 95 percent (i.e., 38/40) disclosure must be made (then z = 1.45 ,４３

p > 0 .07 ).

was 151, in the latter half of the experimental sessions, disclosures were occurred in the
proportions of 31 32 (the cell ①) and 30 34 (the cell ② 48 ). In summary, although aseller was indifferent as to disclose of the realization of the lowest possible value, it can beconcluded that he/she generally moved toward full disclosure. Other Bayesian Nashequilibriums as alternative hypotheses cannot explain the results here.
Now I will conduct some further analyses which focus on whether the subjects behaved inways consistent with the basic model or not.
The theory assumes that, given no disclosure, buyers bid the mean of distribution at firstand gradually revise them downward over time. When the subjects acting as sellers had
sended no messages at the first time 49, the averages of the buyers’ bids were 35.83 for thecell ① and 37.25 for the cell ②. These values are significantly different from the mean of

48 All four non-disclosures here were happened in the range of commodity’s value[85,...,115] , which isnamed ‘the neutral news’. And 3 in 4 were due to a single subject acting as a seller in one market. She
replied to the question 7 of the post-experiment questionnaire that she randomly made her disclosure
decisions to intend the disturbance of market because she had been suffering the low payoffs from too
much ‘solid’ bidding behaviors by the buyers. However such her strategy drove her to lower her payoffs lessand less, and she replied to the next question 8, which was asked what the payoff-maximizing strategy had
been she thought, that ‘to disclose all the commodity’s values or not to disclose anything’. There is an
opinion that only experimental datas can tell its results. So I do not enter this issue further, but at last I
denote as an interesting fact that these non-disclosure behaviors were strategic outcomes and she hadreached both two extreme Bayesian Nash equilibrium introduced in the section 2.
49 In all of eight markets with an antifraud rule, the case which sellers had sended no message occurred

４４

distribution 100 ( t = 8.488 for the cell ① and t = 16.62 for cell ②, both p < 0.0001 ).
However, in the cell ②, the average bid is significantly different from 25 ( t = 3.25 ,p < 0.005 ), which is the lowest possible value. This result shows that the buyers could
have appreciated that making on disclosure was synonymous with possession of bad news.
From the unraveling process referred in the section 2, it would be interesting to examine
further as follows. For subjects acting as sellers,(a) Non-disclosures involving commodity’s value greater than the values he once had
disclosed,(b) Disclosures involving commodity’s values less than the previous highest bid price given
no disclosure,(c) Non-disclosures involving the commodity’s value greater than the previous highest bid
price given no disclosure,and for those acting as buyers,(d) To bid above the previous lowest commodity’s value in the case of no disclosure, andmore severely,(e) To bid above the average of 25 and the previous lowest commodity ’s value given no
message 50.

by the 4 th period at latest.
50 Explaining (c), if a seller obtained the bid price of 60 when he/she had sended no message lately, he/she

４５

These behavioral patterns deviating from the unraveling process are exhibited in Table 2.
The number of ‘total periods’ corresponds to the seller’s behavior in each market, anddepends on the first non-disclosure, i.e., the number is 18 (= 20−2) if a seller didn’t disclosein the 2nd period.

Table 2: Behaviors deviating from the unravelling process
Cell ①
Cell ②Market 1 Market 2 Market 3 Market 4 Market 1 Market 2 Market 3 Market 4
(a)
1
0
0
4
0
4
3
2
(b)
1
0
0
0
0
2
0
2
(c)
3
2
0
3
4
4
4
4
(d)
4
0
0
7
0
5
0
0
(e)
11
0
0
22
3
15
7
8
Total periods
18
19
17
16
18
17
16
18
On equal terms with Chow et al. (1996), calculating the proportions of the number ofdeviating times to the possible largest unraveling processes, those are 20.86 percent( = 29 139 ) for the sellers and 15.83 percent (= 66 (139 × 3) ) for the buyers. In view of thefact the subjects acting as buyers deviated these in the proportions of about 55 percent in
Chow et al. (1996), it might to be said that somewhat contractive results are due to theexistence of the buyers who were able to take their actions consistent with the theory. The
subjects acting as buyers were able to make game-theoretic reasoning sufficiently, and thesubjects acting as sellers unwillingly made voluntary disclosures of the commodities’ values
in response to the buyers’ behaviors.
The results support Hypothesis 1. In the cells with an antifraud rule, the equilibriumis thought to be unreasonable not to disclose the commodity’s value above 60, for example 100. He/she will

４６

seemed to be one of full disclosure, although there are some methodological limitations asmentioned. In general, sellers disclosed all the realization of commodity’s value but those of
the lowest one, and buyers were able to adjust such sellers’ behaviors.
Hypothesis 2 was motivated from the reviews of prior experimental researches to examine
the relation between the number of possible commodity ’s values and the experimental
results. Table 1 shows that both for all 20 periods (from 68.8 percent to 67.5 percent) andfor the latter half (from 77.5 percent to 75.0 percent), proportions of disclosures were notsignificantly different between the cell ① and the cell ② ( χ 2 = 0.029 and 0.069) .
Therefore, Hypothesis 2 cannot be rejected. The number of possible states had, in thesettings of this experiment, little influence on the results. It is unclear why such aninconsistent result between the prior researches and this paper happened.

Results from the cells without an antifraud rule (the cell ③ and the cell ④)
As stated in the section 5-1, there is no solid theoretical prediction in the cells without anantifraud rule. Therefore, what happened in these cells is reported first, and next, I willattempt to compare them with the cells with an antifraud rule.
Figures 2 (Figure 2-1 and 2-2) represent ‘the commodity’s value vs. message’ in the cells
without an antifraud rule. Fig ure 2-1 displays the result of the cell ③ and Figure 2-2

get nearly 100 (>60) if the commodity’s value is revealed.

４７

displays that of the cell ④, graphically depicting what message the seller sended in
response to the commodity’s value nature had selected. For the cell ③, the third dimension‘frequency ’ is set up additionally because each coordinate potentially has pluralobservations. For example, if a seller sended a message of 100 in one market period when
the commodity’s value was 100 (i.e., he/she disclosed truthfully), this corresponds tocoordinate (100, 100) and Figure 2-1 tells us there was one case like this. Given no
antifraud rule, the seller was able to send a message of the value other than its real
realization, he/she had sometimes informed the buyers of 75, 125, and so on when therealization was 100. For the cell ④, Figure 2-2 is easier to understand, and the diagonalline presents the cases which the commodities’ value were equal to the messages, that is,truthfully disclosures occurred, and the points upper left-hand of the diagonal line
represent the cases where the commodities’ value were less the messages, i.e.,
overdisclosures occurred, and the points lower light-hand represent those where thecommodities’ values were more than the messages, i.e., underdisclosures occurred.
Figures 2, in general, show the di sclosure of value is either equal to or more than therealization, namely truthful disclosures or overdisclosures. Though underdisclosures might
be disadvantageous to the sellers, King (1996) reports that sellers under-reported 11４８percent of the time in his NC sessions, whereas there was few under-report51. Clearly, theexperimental results are fairly consistent with the informal behavioral prediction thatmaintains overdisclosures occur generally given no antifraud rule. Also, this tendency
towards overdisclosures seems to strengthen as the number of possible states increased. To
compare with the cell ④ in which only one underdisclosure in 66 message sending
opportunities occurred, 6 underdisclosures and 29 truthful disclosures in 62 opportunities
occurred in the cell ③ . In the cells without an antifraud rule, two possible seller ’s
behaviors were non-disclosure and ‘choosing one of possible commodity’s values’. Thus , inthe cell ③, sellers were forced to announce one of possible values and were not allowed tosend messages of the values other than possible commodity’s value (i.e., announcing 105
when it is 100). There were therefore only 8 message-sending patterns including nodisclosure in the cell ③. If underdisclosure is intuitively unreasonable, a seller’s option ofsending message becomes smaller and smaller as the higher realization of commodity ’svalues is selected by nature. Because of this small set from which the seller was able tosend messages, these results may be caused.
Given no antifraud rule, truthful disclosures of the commodities’ values are difficult totake place in general, and have a tendency toward less unfavorable as the prior uncertainty
of commodity’s value increase. As regards this issue, I am interested in examined how the51 In King (1996), the number of possible states was 101.

４９

buyers responded to such sellers’ behavior.
Ｔａｂｌ
ｅ3: Trading profit (= the commodity's value minu the purchasing price)
Av.
s.
利益 損失
Av.
s.
利益
6.45 8.19
セル③ Disclosure 18.95 48.58
No Disclosure
6.84 37.87 66
12
No Disclosure
2.22 55.96 51
Cell ② Disclosure
8.78 9.13
セル④ Disclosure 12.92 33.23
No Disclosure 24.58 27.77
71
4
No Disclosure
1.57 36.05 56(Note) Column 'Profit' and 'loss' represent its frequency. 's.' is the standard diviation.

損失

Cell ① Disclosure

28
23

Table 3 displays averages (column ‘Av.’) and standard deviation (column ‘s’) for the buyers’
trading profits and losses (using data from all periods), and shows how many times thebuyers made trading profits (column ‘Profit’) or suffered the losses (column ‘Loss’) among
all 80 trading periods in all 4 cells 52. Regardless both of the cells and of the existence or
inexistence of disclosures, the buyers made profits from trades in average (all Av.>0).
However, the amounts and standard deviations have considerable differences among every
cell. In the cells with an antifraud rule (the cells ① and ②), the buyers gained more profit
in the case of non-disclosure. In contrast, the buyers gained much more profits when
making disclosures in the cells without an antifraud rule (the cells ③ and ④). Comparing
the cells with an antifraud rule to the cells without it, both the proportion suffering losses(31.9 percent = 51/160) and the standard deviations of trading profits in the cells without
an antifraud rule are larger than those (10 percent = 16/160) in another cells. This maymeans that, an antifraud rule plays the critical role in both the avoidance of losses from thetrade and the belittlement of variances in trading profits. Also, the larger the number of

52 The existence of some cases that the commodity’s value equaled bid price (i.e., trading profit/loss was

５０possible commodity’s value, the smaller the number and amount of trading losses. Taking
these all into considerations, it may be concluded that the buyers might have conducted
deliberately in order to avoid losses as the complexity of their conjectures at the moves had
increased.
In order to investigate the influence of an antifraud rule further, it is significant to discuss
the buyers’ responses to sellers’ message. Figure 3 (Figure 3-1 and 3-2) shows the price (i.e.,the highest bid)53 versus messages and displays graphically the results of regressions of
the price on message as the independent variable. Figure 3-1 and Figure 3-2 represent theoutcomes with and without an antifraud rule, respectively.
When with an antifraud rule, a slope of the regression was 0.9672 , an intercept was− 3.6192 , and this fitted model explained virtually all variances ( R 2 = 0.955 ).
On the contrary, the result of the regression was widely different in the cells without anantifraud rule.

The explanatory power of the model without an antifraud rule wasconsiderably less ( R 2 = 0.4918 ). However one of the behavioral prediction here was thatseller ’s message would be completely ignored. This was not the case. The slope was 0.4734
and the intercept was 30.207 . That is, the buyers took the sellers’ message intozero) prevents the total times from being 80.
53 It can be thought as the measure which is able to infer the buyers’ responses other indexes such as all

bids, average bid or median bid, and so on. However, I used the price as a substitute for those because of
the practice of the first-price sealed-bid auction in this experiment.

５１

consideration to some extent, and the tendency that a higher message generated a higher
price is at least admitted.

6. Summary and concluding remarks
While it is necessary to assume an antifraud rule as one of critical factors, the predictionof full disclosure seems to be correct as the basic model suggests. Sellers (i.e., managers inaccounting context) were not indifferent between disclosures of the worst news and nondisclosures of those, but they generally moved to disclose their private informations
completely. Unlike prior researches, in the setting of this experiment, the number ofpossible states (i.e., commodity’s values or liquidating dividends) had little influence on the
results. The causes for this divergence between the results from prior researches and theexperimental result in this paper remain unresolved. The reason why the theoreticalprediction was generally supported is mainly due to the existence of the buyers (i.e.,
investors), who were able to appreciate at earlier period that the commodity’s value(liquidating dividend) was lowest when a seller (a manager) made no disclosure. I can say,such buyers urged sellers to make full disclosures.
In the cells without an antifraud rule, overdisclosures, that are the case where a seller (amanager) informs the commodity’s value (liquidating dividend) beyond its realization,
occurred in general. Furthermore, such tendency become outstanding as the number of５２

possible states increased. On the contrary, underdisclosures were of rare occurrence(particularly in the cell ④), and this is fairly different from King (1996), which reports thatsellers under-reported 11 percent of the time in his NC sessions.
While buyers (investors) valued the commodity (liquidating dividend) and bid based on
only seller’s (manager’s) disclosure in the cells with an antifraud rule, the buyers(investors) discounted fairly the value disclosed by the sellers (managers) in the cells
without it, though it was not as perfect as predicted. Though the buyers (investors), in
average, did not suffer trading losses, but there were obviously more periods of losses in thecells without an antifraud rule than in the cells with it.
These are main results in this paper. The attempt to find some linkage between theseexperimental results and the naturally occurring markets can be severely limited atpresent. The reason is that the model tested in this experiment was too simple and a lot offactors in which will be necessary to apply to the real world were omitted and not virtuallyconsidered 54. Also, as pointed out repeatedly in the chapter 1 of Kagel and Roth (1995), notone single experiment but a series of experiments can only explain something more about
the real world. But, it is true that the results of this experiment suggest some possibility offurther sophisticated experiments on this realm that are motivated from the brand-new
modified models grounded on the real world. From now on, it is necessary to grasp the

５３

situation of real world (particularly, Japan), to comprehend the theoretical models entirely
and to increase their tractability as much as possible, in order to understand managers’
incentives to voluntary disclosure more precisely.
Like all of the other experimental researches, this experiment also continually have to bequestioned about, (1) whether I had given some bias to the subjects and led to somearbitrary result or not throughout all the phases of experiment, and (2) whether the design
was suitable for the experimental test of the basic model or not. Also, conducts ofexperiment taught me how difficult to bring out the subjects’ incentives to involve hardly(by responses to the post-experiment questionnaires and postures in the laboratory). The
design that the cash payment depends more directly on the quality of subject’s decision
making55, and producing the experimental task with more challenge seem to be strongly
requested. These all may suggest some modifications on the design of this experiment.

54 For further discussions of this issue, see King (1991, p.194).
55 On a parallel with the trade of lottery ticket in King (1991), if the setting is changed that theexperiment task of an investor is making some investment decision to one project, nature selects its
probability of success, and a manager is informed and decides to disclose this probability or not, thisproblem may be mitigated in some degree. However such a setting needs to be set up a new experimental
session, in which asks subjects their attitudes towards risk directly (that is, for example, ‘How much doyou invest a project which brings you in one return of ¥1,000 with probability 50 percent?’). Allowing
subjects transact plural commodities in each period may submit one of the solutions for this problem, suchas in Forsythe et al. (1989).

５４

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５８

―Figures―

Figure 1-1. The proportion of disclosures for Cell ①

100%
80%
60%

All 20 periods
The latter half

40%
20%
0%
25

50

75

100

125

150

175

Figure 1-2. The proportion of disclosures for Cell ②

100%
80%
60%

All 20 periods
The latter half

40%
20%
0%
25

55

85

115

59

145

175

Figure 2-1.Commodity's value vs. message (Cell ③)

14
12
10
Frequency

8
6
4
2
−

25 50 75 100
125 150

175
150
125
100 Message
75
50
25
175

Commodity's value

Figure 2-2. Commodity's value vs. Message (Cell ④)
175
145
115
Message
85
55
25
25

55

85
115
Commodity's value

60

145

175

Figure 3-1. Cells with an antifraud rule (Cell ① and ②)
175
y = 0.9672x - 3.6192
2
R = 0.955

150

y：Price

125
100
75
50
25
25

50

75

100
x：Message

125

150

175

Figure 3-2. Cells without an antifraud rule (Cell ③ and ④)
175
y = 0.4734x + 30.207
R2 = 0.4918

150
y：Price

125
100
75
50
25
25

50

75

100
x：Message

61

125

150

175