Discussion Paper No. 494

VOLUNTARY PARTICIPATION GAME EXPERIMENTS
WITH A NON-EXCLUDABLE PUBLIC GOOD:
IS SPITEFULNESSA SOURCE OF COOPERATION?

Tatsuyoshi Saijo
Takehiko Yamato
Konomu Yokotani
andTimothy N. Cason

January 2000

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

Voluntary Participation Game Experiments with a Non-Excludable Public Good:Is Spitefulness a Source of Cooperation?1

by

Tatsuyoshi Saijo*
Takehiko Yamato**
Konomu Yokotani***andTimothy N. Cason****May, 1997; Revised April, 1999

1 We thank Takenori Inoki, Hajime Miyazaki, Toru Mori, Mancur Olson, Mitsuo Suzuki, and participantsat the Fall 1996 Economic Science Association conference for their helpful comments and discussions.
This research was partially supported by the Zengin Foundation for the Studies on Economics andFinance, Grant in Aid for Scientific Research 08453001 of the Ministry of Education, Science and Culture
in Japan, and the Tokyo Center for Economic Research Grant.
* Institute of Social and Economic Research, Osaka University, Ibaraki, Osaka 567-0047, Japan, andCREST, Japan Science and Technology Corporation, 3-12-40 Hiroo, Shibuya, Tokyo 150-0012, Japan.
E-mail address: saijo@iser.osaka-u.ac.jp** Faculty of Economics, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan. E-mailaddress: yamato-takehiko@c.metro-u.ac.jp*** Research and Survey Department, The Government Housing Loan Corporation, 1-4-10 Koraku,
Bunkyo, Tokyo 112-8570, Japan. E-mail address: QZT03105@niftyserve.or.jp****Department of Economics, Krannert School of Management, Purdue University, West Lafayette, IN
47907-1310, USA. E-mail address: cason@mgmt.purdue.edu

Abstract

Economic theory predicts that it is impossible to have cooperation in finitely
repeated games such as a prisoners' dilemma game without communication. Yet
experimental results follow a contradicting pattern: for example, cooperation is generally
observed in public-goods experiments, at least in early rounds. This cooperation is often
interpreted as kindness or fairness. In an experiment on a voluntary participation gamewith a non-excludable public good that is a version of a Hawk-Dove game, we observedthat evolutionary stable strategies did not appear, but cooperation emerged through atransmutation from the Hawk-Dove game to a game where a dominant strategy outcome
is Pareto efficient. We found that this transmutation is not due to kindness, but tospitefulness among subjects.

Correspondent:
Tatsuyoshi Saijo
Institute of Social and Economic Research
Osaka University
Ibaraki, Osaka 567-0047
Japan
Phone 81-6 (country & area codes)
879-8582 (office)/878-2766 (fax)E-mail: saijo@iser.osaka-u.ac.jp

1. Introduction
Economic theory usually predicts that it is impossible to have cooperation in
finitely repeated games such as a prisoners' dilemma game without communication.2 Yetexperimental results follow a contradicting pattern: some cooperation is generally
observed in public-goods experiments, for example, particularly in early rounds (seeLedyard, 1995). This cooperation is often interpreted as kindness or fairness. Andreoni(1995) confirmed that it comes from kindness or altruism of subjects. Most previous
public goods experiments employ the voluntary contribution mechanism, in which eachsubject contributes some money to provide a public good so as to maximize her payoff orutility. A well-established theoretical result is that the Nash equilibrium outcomes of thevoluntary contribution mechanism are not Pareto efficient.
Another line of experimental research in public goods is to investigate
performance of mechanisms achieving Pareto efficient outcomes such as the GrovesLedyard mechanism (1977). As Chen and Plott (1993) showed, the Groves-Ledyard
mechanism works very well under some suitable punishment parameters.
Recently, Saijo and Yamato (1997, 1999) shed a new light on the meaning ofvoluntary participation in public goods provision mechanisms. Agents may have a choice
not to participate in the mechanism proposed and hence some of them can free-ride on thebenefit from a public good provided by others. In other words, most of the mechanisms
designed so far -- including the voluntary contribution mechanism -- implicitly ignore
non-excludability, which is one of the important features of a public good. Instead,designers assume that all agents must participate in the mechanism. Saijo and Yamato

2

Many theorists have been trying to explain cooperation with finitely repeated games. A basic idea is tointroduce some irrationality with or without complete information. See Radner (1980), Kreps, Milgrom andWilson (1982), Benoit and Krishna (1985), and Conlon (1996).

1

(1997) proved an impossibility theorem demonstrating that no mechanism satisfying
voluntary participation exists in very reasonable environments.3
This participation problem is important in many practical circumstances, such as
for international treaties. For example, it took 24 years to reach agreement on thedisposition of chemical weapons in the chemical weapons treaty, and the number ofsignatories was more than 160 by the end of 1995. The treaty is a mechanism creating apublic good, i.e., a greater likelihood of world peace. The treaty requires that at least 65
signatories must ratify it in order to make it effective. In October 1996, Hungary was the65th country to ratify it, and the treaty was effective after a half year. However, China
and Russia have the most chemical weapons have not ratified this treaty. This could limit
the treaty's effectiveness. Another example is the League of Nations. Following WorldWar I President Woodrow Wilson strongly supported the League, but the U.S. Congress
never ratified the Treaty of Versailles. Another more contemporary example is the Kyoto
Protocol on climate change in 1997 to reduce greenhouse gas emissions. A large numberof countries appear unwilling to participate in the provision of this obviously nonexcludable public good.
Voluntary public goods provision by individuals -- such as for public broadcasting-- also faces this participation problem. For example, part of public broadcasting in Japanis supported by the public broadcasting fee. Every family must pay the fee by law, butmany choose not to since enforcement is practically non-existent. A natural question to
ask is what would happen if we allow voluntary participation in the voluntary
contribution mechanism.
We conducted an experiment to study the voluntary contribution mechanism withvoluntary participation in a two-stage game. In the first stage, two subjects choose3

See also Dixit and Olson (1997) for the voluntary participation problem in the context of the Coase theorem.

2

simultaneously whether or not they participate in the voluntary contribution mechanism.
In the second stage, knowing the other subject's participation decision, subjects who
selected participation in the first stage choose contributions to the public good. Subjects
receive payoffs based on a Cobb-Douglas transformation of their consumption of the
public good and their private good. The normal form game representation of the firststage participation decision is a Hawk-Dove game rather than the Prisoners’ Dilemma
game that represents the typical voluntary contributions mechanism with mandatory
participation. As usual, this Hawk-Dove game has two pure strategy Nash equilibria andone mixed strategy Nash equilibrium which is the unique evolutionarily stable strategy(ESS) equilibrium.
We conducted two treatments. Both subjects were required to participate in thevoluntary contribution mechanism in the control Treatment A. Each subject could choose
her participation decision before her contribution decision in Treatment B. Thus,
Treatment A only included the second stage, while Treatment B included both stages.
Each treatment had twenty subjects and each subject was randomly paired with eachother subject one at a time – a so-called “strangers” design. The same game was repeated
19 rounds, 4 for practice and 15 for monetary reward, so as not to pair the same two
subjects more than once.
In Treatment A, subjects on average contributed (or "invested") close to the Nashequilibrium level, although some subjects exhibited spiteful behavior. A spiteful subject
explicitly stated on her record sheet that she chose an investment number less than the
Nash equilibrium investment so as to reduce her opponent's payoff more than her own
payoff reduction.4

4 Saijo and Nakamura (1995) observed spiteful behavior in a traditional voluntary contribution mechanism

experiment. See also Ito, Saijo, and Une (1995). Spiteful behavior is also observed in biology. Iwasa,

3

In Treatment B, the participation rate rose as rounds advanced, and the average
investment in the final rounds in Treatment B was very close to that in Treatment A.
Consequently, in the final two-thirds of Treatment B, subjects' participation rate nearly
always exceeded the ESS participation rate. A typical subject behaved as follows: at the
beginning she did not participate in the mechanism, expecting high payoff with freeriding. However, her opponent who decided to participate in the mechanism did notinvest the number that maximized his own payoff. Rather, he invested a smaller amountso as to reduce his opponent's payoff more than his own payoff reduction. The nonparticipating subject thus learned that non-participation was not beneficial to her andhence she began regularly participating in the mechanism. That is, it seemed that thesource of cooperation was not altruism or kindness but was a payoff-maximizing responseto the spiteful behavior of other subjects. What we call cooperation here means that bothsubjects participate in the mechanism.
The remainder of the paper is organized as follows. In Section 2 we explain thevoluntary contribution mechanisms with and without voluntary participation. Section 3
describes the experimental design. We present the results on the experiment of thevoluntary contribution mechanism without voluntary participation in Section 4 and thoseon the experiment of the voluntary contribution mechanism with voluntary participationin Section 5. Section 6 concludes.

2. The Voluntary Contribution Mechanism
We employ the voluntary contribution mechanism with or without voluntary
participation as our model.

Nakamaru, and Levin (1998) set up a model explaining spiteful behavior of colicin-producing bacteria against
colicin-sensitive bacteria.

4There are two subjects, a and b, and subject i (=a,b) has wi units of initialendowment of a private good. Each subject faces a decision of splitting wi between her
own consumption of the private good ( x i ) and investment ( y i ). From the investment,each subject receives y = y a + y b + wy , where wy is the initial level of the pubic good.
That is, the level of the public good is the sum of the investments of two subjects and theinitial level of the public good. Therefore, each subject's decision problem ismax u i ( x i , y ) subject to x i + y i = wi ,where ui (x i , y ) is subject i's payoff function. We use a Cobb-Douglas type payoff function
to transform contributions and the private good into subject payoffs, and all subjects havethe same payoff function. That is, ui ( xi , y ) = xiα y1−α , where α ∈( 0 ,1). Using a monotonic
transformation, we specify the payoff function as follows:(1)

ui (x i , y ) ={ x iα y 1 −α }β+ 500 .
50

In our experiment we set ( wa , wb , wy ) = (24 ,24 ,3) , α = 0 .47 , and β = 4 .45 . With theseparameters the Nash equilibrium investment pair of the voluntary contribution
mechanism is ( y a , yb ) = ( 7 .69 , 7 .69 ) and the payoff is ui ( xi , y ) = 7089 , wherex i = 24 − 7 .69 = 16.31 and y = y a + y b + w y = 18.38 . The Pareto efficient level of the public

good is determined uniquely by the Samuelson condition and the feasibility condition. Its
symmetric contribution level is 12.02. Therefore, the Pareto efficient level of the public
good is 27.04=12.02+12.02+3. Clearly, the level of the public good with the voluntary
contribution mechanism is less than the Pareto efficient level of the public good.

5

So far we have assumed implicitly that subjects must participate in the voluntary
contribution mechanism. Saijo and Yamato (1997) found that there is a wide class of
mechanisms with public goods where subjects have incentives not to participate. The
voluntary contribution mechanism is one of them. That is, the voluntary contribution
mechanism is not voluntary from the viewpoint of participation incentives.
Consider now a two-stage game (see Figure 1). In the first stage, each subject
simultaneously decides whether or not she should participate in the voluntary
contribution mechanism without knowing the other subject's decision. In the second
stage, each subject decides how many units of her initial endowment she should invest
after knowing the other subject's participation decision.
-------------------------------Figure 1 is around here-------------------------------Notice that non-participation is different from zero investment with participation.
Once subject a decides to participate in the mechanism, subject b must take account of thisfact when she chooses her investment number without knowing subject a's investment
number. On the other hand, if subject a chooses non-participation, then subject b knowsthat subject a invests nothing.
In our experiment, subjects choose integer investment numbers only. If bothsubjects decide to participate in the mechanism, then the Nash equilibrium of thatsubgame is for each subject to contribute 8 and obtain a payoff of 7345. No other Nashequilibria sneak into our model due to the discrete strategy choice set. If one subject
participates in the mechanism and the other does not, then the participant maximizes her
payoff at y i = 11 and obtains a payoff of 2658, and the non-participant clearly invests
nothing and obtains a payoff of 8278. If both choose not to participate in the mechanism,

6both subjects end up with a payoff of 706. These payoffs are summarized in the normal
form game payoff table shown in Table 1.
-------------------------------Table 1 is around here-------------------------------The game in Table 1 is a well-known Hawk-Dove game. Although the usual
simplification of the public good problem is a Prisoners' Dilemma game, we find that theproper simplification is a Hawk-Dove game when we allow participation in themechanism as a choice variable. There are two pure strategy Nash equilibria: either one ofsubjects participates in the mechanism. One more Nash equilibrium is a mixed strategy
equilibrium: each subject i chooses 0.68 as her participation probability p i . Among thesethree equilibria, the mixed strategy equilibrium is a unique ESS equilibrium.5

3. Experimental Design
Our experiment consisted of three treatments, A, B, and B’. Treatment A
corresponded to the voluntary contribution mechanism without voluntary participation
and Treatments B and B’ corresponded to the voluntary contribution mechanism withvoluntary participation. We will explain the difference between Treatment B and
Treatment B’ below.
We conducted one session in Treatment A and one session in Treatment B at the
University of Tsukuba during December of 1995, and one session in Treatment B and one
session in Treatment B’ at the Tokyo Metropolitan University during December of 1997.
We recruited twenty students for each session by campus-wide advertisement. Thesestudents were told that there would be an opportunity to earn money in a research

5 See Maynard Smith (1982).

7

experiment. None of them had prior experience in a public good provision experiment.
No subject attended in more than one session. The Treatment A session required
approximately 90 minutes and the Treatment B and B’ sessions required approximately
two hours to complete. The mean payoff per subject was $26.31 ($1=100 yen). The
maximum payoff among the eighty subjects was $36.25, and the minimum payoff was$17.28.
Let us describe Treatment A first. Twenty subjects seated at desks in a relatively
large room had identification numbers between one to twenty randomly. These
identification numbers were not publicly displayed, however, so subjects could not
determine who had which number. We made ten pairs out of twenty subjects. In eachround, ten pairs played the game without the participation decision as described in theprevious section. The pairings were determined in advance by experimenters so as not topair the same two subjects more than once. The first four rounds were for practice and theremaining fifteen determined the subjects' monetary payoffs. Each subject received anexperimental procedure sheet, a record sheet, payoff tables, 15 investment sheets, and 4
practice investment sheets.6 Instructions were given by tape recorder to minimize theinteraction between subjects and experimenters. Each subject determined her investment
from an integer number between 0 and 24 by using payoff tables and then marked anumber on an investment sheet. Experimenters collected these investment sheets andthen redistributed them to the paired subjects. During the redistribution, subjects wereasked to fill out the reasons why they chose these numbers. After the redistribution,subjects calculated their payoffs from the payoff tables. Then the next round started.

6 The use of practice periods permits subjects to send signals costlessly prior to the paid rounds.

However,subjects interacted with each other in only one period and there was no public information after the
instructions were completed and data collection began. Therefore, the impact of these signals is somewhat
limited. Nevertheless, see footnote 14 for some minor evidence of spillover from the practice periods.

8Treatment B had one additional step. Before choosing investment numbers,
subjects decided whether or not they would participate in the voluntary contribution
mechanism. These decisions were collected by experimenters and then redistributed totheir paired subjects. After this procedure, subjects who decided to participate in themechanism chose their investment numbers.
Treatment B’ is exactly the same as Treatment B except what term was used todescribe the person that each subject is matched with at each period. The term "youropponent" was employed in the instructions, record sheets and payoff tables for bothTreatment A and Treatment B. The phrase "the person you are paired with" replaced"your opponent" in all materials of Treatment B’. One might say that the term “opponent”
forces subjects to think in relative terms. However, there was no essential difference
between the results for Treatment B and those for Treatment B’, as we document below.
Every subject had the same payoff function and every subject knew this fact. We
distributed three kinds of payoff tables to avoid any possible misunderstanding. The
payoff tables used in Treatments A and B are Tables 2, 3, and 4. Table 2 is a detailed
payoff table: the rows are for the subject's own investment numbers and the columns arefor the other subject's investment numbers. Table 3 is a rough payoff table and Table 4 has
an iso-payoff map. The payoff tables distributed in Treatment B’ are the same as Tables 2,
3, and 4 except that the term "your opponent" is replaced by the term "the person you arepaired with".
We allowed subjects three minutes to examine the three payoff tables before thepractice rounds and ten minutes to examine the three new payoff tables before the realrounds. The tables used for practice and real rounds were different.
--------------------------------------------Tables 2, 3 and 4 are around here---------------------------------------------

9

We declared that the experiment would be stopped if communication among the
subjects was observed. This never happened.

4. Experimental Results for Treatment A
Treatment A was a control treatment intended to permit a comparison between
mandatory participation and voluntary participation.
The Nash equilibrium investment pair was (8, 8) from Table 2, and no other Nashequilibrium exists. Since each round had 10 pairs and 15 rounds were conducted, we have
150 pairs of data. The order of investment numbers does not matter, so we rearranged
each pair (x,y) with x ≥ y . Figure 2 shows the frequency distribution of investment data.
The maximum frequency pair was (8, 8) with 36 pairs, the second was (8, 7) with 35 pairs,
the third was (8,6) with 14 pairs, and the fourth was (7, 7) with 11 pairs. The average
investment across all subjects was 7.24.
-------------------------------Figure 2 is around here-------------------------------Figure 3 shows the average investment pattern from round 1 to 15. The average
investment was less than the Nash equilibrium level of investment (8) in all but one round.
In order to understand why this happened, we checked the record sheets andquestionnaire sheets of subjects. The record sheet was not only for keeping theinvestment record but also for specifying the reasons why a subject chose her investment
numbers. We found four subjects who explicitly stated the following reasoning: they
estimated that their opponent would chose 8, and then they chose 6 or 7 explicitly because
this would make their opponent's payoff much lower than their own payoff. For example,

10

consider the case that subject a chooses 7 and subject b chooses 8. Then subject a obtains
7340, and subject b obtains 6526. At the Nash equilibrium (8, 8), both subjects obtain 7345.
From the viewpoint of subject a, the reduction of 5 units of payoff is minor, but subject a
can make the reduction of subject b's payoff (819) much greater than his own reduction.7, 8
We label these subjects as spiteful subjects, and Figure 3 also presents mean investments
after excluding those subjects.
-------------------------------Figure 3 is around here-------------------------------We tested the hypothesis that mean investment equals the Nash equilibrium
investment (8) first by pooling investments across rounds. Because each subject made 15
investment choices the data are clearly not independent. Therefore, we accounted for thepanel nature of the data using a random effects error specification vit = ei + ε it, where ei is asubject-specific error term and ε it is an iid error. The pooled data strongly reject the Nashequilibrium (t=3.28), and also reject the Nash equilibrium when spiteful subjects are
excluded (t=4.45) and when spiteful subjects and their opponents' data are excluded(t=3.75). We then focused on round by round tests of the Nash equilibrium. Without
excluding any data, a nonparametric Wilcoxon signed rank test rejects the Nashequilibrium hypothesis in ten out of fifteen rounds at the five percent significance level.
Excluding spiteful subjects' data, this test rejects the Nash equilibrium hypothesis in fiveout of fifteen rounds. Finally, excluding spiteful subjects' and their opponents' data, thistest rejects the Nash equilibrium hypothesis in four out of fifteen rounds. Nevertheless,
7 Akerlof and Yellen (1985a, 1985b) observed similar phenomena in Keynesian business cycles and industrialorganization theory. A small amount of nonmaximizing behavior may cause some amount of changes atequilibrium that is larger in its magnitude than the losses due to nonmaximizing agents.
8Note that this spiteful (non-maximizing) behavior would not be observed in a usual two-by-two game. In
our experimental setting, subjects can choose a slight deviation from an optimal investment strategy. That is,
the two-by-two game approach is not rich enough to capture economic implications in public goods
environments.

11the fact that many subjects chose the Nash equilibrium investment indicates that at least
economically the Nash equilibrium has attracting power for the data.9

These Treatment A results lead to the following observation.
Observation 1:
The mean investment across all rounds is significantly less than the Nash equilibrium
investment, regardless of whether spiteful subjects' data are excluded. Overall, mean investments
were approximately ten percent below the Nash equilibrium.

5. Experimental Results for Treatments B and B’
The session in Treatment B conducted at the University of Tsukuba, the session in
Treatment B at the Tokyo Metropolitan University, and the session in Treatment B’ at theTokyo Metropolitan University are called the Tsukuba B session, Tokyo B session, andTokyo B' session, respectively. As shown in the appendix, the data from these three
sessions are statistically indistinguishable in virtually all cases. This provides strong
evidence that neither the experiment site (Tokyo versus Tsukuba) nor the experimentwording (“your opponent” versus “the person you are paired with”) affect choices.
Therefore, in the subsequent analysis we pool the data across the three Treatment B
sessions, i.e., Tsukuba B, Tokyo B, and Tokyo B' sessions.

5.1 Investment Data

9 This result is similar to Andreoni (1993) and Chan et al. (1998), who study the crowding out hypothesis in

public good experiments with an interior Nash equilibrium and minimum contribution “taxes” in sometreatments. In both of these previous experiments contributions were close to but slightly below the Nashequilibrium prediction when no tax was imposed.

12Figure 4 shows that the distribution of investment pairs in Treatment B are very
different from that of Treatment A (Figure 2). The maximum frequency pair was (8,7)
with 57 pairs, the second was (11,0) with 44 pairs, followed by (8,8) and (0,0) with 37 pairseach.
-------------------------------Figure 4 is around here-------------------------------Also unlike Treatment A, the average investment (including the investments ofzero by nonparticipants) changed across rounds in Treatment B. Figure 5 illustrates thatthe average investment in Treatment B was clearly less than in Treatment A, but the
average investment in Treatment B ascended across rounds. In the late rounds theaverage investments in the two Treatments were very similar; for example, in the final
round the average investments in Treatments A and B were 7.0 and 6.47 respectively. The
average investments were not significantly different by round between Treatments A and
B after round 4, according to the nonparametric two-sample Wilcoxon rank sum test.
-------------------------------Figure 5 is around here-------------------------------Using a random-effects panel data model that is the same as that for Treatment A,
we tested the hypothesis that mean investment equals the Nash equilibrium investment(8) in the case of both participating. The mean investment in this case was too low (7.26),
and we rejected the hypothesis (t=4.21).10 However, like the result for Treatment A, a
substantial number of subjects selected the Nash equilibrium, so the Nash equilibrium ismeaningful at least economically in the case of both participating.
10

For those who prefer nonparametric tests, we also conducted Wilcoxon signed rank tests separately for eachof the 15 periods. This test rejects the null hypothesis that average investment equals 8 at the five percent levelin 12 of the 15 periods.

13

5.2 Participation Data
We next examined whether the participation data in Treatment B were compatible
with the mixed strategy equilibrium of the Hawk-Dove game described in Table 1. The
null hypothesis is the ESS participation probability of 0.68. We first conducted a binomial
test separately by round in order to avoid pooling dependent participation decisions madeby the same subject in the same test. Under the ESS null hypothesis, the probability ofobserving 10 non-participation decisions or less out of 60 is less than one percent, and theprobability of observing 12 non-participation decisions or less out of 60 is less than five
percent. As Figure 6 shows, the participation rate rose as rounds advanced (although abrief decline was observed in rounds 8 and 9). The smooth curve is a simple log-linear
regression. More to the point for this binomial test, the low non-participation rate permits
the binomial test to reject the ESS null hypothesis in 9 rounds of the 15 total rounds (inrounds 5, 6, 7, 10, 11, 12, 13, 14, and 15) at the five percent (usually one percent)significance level.
-------------------------------Figure 6 is around here-------------------------------We also examined the overall participation rates for each of 60 subjects separately.
The mean participation rate was 80% (12 of 15 decisions), and the median participation
rate was 86.7% (13 of 15 decisions). Note that the ESS rate of 0.68 implies on averageslightly more than 10 participation decisions. Only 14 of the 60 subjects (23.3%)
participated 10 times or less, while the other 46 subjects (76.6%) participated 11 times ormore. 15 of the 60 subjects (25%) were apparently using a pure strategy, as they
participated in 15 out of 15 periods. Using the 60 separate subject observations, the data14

reject the ESS prediction of 0.68 at better than the 0.0001 significance level using the nonparametric Wilcoxon signed-rank test.
Furthermore, we conducted a binomial test of the mixed strategy of p = 0.68
separately for each subject. Under the null hypothesis that subjects play this mixed
strategy, participation decisions--even for an individual subject--are statisticallyindependent. At the five percent significance threshold, 23 of 60 subjects (38.3%)
participated too much (either 14 or 15 times), rejecting p = 0.68; 6 of 60 subjects (10%)
participated too little (7 times or less), rejecting p = 0.68 in the other direction. At the ten
percent significance threshold, 32 of 60 subjects (53.3%) participated too much (13, 14 or 15
times), rejecting p = 0.68; 9 of 60 subjects (15%) participated too little (8 times or less),
rejecting p = 0.68 in the other direction.

5.3 Why were Participation Ratios High?
In order to understand these rather high participation ratios, consider the case inwhich only one subject in a pair participated in the voluntary contribution mechanism.
When a subject did not participate in the mechanism, the other could obtain her
maximum units of payoff by investing 11 (see Table 2). There were 139 observations withexactly one participant. In these cases the participant invested eleven 43 times, invested
less than eleven 95 times (zero 17 times, invested one 3 times, invested two 7 times,
invested three 8 times, invested four 7 times, invested five 1 times, invested six 16 times,
invested seven 19 times, invested eight 9 times, invested nine 6 times, and invested ten 2times), and invested more than eleven (twenty-four) only 1 time. In fact, the mean
investment (6.90) was lower than when both subjects participated! Using a random effects

15

model, we soundly reject the hypothesis that mean investment equals 11 in the case of one
participant (t=8.14).11
As shown in Table 2, by investing 11 in response to the other not participating, thenon-participating subject earns 8278 while the participating subject earns 2658. On theother hand, by investing 7 in this situation, the non-participating subject earns 4018 while
the participating subject earns 2210. That is, the reduction of the participant's payoff(448=2658-2210) was relatively small, while the reduction of the non-participant's payoff(4269=8278-4018) was relatively large. This appears to be stronger evidence of spitefullike behavior than we observed in Treatment A. The “spite rate”, which is the ratio of thenumber of participants investing less than 11 to the number of observations with a single
participant, is equal to 95/139 = 68%.
One might say that in the two-stage game of Treatment B, the low investment by
the single participant could be interpreted as belonging to a tit-for-tat strategy to “teach”
others to cooperate. Because subjects were re-paired with a new opponent each period
and never interacted with the same subject in more than one period, however, such a
strategy is not subgame perfect. Furthermore, although there is no need to take a tit-for-tat
strategy at the final period of the experiment, the spite rate of the final period is equal to
6/9 = 67 percent.12
Our interpretation that this behavior is spiteful hinges on the low contributions
made by subjects when they are the only participant. An alternative interpretation ofaltruism is also consistent with our finding that the participation rate exceeds the ESS
prediction; altruistic subjects should always participate. Altruists, however, should also
11

The nonparametric Wilcoxon test rejects the null hypothesis that average investment equals 11 at the five
percent level in 9 of the 15 periods, even though the average sample size per period is only about 9 because of
the high participation rate.
12 The full distribution of the 9 final period observations with exactly one participant is as follows: one
participant invested two, one participant invested seven, three participants invested eight, one participant
invested nine, and three participants invested eleven.

16

invest as least as much as the level that maximizes their own earnings—which is 11 in thecase of a single participant—if not more, since the non-participant’s earnings strictlyincrease in the participant’s investment (see Table 2). Therefore, choices below 11 areinconsistent with pure altruism. These choices could, however, be consistent with notionsof “inequality aversion” or reciprocal altruism advanced recently by some researchers (forexample, see Fehr and Schmidt (1999) and Levine (1998)). What we refer to as spite in thiscontext is a response to the nonparticipation of one’s opponent, so it is a form of (negative)
reciprocity.13-------------------------------Figure 7 is around here-------------------------------Figure 7 shows average payoffs by round depending on participation.
Curve α denotes the average payoffs when both subjects participated in the mechanism.
As Table 1 shows, the payoff should be 7345 according to the Nash equilibrium prediction,
but actual data showed that average payoffs were less than 7000 units in all 15 rounds.
Curve β denotes the average payoffs when only the other participated in the mechanism.
According to the Nash equilibrium, this should lead to 8278 units of payoff, but actual
payoffs were less than 6000 in 12 of 15 rounds. According to Table 1, curve β should beabove curve α, but Figure 9 shows that curve α was above curve β in all but round 9. Thatis, participation became a dominant strategy even in early rounds, as illustrated in Table 5.

-------------------------------13

This is different from simple rivalistic behavior in which a subject seeks merely to earn more than his
opponent earns. The data are inconsistent with such rivalistic motivations, because such motivations are more
likely to lead to less participation than the ESS prediction since nonparticipation guarantees payoffs greaterthan or equal to those of the opponent. It is also unlikely that rivalistic choices would be so close to the Nashequilibrium when both subjects participate because rivalistic subjects have a strong incentive to reduce their
public good investment.

17

Table 5 is around here-------------------------------Our interpretation of this conversion to the dominant strategy game is based on
subject learning and proceeds roughly as follows. After inspection of the payoff tables,some subjects initially do not participate in the mechanism hoping the other will
participate and invest 11. They therefore expect (perhaps with the ESS probability of 0.68)
to receive a payoff of 8278. However, since their participating opponent invested less than11, the subject realized that her earnings in this subgame fell below 6000 on average. Afterlearning this, she chose to participate in the mechanism in later rounds and frequently
earned more than 6000.14

5.4 Learning Processes for Participation
Essentially, subjects learn (contrary to the ESS equilibrium) that expected profits
from participation tend to exceed those from non-participation. In this final subsection we
provide a simple model of this learning process. Many alternative approaches to learning
have been advanced recently in the literature, including reinforcement learning (e.g., Erev
and Roth, 1998), belief-based learning, and creative hybrid approaches (e.g., Camerer andHo, 1999). Rather than provide an exhaustive evaluation of the various learning models

14 As Figure 9 in the appendix shows, the average participation rates at early rounds in the Tokyo B session

were relatively high. To see why this happened, we looked at the record sheets for the four practice periods,
since the experiences of subjects in the practice periods might affect their participation decisions in the actual
experiment. We found that spiteful behavior during the practice periods would lead to high participation
rates in early periods. First of all, we counted the number of subjects who explicitly wrote that they realizedthat non-participation was not beneficial because the participant would act spitefully in the practice periods.
This number in the Tokyo B session (8) was much larger than both that in the Tokyo B’ session (1) and that in
the Tsukuba B session (1). We also calculated the number of subjects who had no chance to experience spiteful
behavior in the practice periods. Consider a subject who experienced the following: (a) no cases in which only
one subject participated, or (b) if only one subject participated (either himself or his opponent), the payoffmaximizing (non-spiteful) investment was selected. Call such a subject a "spite-free" subject. The number ofspite-free subjects in the Tokyo B session was 5, the number in the Tokyo B' session was 8, and at the numberin the Tsukuba B session was 11. As the number of spite-free subjects was larger, the participation rate atperiod 1 was smaller.

18

using our data, we simply report results of an adaptive, reinforcement-based learningmodel. In particular, we estimate a probit model in which the probability of participation
depends on the ratio of expected participation earnings (EPE) to expected nonparticipation earnings (ENE):(2)

Probability(Participation) = f(EPE/ENE)

The next step is to specify the process underlying subjects' expectations. We use
two polar cases for this simple model: (1) Cournot (or myopic) expectations and (2)Fictitious Play expectations (e.g., Cheung and Friedman, 1997; Cox and Walker, 1998).
According to Cournot, EPE are simply the realized earnings the last time thesubject participated; and ENE are simply the realized earnings the last time the subject did
not participate. In other words, subjects maintain a very short (myopic) memory length-of one observation for each (participate or not) decision. By contrast, according to
Fictitious Play, subjects have a long memory, and each observation updates the
expectation with a declining weight. For example, if a subject has participated N times up
to this round, and they participated in this round, they update EPE as follows:(3)

EPE=((N*previous EPE)+current participation earnings)/(N+1).

In other words, as subjects accumulate evidence they simply include it in their runningaverage of the payoffs from participation for EPE. ENE is, of course, analogous.15

15 For both Cournot and Fictitious Play, we need the expectations to start somewhere when no evidence has
yet accumulated. For these initial expectations we employ the ESS expected payoffs, which are 5829 for both
EPE and ENE. Therefore, the EPE/ENE ratio is 1 in round 1.

19

The empirical model is probit maximum likelihood, with a random subject effect.
Table 6 presents the estimation results separately and pooled for the three Treatment B
sessions. For Fictitious Play, the expected payoff ratio is insignificantly different fromzero except in the Tokyo B session, where the coefficient estimate has the wrong sign. For
the Cournot specification, the ratio is significantly positive except in the Tokyo B session.
The positive coefficient on the ratio implies that as the relative profitability ofparticipation increases, the likelihood of participation increases. So, we can conclude that(1) subjects' participation decisions respond to their experience, and (2) subjects appear to
update their expectations in this environment using a short (Cournot) memory length.
-------------------------------Table 6 is around here--------------------------------

Summarizing the above observations, we have the following.
Observation 2:(a)The ESS prediction regarding the participation ratio is rejected.
(b) The participation ratio rises as rounds advanced and the average investment in the final twothirds of Treatment B is not significantly different from that in Treatment A.
(c) It seems that the source of cooperation is not altruism or kindness but is spiteful behavior of
subjects. Subjects learn that non-participation will invoke a spiteful response, which reduces thepayoff of non-participation below the payoff of participation. This converts participation into adominant strategy.

6. Concluding Remarks
We found that the ESS prediction in a Hawk-Dove game was rejected and somecooperation among subjects emerged across time. Furthermore, this cooperation did not20

come from altruism or kindness among subjects, but from an optimal response to othersubjects' spiteful behavior. Acting spitefully in this way is costly, and this kind of spitefulor negative reciprocal behavior has also been observed recently by independent researchon public goods (Fehr and Gachter, 1998) and in the ultimatum game (Ochs and Roth,1989 and Prasnikar and Roth, 1992).
In neo-classical economic theory, it is assumed that each agent cares only about
himself and maximizes his own payoff subject to some constraints. If people care about
how they are doing relative to others (for example, see Hume, 1739),16 however, then it isnatural to think that they might often take spiteful actions in an attempt to decrease thehappiness of others. One would think that such spiteful behavior might result in outcomesthat are socially inferior to outcomes arising from the interaction of purely selfish
individuals. We find that the opposite may occur: spitefulness leads to greater cooperation.
This finding suggests a need to rethink our fundamental assumptions of human nature
underlying our models.
In our experiment, each subject knew that every subject had the same payoff table.
This might trigger spiteful behavior since every subject could understand opponent's
payoff structure. In future experiments we plan to conduct a systematic exploration ofthis information effect. It is also possible that spiteful behavior is more likely in twoperson games such as this because it encourages relative payoff comparison. Future
experiments can test this conjecture using larger groups. We also leave for future researcha comparison of American subjects to these Japanese subjects in the present environment.
If the propensity for spiteful behavior differs across cultures, outcomes could be
16“Now as we seldom judge of objects from their intrinsic value, but form our notions of them from acomparison with other objects; it follows, that according as we observe a greater or less share of happiness ormisery in others, we must make an estimate of our own, and feel a consequent pain or pleasure. The misery of
another gives us a more lively idea of our happiness, and his happiness of our misery. The former, therefore,
produces delight; and the latter uneasiness.” (David Hume, 1739)

21

substantially different for these two subject pools. Finally, the ESS participation rate in thepresent experiment was 0.68. We are currently conducting experiments in which the ratio
is less than 0.5.

22

APPENDIX: Comparisons of Tsukuba B, Tokyo B, and Tokyo B’ Sessions
First of all, we compare investments conditional on participation across the three B
and B’ sessions. Figure 8 illustrates how the average investment conditional onparticipation, which equals the sum of investment numbers for participants divided by
the number of participants, changed from round 1 to 15 for each of the three B and B’sessions. The average investments conditional on participation were different in only ahandful of periods according to the nonparametric Wilcoxon rank sum test. In 14 of the 15
periods there is no statistical difference between the Tokyo B and Tokyo B’ sessions at thefive percent significance level, which indicates that the “opponent” wording did not affectinvestments conditional on participation.17 Likewise, the Tokyo B and Tsukuba B sessions
are not statistically different in 12 of the 15 periods, indicating that investments
conditional on participation differed very little across sites.18-------------------------------Figure 8 is around here-------------------------------Figure 9 illustrates the average participation rate patterns from round 1 to 15 inTsukuba B session, Tokyo B session, and Tokyo B’ session. There are some statisticallysignificant differences in the participation rates between the Tsukuba B and Tokyo B

17 In period 8 the average investment in the Tokyo B’ session was significantly higher than in the Tokyo B

session.
18 The average investment was significantly higher in the Tsukuba B session in periods 1, 9 and 13.

23

sessions in periods 1 and 2.19 After period 2, there are basically no systematic differencesamong the participation rates across sessions.20-------------------------------Figure 9 is around here-------------------------------Overall, we conclude that there are virtually no statistically significant differencesin the data based on the experiment site or the experiment wording.

19 Fisher’s exact test p-values for the Tokyo B versus Tsukuba B comparison are 0.022 in period 1 and 0.020 inperiod 2. We discuss the reasons for these differences in footnote 12. Fisher’s exact test uses thehypergeometric probability distribution to calculate the exact probability of observing the distribution ofparticipation rates (and those more unequally distributed) under the null hypothesis of no differences in rates
across treatments.
20 In period 5 the participation rate is significantly higher in the Tokyo B’ session than in the Tokyo B session,
but in period 10 the participation rate is significantly lower in the Tokyo B’ session than in the Tokyo B session.

24

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27

1Participate

2
Participate

1
8

0

2

24

Not
participate

Not
participate Participate

2

1
11

11

(2658,8278)(8278,2658)

8(7345,7345)
Figure 1. The game tree when subjects canchoose their participation in the voluntary
contribution mechanism.

Not
participate(706,706)

p2
Participate
Participate

p1

1 Not

participate

1 - p12

1 - p2

Not
participate

7345
8278
2658
7345
706
2658
8278
706

Nash equilbrium:( p1, p2 ) = (10),, ( 0,1),( 0.68,0.68)
Evolutionarily stable strategy, ESS:

pi = 0.68
Table 1. The payoff table becomes a Hawk-Dove game.

Your Investment Number
Your

Your
Opponent's
Investment
NumberPayoff

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

0

706

871

1072

1297

1536

1775

2003

2210

2386

2523

2615

2658

2648

2585

2470

2309

2106

1871

1614

1349

1091

858

669

543

500

1

905

1127

1379

1647

1919

2183

2427

2641

2816

2944

3019

3039

3001

2905

2755

2555

2313

2038

1743

1443

1154

894

685

548

500

2

1186

1465

1764

2072

2374

2658

2913

3129

3297

3411

3465

3456

3385

3252

3061

2819

2534

2217

1881

1543

1220

933

703

552

500

3

1554

1888

2232

2575

2902

3202

3463

3675

3831

3925

3952

3911

3801

3626

3391

3102

2770

2406

2027

1648

1290

973

721

556

500

4

2017

2401

2787

3160

3508

3817

4078

4281

4420

4488

4483

4403

4250

4028

3743

3404

3020

2608

2181

1759

1363

1015

740

561

500

5

2578

3010

3432

3831

4193

4507

4762

4950

5064

5101

5057

4934

4733

4459

4119

3725

3287

2821

2344

1877

1441

1060

760

566

500

6

3244

3718

4171

4590

4960

5272

5515

5681

5766

5765

5677

5504

5249

4918

4519

4065

3568

3045

2516

2000

1522

1106

781

571

500

7

4018

4529

5008

5440

5812

6115

6339

6478

6526

6481

6343

6114

5800

5406

4944

4425

3866

3282

2696

2129

1607

1155

802

576

500

8

4904

5447

5944

6383

6751

7038

7237

7340

7345

7250

7056

6765

6385

5924

5393

4806

4179

3532

2886

2265

1696

1206

825

582

500

9

5907

6475

6984

7422

7779

8043

8209

8271

8225

8073

7816

7458

7007

6472

5867

5207

4508

3793

3084

2407

1789

1259

849

588

500

10

7031

7616

8130

8561

8897

9132

9257

9270

9168

8951

8624

8193

7664

7051

6367

5628

4854

4067

3292

2555

1886

1315

874

594

500

11

8278

8873

9384

9800 10109 10306 10384 10339 10173

9886

9482

8970

8359

7661

6892

6070

5217

4354

3509

2710

1987

1372

899

600

500

12

9653 10250 10750 11142 11416 11567 11589 11480 11242 10877 10390

9791

9090

8302

7444

6534

5596

4654

3736

2871

2092

1432

926

606

500

13

11158 11749 12229 12589 12820 12916 12875 12694 12376 11925 11349 10656

9860

8976

8022

7019

5992

4967

3972

3039

2201

1494

953

613

500

14

12796 13372 13824 14144 14323 14356 14243 13982 13576 13033 12358 11565 10667

9681

8627

7526

6406

5292

4217

3213

2315

1559

982

620

500

15

14570 15123 15538 15808 15925 15888 15694 15344 14844 14199 13420 12520 11514 10419

9258

8055

6836

5631

4473

3394

2433

1626

1012

627

500

16

16484 17003 17372 17583 17630 17513 17229 16783 16179 15426 14535 13521 12399 11191

9918

8606

7285

5984

4738

3582

2555

1695

1042

635

500

17

18539 19016 19328 19471 19439 19232 18850 18299 17583 16714 15704 14568 13324 11995 10605

9180

7751

6350

5013

3777

2681

1767

1074

642

500

18

20739 21163 21409 21474 21353 21047 20559 19893 19057 18064 16926 15661 14290 12834 11320

9776

8235

6730

5298

3978

2812

1841

1107

650

500

19

23086 23447 23617 23594 23374 22960 22355 21566 20602 19476 18203 16803 15296 13706 12063 10395

8737

7123

5593

4187

2947

1917

1141

659

500

20

25583 25870 25954 25832 25504 24972 24241 23319 22218 20951 19536 17992 16342 14614 12835 11038

9257

7531

5899

4403

3087

1996

1176

667

500

21

28231 28433 28420 28190 27743 27083 26217 25154 23907 22491 20924 19230 17431 15556 13636 11704

9796

7953

6214

4625

3231

2078

1212

676

500

22

31034 31141 31020 30670 30094 29296 28285 27071 25669 24095 22370 20516 18561 16533 14465 12393 10354

8388

6540

4855

3380

2162

1249

685

500

23

33993 33993 33753 33273 32557 31611 30445 29071 27505 25764 23872 21852 19733 17546 15325 13106 10930

8838

6877

5092

3533

2248

1287

694

500

24

37111 36993 36622 36001 35135 34030 32699 31155 29416 27500 25432 23239 20949 18595 16214 13843 11525

9303

7224

5337

3691

2337

1326

703

500

Table 2. Detailed Payoff Table

Your Investment Number
Your
Payoff

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

0
1
2

1484

2446

3066

3246

2902

2127

1200

581

3245

4512

5057

4921

4109

2821

1460

609

5705

7036

7332

6749

5383

3536

1724

636

9122

10295

10154

8952

6883

4364

2024

667

13575

14338

13553

11545

8620

5310

2364

701

19132

19206

17555

14548

10603

6376

2743

739

25855

24939

22187

17973

12838

7567

3163

781

33800

31573

27472

21836

15336

8887

3626

827

3
4
5

Your
Opponent's
Investment
Number

6
7
8
9
10

11
12
13

14
15
16
17

18
19

20
21
22

23
24

Table 3. Rough Payoff Table

24

Your Investment Number
0

0

2

4

6

8

10

12

14

16

18

20

2
4
2000

6
4000

8

Your
Opponent's
Investment
Number

6000
8000

10
10000

12

12000

14

14000
16000

16
18

22000
24000

20

26000
28000

22
24

32000

34000
Table
4. Iso-Payoff Map
36000

Table 4. Iso-Payoff Map

22

24

40
35
30
25
20
15
10
5
0

16

14

12

Smaller
Investment

10

8

6

4

2

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

LargerInvestment

Figure 2. Investment Pattern in Treatment A

15

16

Frequency

8
7

Average Investment

6543Nash equilibrium
all data
data without spite

2
1
0
1

2

3

4

5

6

7

8

9

10

11

PeriodFigure 3. Average Investments in Treatment A.

12

13

14

15

60
50
40
30
20
10
0

14

12

Smaller
Investment

10

8

6

4

2

0 0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

LargerInvestment

Figure 4. Investment Pattern in the Three Treatment B Sessions.

Frequency

8.00

7.00

Average Investment

6.00

5.00

y = 0.5385Ln(x) + 4.7478
2
R = 0.4859

4.00

3.00
Treatment A with no participation decision

2.00

Treatment B with participation decisions (pooled)
Trend (Treatment with participation decisions)

1.00

0.00
1

2

3

4

5

6

7

8
Period910

Figure 5. Comparison of Average Investment Patterns:
Treatment A versus Treatment B.

11

12

13

14

15

1.00

0.90

(Number of Participants)/(Number of Subjects)

0.80

0.70

y = 0.0643Ln(x) + 0.6804
2
R = 0.479

0.60

0.50

0.40

0.30

0.20

0.10

0.00
1

2

3

4

5

6

7

8

9

PeriodFigure 6. Participation Rate Pattern.

10

11

12

13

14

15

Both participate.
I do not participate, but the other does.
I participate, but the other does not.
Neither participates.

8000
7000

a

Average Payoff

6000
5000

b

4000
3000
2000
1000
0
1

2

3

4

5

6

7

8

9

10

11

12

PeriodFigure 7. Average Payoffs by Participation Decision.

13

14

15

p2
Participate
Participate

1 Not

p1

participate

1 - p12

1 - p2

Not
participate

6570
4795
2049
6570
706
2049
4795
706

Table 5. The average values of payoff data up to round 5
for the three treatment B sessions.

Dependent Variable = 1 if Participate
0 if Not Participate
Probit Model with random subject effectVariable or Statistic
Expected Participation Earnings/
Expected Non-Participation Earnings
InterceptaRho

Number of Observations
Estimated Log-likelihood
Restricted (slopes=0) Log-likelihood

Model (1): Cournot Expectations
TsukubaTokyo
Tokyo
B and B’B
B
B’
Pooled
0.051*-0.0440.086**
0.028*(0.022)(0.043)(0.031)(0.015)0.618**
1.279**
1.126**
1.010**(0.187)(0.224)(0.241)(0.115)0.382*
0.339
0.447*
0.344**(0.165)(0.221)(0.191)(0.100)
300
300
300
900
-147.3-123.7-129.8-405.6-161.6-136.5-145.8-450.1Model (2): Fictitious Play Expectations
TsukubaTokyo
Tokyo
B and B’B
B
B’
Pooled-0.013-0.132*0.131-0.002(0.054)(0.064)(0.193)(0.025)0.915**
1.312**
0.935**
1.073**(0.211)(0.240)(0.222)(0.120)0.280*
0.371*
0.382*
0.333**(0.137)(0.176)(0.193)(0.094)
300
300
300
900
-149.0-122.7-130.0-406.7-161.6-136.5-145.8-450.1

Standard errors in parentheses.
* denotes significantly different from zero at the 5-percent level; ** denotes significantly different from zero at the 1-percent level (all twotailed tests except for Expected Participation Earnings/Expected Non-Participation Earnings).
a
Rho is a standard Hausman test statistic for the presence of random effects.

Table 6. Results of Probit Participation Model10.00

9.00

Average Investment Conditional on Participation

8.00

7.00

6.00

5.00

4.00

3.00
Tokyo B

Tokyo B'

Tsukuba B

2.00

1.00

0.00
1

2

3

4

5

6

7

8
Period910

Figure 8. The Average Investment Patterns Conditional on Participationin Tsukuba B, Tokyo B, and Tokyo B' Sessions.

11

12

13

14

15

1.00

0.90

(Number of Participants)/(Number of Subjects)

0.80

0.70

0.60

0.50

0.40

0.30

Tokyo B

Tokyo B'

Tsukuba B

0.20

0.10

0.00
1

2

3

4

5

6

7

8
Period910

Figure 9. The Average Participation Rate Patterns
in Tsukuba B, Tokyo B, and Tokyo B' Sessions.

11

12

13

14

15