Discussion Paper No. 992

EFFICIENCY AND
VOLUNTARY REDISTRIBUTIONUNDER INEQUALITY

Masaki Aoyagi
Naoko Nishimura
Yoshitaka Okano

March 2017

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

Eﬃciency and Voluntary Redistribution under Inequality ∗Masaki Aoyagi
Osaka University

Naoko Nishimura
Shinshu University

Yoshitaka Okano
Kochi University of Technology
March 13, 2017

Abstract
This paper presents an experimental analysis of 2 × 2 coordination games inwhich player 1 earns a substantially higher payoﬀ than player 2 except in theineﬃcient equilibrium where they earn the same payoﬀs. The main focus is on
the comparison of two treatments with and without the ex post redistribution
stage in which both players may voluntarily transfer their payoﬀs earned in thegame to the other player. We ﬁnd that (1) the transfer opportunity raises theprobability of coordination on an eﬃcient equilibrium, (2) a transfer from player
1 to player 2 is positive, and is higher when player 2 chooses the action corresponding to the eﬃcient equilibrium, and hence (3) the transfer opportunity
tends to improve the eﬃciency and equity of the ﬁnal outcome. Furthermore,these tendencies are stronger when the two players have conﬂicting interests
over the two equilibria than when they have common interests.
Key words: heterogeneity, equity, eﬃciency, transfer, reciprocity, laboratory
experiments
Journal of Economic Literature Classiﬁcation Numbers: C72, D03, D31, D63

1Introduction

Inequality is a basic trait of the modern society. The income share of the top 0.1%
in the U.S. exceeds 7%, and the Gini coeﬃcient for the U.S. households rose to .479
in 2015 from .386 in 1968.1 The same increasing trend in inequality is found in manyof the industrialized countries. The coexistence of the haves and the have-nots in∗

Financial support from the JSPS (grant numbers: 21653016, 24653048, 15K13006, 22330061,
15H03328, 23560216， and 16H03597) and the Joint Usage/Research Center at ISER, Osaka University is gratefully acknowledged.
1
US Census Bureau.
http://www.census.gov/data/tables/time-series/demo/incomepoverty/historical-income-households.html

1the society will inevitably create an encounter between them. For example, a CEO
with astronomical salaries manages his company’s blue-color workers who earn alittle more than the minimum wage, or poor students earn their way to college tocompete against classmates from aﬄuent families. While economics in general recognizes the importance of inequality, there is relatively little experimental work on
how distributive inequality may aﬀect the strategic interaction between individuals
with highly asymmetric backgrounds. We are interested in such questions as: Is
the behavior of the less privilege people driven by their anticipation of positive reciprocity from their privileged counterparts? How does inequality aversion interplay
with the strategic interactions between the privileged and non-privileged individuals? Does the opportunity to make voluntary transfers help mitigate inequality andraise eﬃciency through better coordination?
In this paper, we use a laboratory experiment to study how the presence of
inequality between two subjects aﬀects their play in a simple simultaneous-movegame with and without the possibility of income redistribution ex post. Speciﬁcally,
we let subjects play an inequality game. which is a 2×2 coordination game with two
Nash equilibria. Inequality derives from the fact that player 1 earns a strictly higher
payoﬀ than player 2 at every action proﬁle other than the ineﬃcient equilibrium,
where they earn the same payoﬀ. The sum of payoﬀs is substantially higher atthe eﬃcient NE. It follows that the players face a fundamental trade-oﬀ between
eﬃciency and equity in this game: the players achieve equity but not eﬃciency
in one NE, whereas they achieve eﬃciency but not equity in the other NE. The
inequality games are further classiﬁed into common-interest (CM) inequality games
in which both players prefer the eﬃcient NE to the ineﬃcient NE, and conﬂictinginterest (CF) inequality games in which player 1 prefers the eﬃcient NE but player
2 prefers the ineﬃcient NE. The inequality games are also parametrized by the levelof inequality between the two players as measured by the payoﬀ ratio at the eﬃcientNE.
Our main objective is to analyze the play of the inequality game with and without
the ex post redistribution stage in which each player may voluntarily transfer their
payoﬀ to the other player. Of course, in any subgame perfect equilibrium of thetwo-stage game between the self-interested players, no ex post redistribution takes
place and hence the presence of this additional stage makes no diﬀerence to the ﬁnal
allocation.
In our experiment, each subject is randomly assigned the role of either player 1 orplayer 2, and is randomly and anonymously matched with a subject who is assigned
the other role. The subject role stays the same throughout the experiment. Our
ﬁrst treatment is the dictator decision treatment in which one of the paired subjects
chooses one of the four alternatives that correspond to the action proﬁles of theinequality game. We ﬁnd that the subjects’ preferences are best characterized byown payoﬀ maximization rather than inequality or ineﬃciency aversion. The next
two treatments involve strategic interaction between the subjects: The subjects play2

a series of inequality games in each treatment with the ex post redistribution stage
added only in the third treatment. We ﬁnd that the presence of the redistribution
stage signiﬁcantly increases the rate with which the two subjects coordinate on theeﬃcient NE. This eﬀect is more prominent in CF (conﬂicting interests) games thanin CM (common interests) games. An increase in the inequality ratio has diﬀerent
eﬀects in CM and CF games: In CM, increasing inequality makes it more likely thatthe subjects choose the action corresponding to the ineﬃcient but equitable NE andhence reduces eﬃcient coordination. In CF, on the other hand, high inequality increases the choice of the action corresponding to the eﬃcient but inequitable NE andincreases eﬃcient coordination in the redistribution treatment. In the redistribution
treatment, the average transfer amount is signiﬁcantly positive, and as expected, it
is mostly player 1 who makes positive transfer. Whether player 1 makes positivetransfer or not depends crucially on player 2’s action choice, and both the size oftransfer and the frequency of positive transfer are higher when player 2 chooses theaction that corresponds to the eﬃcient NE. On the other hand, increasing inequality
increases the size of transfer but not the frequency of positive transfer. As a result,
we also make the following ﬁndings regarding eﬃciency, as measured by the sum of
the pair’s payoﬀs, and equity, as measured by the ratio of their post-redistribution
payoﬀs: The presence of the redistribution stage raises eﬃciency in CF games, andraises equity in both CF and CM games. Interestingly, we ﬁnd that the increase ineﬃciency is due almost entirely to the increase in role 2’s payoﬀ.
The paper is organized as follows. The next section discusses the related literature. The inequality game and the diﬀerent treatments are described in Section
3. Section 4 describes the experimental design, and Section 5 presents the analysis.
The motive behind the positive transfer and the rationality of the subjects’ choices
are discussed in Section 6. We conclude in Section 7.

2

Related Literature

The present paper is related to a few strands of literature as follows.
As discussed above, our primary focus is on the strategic interaction between
highly asymmetric players. In the experimental literature, eﬀects on behavior ofplayer asymmetry is studied extensively in the context of public good games. Asymmetry is introduced either in the level of the individual return (MPCR - marginal per
capita return) of investment into the public good, or in the level of initial endowment(income) of each individual. The main focus in both cases is how the perception of
inequality aﬀects the individual and aggregate contribution levels. The ﬁndings areinconclusive. Buckley and Croson (2006) study a linear public good game played
by a group of high- and low-income subjects, and ﬁnd that the low-income subjects
give a higher percentage of their income to the public good than the high-income
subjects. Hofmeyr et al. (2007) ﬁnd that heterogeneity has no impact on the contribution and the poor and rich players contribute the same proportion of their3

endowments. Anderson et al. (2008) examine the eﬀect of revealing information
about inequality in the show-up fees for their subjects, and ﬁnd that making it public substantially reduces contribution levels. Oxoby and Spraggon (2013) ﬁnd thatheterogeneity signiﬁcantly reduces contributions to the public good in their public
good experiment with diﬀerent income levels. Maurice et al. (2013) have their subjects play the public good game under both equal and unequal endowments, andstudy how their individual contributions adjust to the circumstances. ? study apublic good game played by rich players in the presence of poor non-active players
who beneﬁt from the good.2
There are also public good game experiments with unequal incomes and redistribution. Uler (2011) studies a public good game with ex post redistribution ofincome by exogenously specifying the tax rates. When the initial income distribution is unequal, Uler (2011) ﬁnds that increasing the tax rates aimed at a moreequal distribution ex post increases contribution to the public good. Belafoutas
et al. (2013) let the subjects choose the redistribution rate before the contribution
decisions, and ﬁnd that when inequality is a result of real eﬀort, the subjects prefer the policy that entails less redistribution. While most public good experimentswith heterogeneity in the literature use models in which each player has a dominantaction of “no contribution,” exceptions are Chan et al. (1996, 1999), who study nonlinear public good games with multiple (interior) equilibria. Instead of examining
coordination, however, Chan et al. (1996) focus on a particular equilibrium withcertain properties, and study how the observed contributions by the rich and poor
subjects diﬀer from the equilibrium prediction.3
The present paper diﬀers from the heterogeneous public good experiments inthe literature in a few important ways. First, to the best of our knowledge, there isno public good game experiment that involves voluntary redistribution of payoﬀs ex
post. Second, as mentioned above, most public good games studied in the literature
have a dominant action of “no contribution,” and hence are fundamentally diﬀerent
from the coordination games studied in this paper.
In our inequality game with the redistribution stage, the poor player 2’s actionthat corresponds to the eﬃcient equilibrium is similar to the sender’s action oftrusting money to the receiver in the well-known trust game. In both cases, ityields beneﬁts to the other player and also implies a higher aggregate payoﬀ.4 The
trust games played by asymmetrically endowed players are studied by some authors.
Among them, Hargreaves Heap et al. (2013) study the eﬀect of endowment inequality
on the agerage trust and return rates, and ﬁnd that inequality has little impact on
2

Tavoni et al. (2011) also ﬁnd that inequality in endowments makes the provision of public goods
diﬃcult in their threshold public good game, but also ﬁnd that the problem can be mitigated by
the introduction of the pre-play communication (“pledge”) phase which works as a coordination
device.
3
Chan et al. (1999) study the interactions of heterogeneity and communication.
4
According to Camerer (2003), the average return to the sender in various trust game experiments can be higher or lower than the amount trusted.

4

the average trust rate, but has a negative impact on the return rate through theless trustworthy behavior of the rich subjects.5 Diﬀerent from the trust game, ourexperiment has player 1 also make an initial action choice, enabling us to examine
the interplay between the strategic interactions and the redistribution motive.
Voluntary redistribution following a strategic interaction is discussed in the context of the real-eﬀort experiments. Erkal et al. (2011) conduct an experiment on areal-eﬀort tournament game with a redistribution stage by a group of four players.
Erkal et al. (2011) ﬁnd that the ﬁrst-ranked subjects give signiﬁcantly less than thesecond-ranked subjects to other members of their group, and attribute this ﬁnding
to the propensity of subjects with self-regarding preferences to rank ﬁrst by working
harder than subjects with other-regarding preferences.6
The relationship between the presence of inequality and the preference for redistribution in the form of tax policies has been the subject of several experiments.
Through the elicited preferences for redistribution rules, Rutström and Williams(2000) ﬁnd that their subjects’ preferences for redistribution under inequality are
best described by self-interest, whereas Tyran and Sausgruber (2006) ﬁnd that voting behavior under inequality is best explained by the inequality aversion hypothesis. Krawczyk (2010) increases dispersion in the probability that each subject winsa prize, and ﬁnds no signiﬁcant increase in the ex ante preference for redistribution
when those probabilities are exogenously speciﬁed. In their experiment with large
inequality, Durante et al. (2014) let the tax rate chosen by one randomly selectedindividual, and ﬁnd that the individual chooses a higher tax rate when he/she knows
his/her relative position in the income distribution. Agranov and Palfrey (2015) ﬁnd
that higher inequality in productivity induces the suggestion of higher redistribution
policies.
The primary focus of the extensive literature on coordination game experiments
is on the comparison between payoﬀ dominance and risk dominance as the eﬀective
predictor of the outcome of subjects’ play. Cooper et al. (1990, 1992), Straub (1995),
Van Huyck et al. (1990), Goeree and Holt (2005), among others, observe that risk
dominance predicts subjects’ play better than payoﬀ dominance.7 We avoid theissue of payoﬀ dominance versus risk dominance by specifying payoﬀs so that theeﬃcient equilibrium, which maximizes the sum of the two players’ payoﬀs, is also risk
5

Greiner et al. (2012) study a dynamic game in which the subjects are randomly matched to play
the trust game over multiple rounds. They ﬁnd that the growth rate of the aggregate endowment
decreases rapidly when the subjects’ initial endowments are the same, but is more stable when they
endowments are diﬀerent.
6
Ohtake et al. (2013) ﬁnd to the contrary that the ﬁrst-ranked subjects give more than thesecond-ranked subjects in their real-eﬀort experiment.
7
Van Huyck et al. (1990) observe that a coordination failure can result from the introductionof a dominated action which yields the eﬃcient outcome. Goeree and Holt (2005) observe thesensitivity of the coordination rates to the detailed payoﬀ speciﬁcation. Furthermore, Van Huyck
et al. (1990) and Goeree and Holt (2005) both ﬁnd that the increased number of players makes
coordination more diﬃcult. This observation leads them to the conclusion that risk dominance isa more eﬀective criterion.

5

dominant. Furthermore, we control for the level of risk dominance of the eﬃcientequilibrium across diﬀerent games so that risk dominance will not be a factor in
our analysis. To the best of our knowledge, there exists no coordination game
experiment in the literature that studies the eﬀect of payoﬀ asymmetry between theplayers.8 One important feature of our experiment is that the subjects’ roles are ﬁxed
throughout the experimental sessions. In other words, once a subject is assigned
the advantageous role (role 1) or disadvantageous role (role 2) at the beginning ofeach session, their role stays the same until the end of the session. This design isintended to mimic the persistence of inequality in reality, and also to avoid the typeof (indirect) reciprocity that a role 1 subject who received transfer as a role 2 player
earlier in the session rewards his current role 2 partner to return the favor.9
In summary, this paper presents a departure from the literature with the combination of the following features:−−−

Strategic interaction under inequality.
Voluntary ex post redistribution of payoﬀs.
Coordination games with a eﬃciency-equity trade-oﬀ.

3Models of Inequality and Redistribution

3.1

Inequality Games

Formally, an inequality game G is a 2×2 coordination game: Each player i chooses
his action xi from the set {0, 1}, and their payoﬀ functions are given by
u1 (x) = ax1 x2 + b(1 − x1 ) + c1 (1 − x2 ),u2 (x) = ax1 x2 + b(1 − x2 ) + c2 (1 − x1 ).

(1)

For the interpretation of these payoﬀ functions, suppose that the players engage inthe production of a public good. Each player i either makes eﬀort xi = 1 or not
xi = 0 toward the production of the good. The public good is produced if and only
if both players make eﬀort, and when produced, it generates utility a to each oneof them. On the other hand, each player i has two outside options that are aﬀectedby one’s own and the other’s action choices as follows: When player i makes eﬀort,
it entails a personal opportunity cost equal to b. On the other hand, when i makes
eﬀort, it inﬂicts negative externalities on player j, and destroys the latter’s outside
option which is worth cj . We can for example suppose that i’s production eﬀort
generates nuisance that prevents j from deriving utility from his alternative activity.
8
Crawford et al. (2008) investigate the eﬀect of payoﬀ diﬀerence between the two players inthe battle of the sexes games and ﬁnd that increasing the diﬀerence reduces the likelihood of
coordination. However, their games are symmetric in the sense that one player’s payoﬀ in the ﬁrst
coordination proﬁle equals the other player’s payoﬀ in the second coordination proﬁle.
9Note that a subject faces a diﬀerent subject in every round according to the random matching
format.

6

We suppose that the parameters satisfy
a > b > 0 and c1 > c2 > 0.
Note that the second condition is the only source of inequality between the twoplayers: the value of player 1’s outside option vulnerable to negative externalities
from 2’s eﬀort is higher than the value of player 2’s corresponding option. Writing
X for no eﬀort xi = 0, and Y for eﬀort xi = 1, we can depict the payoﬀ table as in
Figure 1.
X
P1 \ P2
X
b + c1 b + c2
Y
c1
b

Y
b
a

c2
a

Figure 1: Inequality Game: c1 > c2
Since a > b > 0, both (X, X) and (Y, Y ) are pure NE. We also assume:• c1 + c2 > 2(a − b) ⇔ (X, X) uniquely maximizes the sum of payoﬀs.
⇔ u1 (x) > u2 (x) for x = (Y, Y ).
•c1 > b > c2•
2b > a⇔ (X, X) is risk dominant.
It follows from the second condition that (Y, Y ) is the only proﬁle in which thetwo players earn the same payoﬀ. We further restrict attention to the following
subclasses of inequality games: An inequality game has common-interest (CM) if
b + c1 > b + c2 > a, and has conﬂicting-interest (CF) if b + c1 > a > b + c2 . In
other words, if an inequality game has CM, then both players 1 and 2 prefer theNE (X, X) to the NE (Y, Y ), whereas if it has CF, then player 1 prefers (X, X) to(Y, Y ) and player 2 prefers (Y, Y ) to (X, X).

3.2

Voluntary Redistribution

Our main focus is on the subjects’ behavior in the inequality game with and without
the ex post redistribution stage in which both players may transfer their payoﬀsearned from playing the game to the other player. Let gi denote player i’s ﬁnal payoﬀ
after the possible redistribution of their payoﬀs. First, in the baseline treatment, noredistribution takes place after the play of the inequality game G.
T1: No Redistribution: The players’ ﬁnal payoﬀs equal their payoﬀs from G: gi =ui .
In the redistribution treatment, the players may give part or all of their payoﬀs
to the other player after the play of the inequality game.

7T2: Voluntary Redistribution: After the players play G, they publicly observe theactions and payoﬀs, and then determine how much of their payoﬀ points togive to the other player. If player i chooses to give ti (≤ ui ) payoﬀ points toplayer j (i = j), then the ﬁnal payoﬀs are given by
g1 (x) = u1 (x) − t1 + t2 ,and g2 (x) = u2 (x) − t2 + t1 .

Clearly, if the players are simple payoﬀ maximizers, then no redistribution of
payoﬀs takes place in any SPE of T2, and hence the only SPE payoﬀ proﬁles ofthese games are the NE payoﬀ proﬁles of G. If redistribution takes place, on theother hand, then it may be a consequence of the subjects’ social preferences such as
inequality aversion, or their tendency to reciprocate the other’s behavior. In order
to better understand their preferences, we also include a game form in which theﬁnal allocation is determined by one of the players as follows.
T0: Dictator Decision: One player in each pair makes a choice among four payoﬀ
pairs that correspond to the four cells of the payoﬀ table.

4

Experimental Design

The experiments were conducted at the Experimental Economics Laboratory at the
ISER, Osaka University, with the subjects recruited from undergraduate and graduate students of Osaka University of various majors. There were six sessions with a
total of 124 subjects (four sessions of 20 subjects and two sessions of 22 subjects).
No subject attended more than one session. The subjects in each session were divided randomly into two groups of the same size with the ﬁrst group of subjects
assigned the role of player 1, and the second group of subjects assigned the role ofplayer 2. The player roles stay the same throughout the session. The role assignment is done privately on the PC screen in front of each subject. The instruction
presents the equation (1) that generates the payoﬀs, and provides illustration of theequation by means of numerical examples and graphs.10,11 The payoﬀ matrix is also
shown on the PC screen in front of each subject. At the end of each session, theearning of a subject is computed from the sum of his/her payoﬀ points during thesession with the conversion rate of 1 payoﬀ point to JPY1.3. The average earnings
are JPY9946.1 for the role 1 subjects and JPY3122.8 for the role 2 subjects.12
In each session, each subject faces inequality games with six diﬀerent payoﬀ
tables: CM2, CM4 and CM6 are CM inequality games, and CF2, CF4 and CF6 are
10
The program was coded using z-tree (Fischbacher (2007)). We also had ﬁve other sessions with106 subjects in which no information about the underlying utility function (1) is revealed. This
paper focuses on the treatment with the information.
11
See the Appendix for an English translation of the instruction.
12
These translate to about US$90-127 for role 1 and US$28-40 for role 2 according to the exchange
rates at the time of the experiments.

8

CF inequality games. The suﬃx represents the inequality ratio between the players
as measured by the payoﬀ ratio at (X, X):
u1 (X, X)= k in CFk and CMk.
u2 (X, X)
We seta = 100,andb = 60in all six games, and vary ci as in Table 1. The resulting payoﬀ tables are depicted
in Figures 2 and 3. Note that all CM games are the same in terms of player 2’s
payoﬀs, and so are all CF games. Furthermore, since a and b remain unchanged inall games, so is the risk dominance level of (X, X).
c1
c2

CF2
100
20

CF4
260
20

CF6
420
20

CM2
160
50

CM4
380
50

CM6
600
50

Table 1: Parameter Speciﬁcations

X
Y

X
220, 110
160, 60

Y
60, 50100, 100

X
Y

CM2

X
440, 110
380, 60

Y
60, 50100, 100

X
Y

CM4

X
660, 110
600, 60

Y
60, 50100, 100

CM6

Figure 2: CM inequality games

X
Y

X
160, 80
100, 60
CF2

Y60, 20100, 100

X
Y

X
320, 80
260, 60

Y
60, 20100, 100

X
Y

CF4

X
480, 80
420, 60

Y
60, 20100, 100

CF6

Figure 3: CF inequality games
Each session consists of three diﬀerent blocks that correspond to the three treatments T0-T2 of our main interest as described above. Each block in turn consistsof six rounds that correspond to the six inequality games CF2-CF6 and CM2-CM6.
In all four sessions, the ordering of the blocks is ﬁxed and given by
T0 → T1 → T2.13
9

The six games appear in random order in the six rounds of each block. In the T0
treatment, one subject in each pair is randomly chosen to make a choice.14 Afterthe outcome of play is shown on the PC screen, anonymous rematching takes placein the stranger format.

5

Analysis

Our analysis examines the eﬀects of game forms (T0, T1, and T2), payoﬀ structure(CM and CF), player roles (1 and 2), and inequality ratios (k = 2, 4, 6) on the action
choice, coordination rates, the frequency and size of transfers, and the eﬃciency andequity of the ﬁnal outcome.

5.1

Social preferences in the dictator treatment (T0)

We begin by examining the outcome of the dictator treatment (T0) to understandthe possibility that the subjects are maximizers of some social preferences rather
than their own payoﬀs. Speciﬁcally, we regard the following three types of social
preferences as particularly relevant to their action choice in the present environment.
1. Inequality Aversion (IQA: prefers equitable allocations)
2. Ineﬃciency Aversion (IEA: prefers eﬃcient allocations)
3. Spite/Altruism (SA: prefers reducing or raising the other’s allocation)
Figure 4 shows the frequency of each of four choices (A, B, C, D) for CM and
CF games.15 As seen, the subjects’ choices are almost entirely limited to A and D,
which are NE of the game.16 Additionally, the role 1 subjects choose A more than
94% of the time, whereas the choice of the role 2 subjects is approximately reversed
depending on whether the game is CM or CF. In CM, they choose A more than
90% of the time, whereas in most cases of CF, they choose D on average 80% of thetime.17 The inequality ratio k is mostly insigniﬁcant in both CM and CF.18
13

Based on the results from the preliminary sessions, we ﬁxed the order of the treatments becauseof the concern that the subjects would read into our intention if they experienced T2 before T1.
Each session had one additional treatment T3 which is not discussed in this paper. Since T3 wasgiven at the end of each session, it didn’t aﬀect the subjects’ behavior in the earlier treatments.
14
Once a subject is chosen, he makes a choice in all six rounds of the T0 treatment (against
diﬀerent opponents).
15
The outcome in T0 is denoted as A = (X, X), B = (X, Y ), C = (Y, X), and D = (Y, Y ).
16
The hypothesis that the four outcomes are randomly chosen with equal probabilities is rejected(p = 0.01).
17
A multinomial logit regression over the four outcomes is no more informative than the descriptive statistics because of the skewed distribution of the choice data.
18
The unique exception is the choice by the role 2 subjects who choose D less often in CF4 thanin CF2 (Mann-Whitney U-test, p = 0.1).

10Figure 4: Outcome distribution in T0

For the role 1 subjects, their choice of A is consistent with both own payoﬀ
maximization and IEA, whereas for the role 2 subjects, their choice of A in CM and
D in CF is consistent with own payoﬀ maximization. Even for the role 2 subjects,
however, they have a weak tendency to choose A more often in CF when k is larger.
This may indicate role 2’s concern about the decrease in role 1’s payoﬀ resulting
from 2’s choice of D instead of A, and hence suggests an element of IEA/altruism
in their behavior.
Observation 1 (Single-person decision) The behavior of the role 1 subjects in T0
is consistent with own payoﬀ maximization and IEA. The behavior of the role 2
subjects in T0 is consistent with own payoﬀ maximization, but has a degree of IEA
or altruism.

5.2

What inﬂuences the action choice?

Figure 5 shows the number and frequency of each action (X and Y ) by the gameform (T1 and T2), payoﬀ structure (CM and CF), and subject roles (1 and 2). As
seen, there is a signiﬁcant diﬀerence in the subjects’ action choice between T1 andT2, and the diﬀerence is more prominent in CF. Role 2 subjects choose X more
often in T2 than in T1 for CF but not for CM, while role 1 subjects do so for both
CF and CM. Both role 1 and role 2 subjects choose Y more often in CF than in
CM. This observation is conﬁrmed by the random eﬀects logit regressions in Table 2,
where the dependent variable equals one if a subject chooses Y . Models (1) and (2)are for CM and CF, respectively, and have as explanatory variables the subject role(‘role’= 1 for role 1), the game form (‘t2’= 1 for T2), the inequality ratio (‘k4 ’= 1
if k = 4 and ‘k6 ’= 1 if k = 6), the inverse ‘1/round’ of the round number within11

** and ***: signiﬁcant diﬀerence at 5% and 1%, respectively, between the respective pair of distributions(χ2 -test). Shown in each column are the numbers of each action choice aggregated for k = 2, 4, and 6.

Figure 5: Action choices in T1 and T2

each treatment, as well as cross terms.19 Models (3) and (4) aggregate the data fromCM and CF and have as explanatory variables the payoﬀ structure (‘cf’= 1 if CF)
and the cross term between the subject role and payoﬀ structure (‘cf ∗ role’).
We see that the coeﬃcient for ‘t2’ is signiﬁcantly negative in model (2), suggesting that CF-T2 induces action X signiﬁcantly more often than CF-T1. On the other
hand, no signiﬁcant eﬀect of T2 is observed in CM in model (1). The coeﬃcientfor the cross term ‘role ∗ t2’ is insigniﬁcant in both models (1) and (2), implyingthat these eﬀects of T2 are independent of the subject role. Models (1) and (2)also show no signiﬁcant eﬀect of the subject role on the action choice in CM andCF: ‘role’ is not signiﬁcant by itself, and neither are the cross variables involving‘role’.20 Models (3) and (4) show that the subjects choose Y more often in CF thanin CM, irrespective of the subject role. They also show the diﬀerent eﬀects of theinequality ratio k in CM and CF: In both CM-T1 and CM-T2, higher inequality
overall has a positive impact on the choice of Y , and the positive eﬀect is signiﬁcant
when k = 6. Also in CF-T1, high inequality (k = 6) increases the choice of Y ,whereas increased inequality has a signiﬁcantly positive impact on the choice of X
in CF-T2.21 The observation on the action choice can be summarized as follows:19

The round number is inversed so that it takes values between 0 and 1: This helps us with theregressions in which other regressors are binomial and equal to 0 or 1.
20
In model (3), ‘role*k4 ’ is (weakly) signiﬁcant, while ‘role*k4 ’ is not.
21
In model (3), ‘k6 ’ is signiﬁcantly positive and ‘cf*k6 ’ is signiﬁcantly negative. However, ‘k6 ’ is12ModelConditionrole
t2role*t2
k4
k6
role*k4
role*k6

(1)
CM

(2)
CF

(3)
T1

(4)
T2

-0.33
(0.95)-0.75(0.59)-0.69(0.74)
0.67(0.51)
1.24**(0.60)
0.48(0.89)
0.21(0.98)

0.27(0.57)-0.94***(0.32)-0.45(0.46)-0.51(0.40)-0.07(0.41)
0.77(0.56)-0.45(0.59)-0.36(0.69)-0.53(0.81)

0.74(0.61)-4.66***(0.75)
744-162.84

0.00(0.43)-1.31***(0.47)
744-339.260.51(0.55)
1.06**(0.52)
0.94*(0.57)-0.09(0.58)
2.29***(0.55)
0.36(0.63)-0.87(0.59)-1.00*(0.54)
0.12(0.42)-3.59***(0.53)
744-315.380.92(0.83)
1.74**(0.74)-0.06(0.74)-0.45(0.69)
2.76***(0.84)
0.58(0.74)-1.41*(0.75)-2.20***(0.81)-0.15(0.52)-4.79***(0.93)
744-213.50cf
role*cf
cf*k4
cf*k6
1/roundconstant
Observations
Log-likelihood*, ** and ***: signiﬁcant at 10%, 5% and 1%, respectively.
Robust standard errors are in parentheses.

Table 2: Random eﬀect logit regressions of action choice: y = 1{ai =Y }Observation 2 (Action choice)
1. In both T1 and T2, the subjects choose X signiﬁcantly less often in CF thanin CM.
2. In CF, the subjects choose X signiﬁcantly more often in T2 than in T1.
3. The subject role has no signiﬁcant impact on the action choice in CM and CF.
4. High inequality (k = 6) increases the choice of Y in both CM-T1 and CMT2. High inequality also increases the choice of Y in CF-T1, but increases the
choice of X in CF-T2.

more signiﬁcant (at 5%) than ‘cf*k6 ’ (at 10%), implying the positive impact of k = 6 on the choiceof Y . Similar reasoning implies the positive impact of inequality on the choice of X in CF-T2 inmodel (4).

13

Our central observation is Observation 2.2 on the comparison between T1 andT2, which cannot be explained by the maximization of self-regarding utility. The
insigniﬁcance of the player role in CF in Observation 2.3 is in sharp contrast with
our observation in T0, where the dominant choice is A = (X, X) for role 1 and
D = (Y, Y ) for role 2.22

5.3

What inﬂuences the frequency of coordination?

action proﬁle(X, X)(Y, Y )(X, Y )(Y, X)
p-value (χ2 test):
T0=T1=T2
T1=T2
CM=CF

CM
T0
T1
Role 1 Role 2
94
83
151
2
6
2
0
1
17
0
0
16
0.00

T2
167
0
12
7

0.00
0.00

CF
T0
Role 1 Role 2
93
16
2
73
1
0
0
1
0.00

0.07
0.00

T1

T2

89
14
37
46

130
5
26
25

0.00
0.00

0.00

The three lines in the bottom report the p-values of the χ2 tests of the hypothesis thatthe distributions are the same for T0-T2 (ﬁrst line), between T1 and T2 (second line),and between CM and CF (third line)

Table 3: Realization of action proﬁlesTable 3 describes the realized distribution of four action proﬁles in T0 throughT2. While the diﬀerence among T0-T2 is strongly signiﬁcant in both CM andCF, the diﬀerence between T1 and T2 is strongly signiﬁcant only in CF and only
weakly signiﬁcant in CM (p = 0.07). The diﬀerence between CM and CF is strongly
signiﬁcant in T0, T1 and T2.
Tables 4 and 5 present logit regressions of action proﬁles. Table 4 separates datafrom CM and CF and examines the eﬀect of the inequality ratio (‘k4 ’ and ‘k6 ’), andthe game form (‘t2’). Table 5 combines data from CM and CF and examines theeﬀect of the game form (‘t2’) and the payoﬀ structure (‘cf’). In each table, theﬁrst model has total coordination (1{a = (X, X) or (Y, Y )} ) as the dependent variable,
whereas the second model is a multinomial regression using one of the coordination
proﬁles (X, X) as the base.23 We look at the eﬀect of each explanatory variable
separately.
On the inequality ratio k, we note that ‘k4 ’ or ‘k6 ’ in models (1) and (3) in Table
4 has a signiﬁcant impact on the rates of total coordination for both CM and CF.
22

In addition to some role 2 subjects who switch from D in T0 to X in CF-T1 or CF-T2, there
are also some role 1 subjects who switch from A = (X, X) in T0 to Y in CF-T1 or CF-T2.
23
We choose (X, X) as the outcome base since the distribution of action proﬁles is skewed toward(X, X). The multinomial analysis is feasible only with this choice of a base.

14

CM
Model
Dep. var.
t2
k4
k6
t2*k4
t2*k6
1/roundcons# of obs.
Log-likelihood(1)
1{(X, X) or (Y, Y )}1.05*
(0.55)-0.79**(0.36)-0.84**(0.40)
0.10(0.68)-0.68(0.60)-0.45(0.42)
2.78***(0.45)
372-136.81CF(2)

1{(Y,X)}-15.05***(0.53)
0.23(0.66)
0.39(0.51)
14.16***(0.79)
14.60***(0.75)
1.04(0.74)-2.94***(0.61)
372-186.311{(X,Y )}-0.07(0.86)
1.11*(0.58)
1.04(0.67)-0.91(1.03)-0.20(0.83)-0.56(0.62)-2.74***(0.62)(3)
1{(Y,Y )}-0.12.
15.46***(0.70)
15.75***(1.32)-15.72***(0.99)-15.43***(1.05)
1.81(1.61)-20.51***(0.53)

1{(X, X) or (Y, Y )}0.80***(0.23)
0.23(0.21)
0.69***(0.26)
0.06(0.34)-0.02(0.33)-0.13(0.29)-0.02(0.34)
372-232.96

1{(Y,X)}-0.62(0.52)
0.27(0.46)-0.51(0.53)-0.68(0.83)-0.48(0.89)
0.40(0.48)-0.78**(0.39)
372-382.84(4)
1{(X,Y )}-0.89**(0.41)-0.67(0.42)-0.56(0.42)
0.44(0.72)
0.17(0.61)-0.49(0.55)-0.33(0.39)

1{(Y,Y )}-0.19(1.10)
1.08(0.94)
1.00(0.87)-2.08(1.65)-1.35(1.14)-0.95(0.87)-2.32***(0.70)*, ** and ***: signiﬁcant at 10%, 5% and 1%, respectively. Robust standard errors are in parentheses.

Table 4: Logit and multinomial logit regressions of action proﬁles: CM and CF

Model
Dep. var.
t2
cf
t2*cf
1/roundconstant# of obs.
Log-likelihood(1)
1{(X, X) or (Y, Y )}1{(Y,X)}

0.68**(0.33)-1.45***(0.28)
0.15(0.44)-0.40(0.31)
1.84***(0.29)
744-377.83-0.94**(0.48)
1.62***(0.39)-0.06(0.56)
0.94***(0.39)-2.68***(0.40)
744-581.78(2)
1{(X,Y )}1{(Y,Y )}-0.45(0.39)
1.29***(0.33)-0.28(0.47)-0.40(0.41)-2.02***(0.33)-13.84***(0.73)
2.46***(0.62)
12.43***(0.92)-0.24(0.64)-4.23***(0.57)** and ***: signiﬁcant at 5% and 1%, respectively.
Robust standard errors are clustered with subject id.

Table 5: Logit and multinomial logit regressions of action proﬁles: All data

15

However, it is interesting to observe that while increasing k decreases coordinationin CM, it tends to have the opposite eﬀect in CF. It can be seen from Model (2)that the less coordination in CM for a higher k is caused by a decrease in theeﬃcient coordination (X, X) and an increase in miscoordination (X, Y ).24 On theother hand, model (4) shows that the positive impact of ‘k6 ’ in CF comes mainly
from an increase in (X, X).25
On the comparison between T1 and T2, models (1) and (3) in Table 4 show that
T2 has a signiﬁcant positive impact on coordination in CM (p < 0.1), and strongly
so in CF (p < 0.01). From models (2) and (4), it can be seen that this is associatedwith the negative impact of ‘t2’ on the miscoordination proﬁles ((Y, X) in CM
and (X, Y ) in CF). The same observation can be made in model (1) in Table 5 that
aggregates CM and CF. In this case, ‘t2’ has a positive impact on total coordination
but a negative impact on ineﬃcient coordination (Y, Y ) and miscoordination (Y, X)(model (2)).26 In sum, the presence of a transfer opportunity in T2 signiﬁcantly
facilitates eﬃcient coordination and reduces coordination failures. This tendency iscommon in CM and CF.
On the comparison between CM and CF, Table 5 shows that ‘cf’ has a negative impact on total coordination (model (1)), but a positive impact on ineﬃcient
coordination (Y, Y ) and miscoordination proﬁles (model (2)). This holds for both
T1 and T2 since the cross term ‘t2*cf’ is signiﬁcant only for (Y, Y ) in model (2)and its sign is the same as the eﬀect of ‘cf’.
We summarize our ﬁndings as follows:
Observation 3 (Coordination)
1. In both T1 and T2, increasing the inequality ratio k decreases coordination inCM, but increases eﬃcient coordination in CF.
2. In both CM and CF, the presence of a transfer opportunity in T2 increases eﬃcient coordination and reduces ineﬃcient coordination as well as coordination
failures.
Observation 3.2 is our central ﬁnding, and in the case of CF, it corresponds
directly to Observation 2.2 which ﬁnds the increased choice of action X in CF-T2
compared with CF-T1. In the case of CM, however, the signiﬁcant impact of T2 oneﬃcient coordination is not directly implied by our ﬁnding on the individual action
choice in the preceding section. The positive impact of higher inequality on eﬃcient
coordination in CF-T1 (Observation 3.1) is also something that is not evident fromthe analysis of the individual action choice (Observation 2.4).
24Note that the number of observations of (Y, Y ) is small for any k.
The signiﬁcant eﬀects of the cross terms involving the inequality ratio (i.e., t2*k4 and t2*k6)in the multinomial regression (2) for CM result from small changes in the number of observationsof (Y, X) and (Y, Y ).
26
Although the cross term ‘t2 ∗ cf’ has a signiﬁcant positive impact on (Y, Y ), the overall eﬀect
of ‘t2’ is still negative.
25

16

5.4

What inﬂuences the size and likelihood of transfers?

Figure 6 depicts the average transfer after the realization of each action proﬁle forCM (left) and CF (right). In both CM and CF, the average transfer by the role
1 subjects dominates that by the role 2 subjects. In fact, the average transfer byrole 1 (Figure 6) is statistically diﬀerent from zero in both CM and CF, implyingthat the role 1 subjects are on average not own payoﬀ maximizers. The averagetransfer by role 1 after (X, X) is signiﬁcantly higher than that after (X, Y ) in both
CM and CF (p < 0.01, t-test). The same tendency can be found for role 2 in CM
only (p < 0.01).

Figure 6: Average absolute transfer: CM (left) and CF (right)

Figure 7 shows the number of subjects who made transfers after the realization ofeach action proﬁle for CM (left) and CF (right). Those who made positive transfers
are predominantly role 1. It can be seen that a subject tends to make transfers after
the choice of X by the other player, and also after the realization of the eﬃcient
coordination (X, X).
In order to account for the variation in raw payoﬀ numbers in diﬀerent inequality
games, we also examine the relative transfer, which is deﬁned as the amount oftransfer divided by the payoﬀ earned in the game (i.e., utii ). Figure 8 presents the
cumulative distribution of relative transfer by role 1 subjects. The ﬁgure indicatesthat the distribution of relative transfer in CF dominates that in CM. This diﬀerenceis signiﬁcant (p < 0.04, Kolmogorov-Smirnov test) for role 1, but not for role 2.
For the analysis of possible determinants of transfer decisions, we restrict attention to the role 1 subjects who have chosen X given that positive transfers
are observed almost exclusively in this combination as seen in Figure 7. Table 6
presents the results of three panel regressions based on data from both CM and CF.
Models (1) and (2) are the Tobit regressions of the relative and absolute transfers,
17

Figure 7: Number of subjects who made positive transfers

respectively, whereas model (3) is the probit regression of the likelihood of positivetransfers (i.e., the dependent variable is 1{t1 >0} ).
In the Tobit analysis of the relative and absolute transfer in models (1) and (2),the impact of ‘other’s action’ (= 1 if role 2 chooses Y ) is negative and signiﬁcantin each case. The cross term between ‘other’s action’ and ‘cf’ is signiﬁcant inneither model (1) nor model (2). Thus, the role 1 subjects who have chosen X
increase their absolute and relative transfer in response to role 2’s choice of X in
both CM and CF. The payoﬀ structure ‘cf’ has a signiﬁcant positive eﬀect in bothmodels (1) and (2), and the cross term ‘cf ∗ other’s action’ is insigniﬁcant. In
other words, role 1 tends to make a larger transfer in CF than in CM, and thistendency is not aﬀected by role 2’s action choice. Role 2’s choice of X and CF bothhave signiﬁcantly positive impacts on the likelihood of transfer as seen in model (3).
Turning now to the inequality ratios ‘k4 ’ and ‘k6 ’, we see in both models (1) and (2)that they are positively signiﬁcant while their cross terms with ‘cf’ are insigniﬁcant.
It follows that in both CM and CF, role 1 is willing to make a larger transfer as thedegree of inequality increases. On the other hand, the likelihood of positive transfers
is unaﬀected by k as seen in model (3).
Observation 4 (Size and frequency of transfer)
1. The average transfer by role 1 is signiﬁcantly positive with positive transfer
almost exclusively when his own choice is X.
2. A positive transfer by role 1 is more likely after the choice of X by role 2, andthe absolute and relative transfer is larger in this case.
3. A positive transfer by role 1 is more likely in CF, and the absolute and relativetransfer is also larger in CF.
18

Figure 8: Cumulative distributions of relative transfer by role 1 subjects

4. The inequality ratio k has a positive impact on the (absolute and relative) sizeof transfer in both CM and CF, but has no impact on the likelihood of a positivetransfer.

5.5

Eﬃciency and equity with and without a transfer opportunity

Observations 3.2, 4.1, and 4.2 ﬁnd that eﬃcient coordination is more likely in thepresence of a transfer opportunity and positive transfers do indeed take place. We
now turn to the consequence of these observations in terms of the eﬃciency andequity of the ﬁnal payoﬀs.
Our eﬃciency measure is the total payoﬀ, which simply equals the sum of thetwo players’ payoﬀs (u1 + u2 = g1 + g2 ). The average total payoﬀ in CM is 490.65
for T1 and 513.92 for T2. In CF, the average total payoﬀ for T1 is 301.51 and
340.00 for T2. Statistical signiﬁcance between T1 and T2 is found in CF (p = 0.28
for CM and 0.03 for CF, by t-test). Figure 9 shows the cumulative distributionof the total payoﬀs in T1 and T2. In both CM and CF, the distribution for T2(dashed-line) appears to approximately ﬁrst-order dominate that for T1 (solid-line).
The Kolmogorov-Smirnov test ﬁnds a signiﬁcant diﬀerence in distribution between
T1 and T2 (dashed-line) in CF (two-sided p = 0.07). The transfer opportunity
hence has a more substantial impact on eﬃciency in CF than in CM. These results
are all consistent with our earlier ﬁndings that T2 facilitates eﬃcient coordination(Observation 3.2), and has a stronger impact in CF.

19

ModelDept. var.

(1)
relative(2)
absolute(3)
frequency

other’s action-0.27***(0.09)
0.12***(0.03)
0.05*(0.03)
0.07***(0.03)
0.13(0.09)-0.06(0.04)-0.06(0.04)
0.04(0.03)-0.13***(0.04)
335-13.61-142.89***(40.72)32.16**(15.17)38.73***(14.12)73.15***(13.58)33.08(45.33)-12.61(20.57)-21.27(19.24)24.61*(13.72)-82.57***(16.97)335-788.56-2.47**(1.21)
0.92**(0.39)
0.34(0.37)
0.43(0.36)-0.13(1.23)
0.14(0.55)
0.49(0.54)
0.98**(0.40)-1.61***(0.43)
335-153.66cf
k4
k6
other’s action *cf
cf*k4
cf*k6
1/roundconstant# of obs.
Log-likelihood*, ** and ***: signiﬁcant at 10%, 5% and 1%, respectively.
Standard errors are in parentheses.

Table 6: Random eﬀect Tobit and probit regressions of transfer size and frequency

Further scrutiny of the subjects’ payoﬀs reveals interesting facts. Figure 10
depicts the average ﬁnal payoﬀs (gi ) in T1 and T2 for role 1 (dark) and role 2(light). While role 2’s payoﬀ in T2 is signiﬁcantly higher than that in T1 in both
CM and CF (p < 0.01 in both CM and CF by a t-test and a Mann-Whitney test),
there is no such diﬀerence in role 1’s payoﬀs (by either test).
Table 7 presents the Tobit regression of the ﬁnal payoﬀ. As seen, there is a sharp
contrast between role 1 (left) and role 2 (right): For role 1, neither ‘t2’ nor any crossterm involving ‘t2’ is signiﬁcant. For role 2, on the other hand, ‘t2’ is signiﬁcantly
positive in CF, and the cross terms involving ‘t2’ tend to be signiﬁcantly positive. In
particular, the cross term ‘t2*k6 ’ is strongly positively signiﬁcant in both CM and
CF. The positive impact of ‘t2’ on role 2’s payoﬀ is consistent with the signiﬁcantly
positive transfer by role 1 in T2 as seen earlier. On the other hand, the insigniﬁcanceof ‘t2’ on role 1’s payoﬀ, coupled with Observations 3.2 and 4.2, implies that role 1
transfers away any payoﬀ gain from more eﬃcient coordination achieved in T2.
We now turn to the question of equity, which is measured by the ratio of the20

Figure 9: Cumulative distributions of total payoﬀs in T1 and T2: CM (left) and CF(right)Figure 10: Final payoﬀs gi in CM (left) and CF (right)
ﬁnal payoﬀs:role 1’s ﬁnal payoﬀ
g1
.
=
g2
role 2’s ﬁnal payoﬀ

Figure 11 shows the average of the payoﬀ ratio for T1 (dark) and T2 (light). For
each k, we can see that the average ratio is lower for T2 in both CM and CF.
This indicates that the presence of a transfer opportunity contributes to reducing
inequality between the two players. The hypothesis that there is no diﬀerence in the
average payoﬀ ratio between T1 and T2 is rejected by t-test for all k in CM withp < 0.05, and for k = 2 and k = 4 in CF with p < 0.01.27
Table 8 reports the Tobit regressions of the payoﬀ ratio for each inequality ratio
separately. The improvement in equity in T2 is observed in both CM and CF.28
27

The reduction in the payoﬀ ratio in T2 is also conﬁrmed by the Kolmogorov-Smirnov test
(p < 0.03 for CM and p < 0.01 for CF).
28
This is reﬂected by the signiﬁcant negative impact of ‘t2’ in all three models, together withthe cross term between ‘cf’ and ‘t2’ being either signiﬁcantly negative (model (1)) or insigniﬁcant(model (2) and (3)). By design, the payoﬀ ratio tends to be lower in CF than in CM.

21

Role 1
Model
t2
k4
k6
t2*k4
t2*k6
1/roundconstant# of obs.
Log-likelihood

Role 2

CM
(1)

CF
(2)

CM
(3)

CF
(4)

-3.12
(22.31)
174.39***(23.22)367.64***(22.50)12.18(31.56)-15.65(31.58)12.01(25.48)204.77***(18.08)372-2333.37

7.69(20.45)132.13***(20.53)230.09***(20.32)-6.03(29.98)21.00(28.52)0.71(21.87)115.86***(16.42)372-2283.6033

10.08(7.82)-5.61(8.14)-5.63(7.88)
19.68*(11.06)32.65***(11.07)-0.12(8.93)
103.91***(6.35)
372-1944.21

12.56**(6.04)
3.07(6.07)
5.86(6.00)
11.44(8.87)
23.03***(8.42)
1.75(6.54)
66.93***(4.97)
372-1839.3891*, ** and ***: signiﬁcant at 10%, 5% and 1%, respectively
Standard errors are in parentheses.

Table 7: Random eﬀects Tobit regressions of ﬁnal payoﬀs

These ﬁndings are consistent with our observation from Figure 11.
Observation 5 (Eﬃciency and equity)
1. T2 increases eﬃciency in CF, and the increase in eﬃciency is almost entirely
brought about by the increase in role 2’s payoﬀ.
2. In both CM and CF, T2 increases equity as measured by the ﬁnal payoﬀ ratio.

6

Discussion

One important question concerns what motivates positive transfer in the redistribution stage. Among the social preferences discussed earlier, IEA is found to beconsistent with the subjects’ choice in T0, but is irrelevant in the redistribution
stage since the game is constant-sum then. On the other hand, IQA is not supported by the subjects’ choice in T0, but can be a source of positive transfer by therole 1 subjects. Another possible source of positive transfer is reciprocity, which inthis case is the response by role 1 to role 2 ’s choice of X that contributes primarily
to increasing role 1’s payoﬀ.29 The strength of reciprocity can depend on (i) the29
Reciprocity is a response by player i based on his interpretation of another player j’s intention
when j’s behavior aﬀects i’s payoﬀ. Reciprocity is positive if i rewards j for j’s action that is22

Figure 11: Final payoﬀ ratios g1 /g2 in CM (left) and CF (right)
amount of sacriﬁce that role 2 makes by choosing X, and (ii) the size of the beneﬁtrole 2 provides to role 1 by choosing X.
The following considerations provide us some hint as to which one of IQA andreciprocity motivates positive transfer by role 1. First, in the case of IQA, thetransfer would be driven only by the realized payoﬀ diﬀerence between two roles atthe end of stage 1 in both CM and CF.30 Reciprocity based on the beneﬁt measure
also fails to distinguish between CM and CF: In both games, role 2’s choice of X
unambiguously beneﬁts role 1. On the other hand, reciprocity based on the sacriﬁce
measure has diﬀerent implications for CM and CF. In CM, role 2 prefers (X, X) to(Y, Y ), but in CF, role 2 prefers (Y, Y ) to (X, X). According to reciprocity basedon the sacriﬁce measure, hence, more transfer is expected in CF than in CM. Ourﬁnding (Observation 4.3) supports the latter reasoning.
Examining the eﬀect of the inequality ratio k also provides some hint. Clearly,
a larger k would have a positive impact on the size of transfer based on IQA or
reciprocity with the beneﬁt measure. This is indeed what we ﬁnd in Observation
4.4. On the other hand, we also ﬁnd that the likelihood of positive transfer is
unaﬀected by k, which can be considered evidence against IQA or reciprocity basedon the beneﬁt measure.31 Although the above considerations do not distinguishbetween IQA and reciprocity based on the beneﬁt measure, rejection of IQA by our
ﬁndings from T0 leads us to the following conjecture:
Conjecture 1 Reciprocity based on the sacriﬁce measure plays as the primary motive behind positive transfers in T2, whereas reciprocity based on the beneﬁt measure
plays the secondary role.
interpreted as intending to beneﬁt i, and is negative if i punishes j for j’s action that is interpreted
as intending to harm i. Our experimental design allows us to observe only positive reciprocity.
30
If anything, the payoﬀ diﬀerence u1 (X, X) − u2 (X, X) is larger in CM than in CF for each k,so that more transfer may be expected in CM based on IQA or reciprocity based on the beneﬁtmeasure.
31
The insigniﬁcance of the cross term between ‘cf’ and ‘k4 ’ or ‘k6 ’ indicates that the larger
transfer in CF is not driven by the inequality ratio k.

23

Model

(1)
k=2

(2)
k=4

(3)
k=6

t2

-0.17**(0.08)
0.16**(0.08)-0.21*(0.12)-0.03(0.12)
2.01***(0.07)
248-162.85-0.44**(0.20)-0.12(0.20)-0.08(0.29)
0.03(0.25)
3.85***(0.20)
248-388.26-0.90**(0.41)-0.69*(0.42)
0.38(0.58)
0.34(0.58)
5.62***(0.38)
248-562.18

cf
cf * t2
1/roundconstant# of obs.
Log-likelihood*, ** and ***: signiﬁcant at 10%, 5% and 1%, respectively
Standard errors are in parentheses.

Table 8: Tobit regressions of payoﬀ ratio g1 /g2

The second question concerns whether the subjects’ choice of X instead of Y
in CF (Observations 2.2 and 2.4) can be rationalized ex post in T2. To answer
this question, suppose that the subjects take as given the average transfer fromrole 1 to role 2 in T2 contingent on each action proﬁle. Figure 12 incorporates
the average transfer from role 1 to role 2 in T2 into their payoﬀs in CF with thenumber of observations of each action in the corresponding treatment indicated in
the parentheses. It can be seen that X becomes a more attractive choice for role 2
than in the original game. In fact, X is a dominant action for role 2 when k = 6,
and (X, X) is a payoﬀ dominant equilibrium as in CM when k = 4. Furthermore,
if role 2 expects that role 1’s action choice is given by its empirical frequency, X is
his uniquely optimal action for every k. For role 1, on the other hand, X cannot bea dominant action for any k by construction. Again, however, if role 1 expects thatrole 2’s action choice is given by its empirical frequency, X is the uniquely optimal
action for role 1 for every k.
X(48)Y (14)X (51)
149.1, 90.9
95.4, 64.6
k=2

Y (11)
53.3, 26.7
100, 100

X(53)
Y (9)

X (52)
292.1, 107.9
244.3, 75.8
k=4

Y (10)
60, 20100, 100

X(55)
Y (7)

X (52)
437.6, 122.4
376, 104

Y (10)
59.7, 20.3
100, 100k=6Figure 12: Payoﬀ matrices incorporating the average transfer from role 1 to role 2
in T2 (= (u1 − t̄1 , u2 + t̄1 ))24

7Conclusion

We study the play of a 2×2 coordination game which gives player 1 a large advantage
over player 2, and examine the eﬀect of adding the ex post redistribution stage where
each player may voluntarily transfer their payoﬀ to the other player. We ﬁnd thatthe presence of the redistribution stage induces positive transfer from the role 1
subjects to the role 2 subjects, and more frequent coordination on the eﬃcientaction proﬁle. These tendencies are stronger when the two players have conﬂicting
preferences over the two equilibria of the coordination game than when they havecommon interests.
While the subjects’ choices in the non-strategic situation are mostly consistent
with own proﬁt maximization, their behavior in the strategic situation deviates
signiﬁcantly from it. Through the analysis of the size and frequency of transfer, weconclude that the positive transfer is most likely motivated by reciprocity by the role
1 players and anticipation of it by the role 2 players. We ﬁnd that this interaction
results in the higher levels of eﬃciency and equity.
One interesting extension of the present work is an experiment that involves
elicitation of beliefs from the subjects before the play of the game. In particular, it
would be interesting to ﬁnd out their beliefs about which action they expect fromthe other player, and how much transfer they expect from the other player after therealization of a particular action proﬁle. Such study would provide us with moreinsight into the thinking of subjects in the face of inequality.
Our ﬁnding suggests that the opportunity to voluntarily redistribute wealthcan partially mitigate inequality. In our experiments, inequality is given by theexperimenter and not a consequence of the subjects’ eﬀort. It would be interesting
to see if behavior is diﬀerent in the setting where inequality is “acquired” by the
subjects as a result of their real eﬀort in some preceding task.

ReferencesM. Agranov and T. R. Palfrey. Equilibrium tax rates and income redistribution: Alaboratory study. Journal of Public Economics, 130:45–58, 2015.
L. R. Anderson, J. M. Mellor, and J. Milyo. Inequality and public good provision:
An experimental analysis. Journal of Socio-Economics, 37:1010–1028, 2008.
L. Belafoutas, M. G. Kocher, L. Putterman, and M. Sutter. Equality, equity andincentives: An experiment. European Economic Review, 60:32–51, 2013.
E. Buckley and R. Croson. The poor give more: Income and wealth heterogeneity
in the voluntary provision of linear public goods. Journal of Public Economics,
90(5):935–955, 2006.

25

C. F. Camerer. Behavioral Game Theory: Experiments in Strategic Interaction.
Princeton University Press, 2003.
K. S. Chan, S. Mestelman, R. Moir, and R. A. Muller. The voluntary provision of
public goods under varying income distributions. Canadian Journal of Economics,
29(1):54–69, 1996.
K. S. Chan, S. Mestelman, R. Moir, and R. A. Muller. Heterogeneity, equity andvoluntary contributions toward the provision of a public good. Experimental
Economics, 2:5–30, 1999.
R. Cooper, D. V. DeJong, R. Forsythe, and T. W. Ross. Communication in coordination games. Quarterly Journal of Economics, 107(2):739–771, 1992.
R. W. Cooper, D. V. DeJong, R. Forsythe, and T. W. Ross. Selection criteria in coordination games: Some experimental results. American Economic Review, 80(1):218–233, 1990. ISSN 00028282. URL http://www.jstor.org/stable/2006744.
V. P. Crawford, U. Gneezy, and Y. Rottenstreich. The power of focal points islimited: Even minute payoﬀ asymmetry may yield large coordination failures.
American Economic Review, 98(4):1443–1458, 2008.
R. Durante, L. Putterman, and J. van de Weele. Preferences for redistribution andperception of fairness: An experimental study. Journal of the European Economic
Association, 12(4):1059–1086, 2014.
N. Erkal, L. Gangadharan, and N. Nikiforakis. Relative earnings and giving in areal-eﬀort experiment. American Economic Review, 101:3330–3348, 2011.
U. Fischbacher. z-Tree: Zurich toolbox for ready-made economic experiments. Experimental Economics, 10(2):171–178, 2007.
J. K. Goeree and C. A. Holt. An experimental study of costly coordination. Gamesand Economic Behavior, 51:349–364, 2005.
B. Greiner, A. Ockenfels, and P. Werner. The dynamic interplay of inequality andtrust? An experimental study. Journal of Economic Behavior & Organization,81(2):355–365, 2012.
S. P. Hargreaves Heap, J. H. W. Tan, and D. J. Zizzo. Trust, inequality and themarket. Theory and Decision, 74:311–333, 2013.
A. Hofmeyr, J. Burns, and M. Visser. Income inequality, reciprocity and public
good provision: An experimental analysis. South African Journal of Economics,
75:508–520, 2007.
M. Krawczyk. A glimpse through the veil of ignorance: Equality of opportunity andsupport for redistribution. Journal of Public Economics, 94(1-2):131–141, 2010.
26

J. Maurice, A. Rouaix, and M. Willinger. Income redistribution and public good
provision: An experiment. International Economic Review, 54(3):957–975, 2013.
F. Ohtake, Y. Kinari, N. Mizutani, and T. Mori. Income, giving, and egalitarianism:
A real-eﬀort experiment in japan. Journal of Behavioral Economics and Finance,
6:81–84, 2013. (in Japanese).
R. J. Oxoby and J. Spraggon. A clear and present minority: Heterogeneity in thesource of endowments and the provision of public goods. Economic Inquiry, 51(4):2071–2082, 2013.
E. E. Rutström and M. B. Williams. Entitlements and fairness: an experimental
study of distributive preferences. Journal of Economic Behavior and Organization,
43(1):75–89, 2000.
P. G. Straub. Risk dominance and coordination failures in static games. Quarterly
Review of Economics and Finance, 35(4):339–363, 1995.
A. Tavoni, A. Dannenberg, G. Kallis, and A. Lösche. Inequality, communication, andthe avoidance of disastrous climate change in a public goods game. Proceedingsof the National Academy of Science, 108(29):11825–11829, 2011.
J.-R. Tyran and R. Sausgruber. A little fairness may induce a lot of redistribution
in democracy. European Economic Review, 50(2):469–485, 2006.
N. Uler. Public goods provision, inequality and taxes. Experimental Economics, 14:
287–306, 2011.
J. B. Van Huyck, R. C. Battalio, and R. O. Beil. Tacit coordination games, strategic
uncertainty, and coordination failure. American Economic Review, 80(1):234–248,
March 1990.

27

1

Appendix
Instruction
For those who will participate in the experiment
The experiment we are about to conduct will be used as academic material to analyze your choice behavior.
You will be asked to make choices according to the following rules. Through those choices, you will earnpoints. All the points you earn will be converted to cash at a rate of 1.3 yen per point, which will be paid toyou at the end of the experiment. All instructions for making the choices will be shown on the computer
screen in front of you. The experiment is divided into four parts.

Part 1
Explanation of the experimentOnce the experiment begins, the computer will first randomly choose half of the participants as selectors. In
Part 1, only these selectors will make choices. There is nothing for those who were not chosen as a selector
to do in Part 1 of the experiment; if you were not chosen, please wait until Part 2 begins.

Those who were chosen as selectors will be asked to make six rounds of selections, as explained below. First,
a selector will be paired with an individual who was not chosen as a selector. A selector will not be pairedwith another selector. Likewise, individuals who were not chosen as selectors will not be paired together.
The individual you are going to be paired with will be randomly determined by the computer for each roundof selection.

The selector will choose one of four options, A, B, C, and D. Based on the choice made by the selector,
points are determined for you (the selector) and your counterpart (an individual who was not chosen as aselector).

Points for Your

OptionsYour Points

A

Numerical value a

Numerical value b

B

Numerical value c

Numerical value dCNumerical value e

Numerical value fD

Numerical value g

Numerical value hCounterpart

The table above shows the four options and their corresponding points for you and your counterpart. During
the experiment, a through h will have specific numerical values and will change in each round.

2
For example, when, as the selector, you choose B, you will the receive points shown for the numerical valuec, while your counterpart (an individual who was not chosen as a selector) will receive the points shown for
numerical value d.

Formulae to Derive Points
Points for you (the selector) and your counterpart (an individual who was not chosen as a selector) arecalculated according to the following formulae.
Your points ＝ 100 × M × N ＋ 60 × (1 － M) ＋ s × (1 － N)
Points for your counterpart ＝ 100 × M × N ＋ 60 × (1 － N) ＋ t × (1 － M)
M and N will each have a value of either 0 or 1; their combinations correspond to the options as follows:
Option A in the table above: M = 0 and N = 0
Option B in the table above: M = 0 and N = 1
Option C in the table above: M = 1 and N = 0
Option D in the table above: M = 1 and N = 1
The values of s and t are different and change in each round.

Numerical Value Example 1
Let us say the value of s is 30 and the value of t is 100. In this case, points will be given as follows:

When you choose Option A (M = 0, N = 0),
Your points = 100 × 0 × 0 + 60 × (1 - 0) + 30 × (1 - 0) = 90
Points for your counterpart = 100 × 0 × 0 + 60 × (1 - 0) + 100 × (1 - 0) = 160.

When you choose Option B (M = 0, N = 1),
Your points = 100 × 0 × 1 + 60 × (1 - 0) + 30 × (1 - 1) = 60
Points for your counterpart = 100 × 0 × 1 + 60 × (1 - 1) + 100 × (1 - 0) = 100.

When you choose Option C (M = 1, N = 0),
Your points = 100 × 1 × 0 + 60 × (1 - 1) + 30 × (1 - 0) = 30
Points for your counterpart = 100 × 1 × 0 + 60 × (1 - 0) + 100 × (1 - 1) = 60.

When you choose Option D (M = 1, N = 1),
Your points = 100 × 1 × 1 + 60 × (1 - 1) + 30 × (1 - 1) = 100
Points for your counterpart = 100 × 1 × 1 + 60 × (1 - 1) + 100 × (1 - 1) = 100.

In other words, the point table in this example will be as follows.

3
Points for Your

OptionsYour Points

A

90

160

B

60

100

C

30

60

D

100

100

Counterpart

Numerical Value Example 2
Let’s say the value of s is 140 and the value of t is 55. In this case, the points will be as follows:

When you choose Option A (M = 0, N = 0),
Your points = 100 × 0 × 0 + 60 × (1 - 0) + 140 × (1 - 0) = 200
Points for your counterpart = 100 × 0 × 0 + 60 × (1 - 0) + 55 × (1 - 0) = 115.

When you choose Option B (M = 0, N = 1),
Your points = 100 × 0 × 1 + 60 × (1 - 0) + 140 × (1 - 1) = 60
Points for your counterpart = 100 × 0 × 1 + 60 × (1 - 1) + 55 × (1 - 0) = 55.

When you choose Option C (M = 1, N = 0),
Your points = 100 × 1 × 0 + 60 × (1 - 1) + 140 × (1 - 0) = 140
Points for your counterpart = 100 × 1 × 0 + 60 × (1 - 0) + 55 × (1 - 1) = 60.

When you choose Option D (M = 1, N = 1),
Your points = 100 × 1 × 1 + 60 × (1 - 1) + 140 × (1 - 1) = 100
Points for your counterpart = 100 × 1 × 1 + 60 × (1 - 1) + 55 × (1 - 1) = 100.

The point table in this example will be as follows.

Points for Your

OptionsYour Points

A

200

115

B

60

55

C

140

60

D

100

100

Counterpart

4
Explanation of the Computer Screens and Tasks to Be Performed During the Experiment
Screen for the selector
Round

OptionsYour Points

Points for YourCounterpart

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Numerical
数値 value

Value of s

Numerical value
数値

Value of t

数値
Numerical value

Please choose one of the above Options A, B, C, and D.

The above screen will be displayed for those who are chosen as selectors. The selection round is shown at
the top of the screen. In the above example, the round is the first of six.

Four options and their corresponding points for you and your counterpart are shown in the center of thescreen. These points will change each round. Below that, you will find the values of s and t that are used in
the formulae to derive the points. Below that are the selection buttons.

First, please choose one option from A, B, C, and D and write it under “Your Choice” on the record sheet.
Please also write why you made that choice in the “Reasons for Your Choice” section.

When you’ve finished writing, please click on the button for the option you wrote in “Your Choice.”

Once all selectors click on an option button, the next round will begin. This completes one round of selection.
This is repeated six times.

5
Screen for those who were not chosen as a selector

You were not chosen as a selector.
You will not make choices during Part 1 of the experiment.
Please wait until Part 2 begins.

The above screen will be displayed for those who were not chosen as selectors. Please wait until Part 2
begins, as you will not make choices in Part 1 of the experiment.

You will now have three minutes to review the details of the experiment. If you have a question, please raise
your hand quietly and the experimenter will answer you one-to-one. Please note that you are not allowed tocommunicate with the other participants.

1Part 2
Explanation of the Experiment Details
Everyone will be asked to make choices starting in Part 2. You will make six rounds of selections as
explained below. First, you will be paired with another participant. The individual you are paired with will
be randomly chosen by the computer for each round of selection.

You will choose one of two options, X and Y. The points for you and your counterpart will be determined on
the basis of the choices you and your counterpart make.

Choice of Your Counterpart

X

X

Y

Numerical value a,

Numerical value c,

Numerical value b

Numerical value d

Numerical value e,

Numerical value g,

Numerical value b

Numerical value hYour ChoiceY

The X and Y on the left side represent your choice and the X and Y on the top represent the choice of yourcounterpart. The two numerical values in each cell represent the points for you and your counterpart
corresponding to each combination of choices. The value on the left in each cell is your points and the valueon the right is the points for your counterpart. During the experiment, numerical points a through h will havespecific values and will change in each round.

For example, when your choice is X and the choice of your counterpart is Y, you will receive the points
shown by numerical value c and your counterpart will receive the points shown by numerical value d.

Formulae to Derive Points
Your choices are 0 (X) and 1 (Y). Points for you and your counterpart are calculated according to thefollowing formulae.
Your points ＝ 100 × (your choice) × (choice of your counterpart)＋ 60 × (1 － your choice) ＋ s × (1 － choice of your counterpart)
Points for your counterpart ＝ 100 × (your choice) × (choice of your counterpart)＋ 60 × (1 － choice of your counterpart) ＋ t × (1 － your choice)
The values of s and t are different and change in each round.

2
Numerical Value Example 1
Let us say the value of s is 30 and the value of t is 100. In this case, the points will be as follows:

When you choose 0 (X) and your counterpart chooses 0 (X),Your points ＝ 100 × 0 × 0 ＋ 60 × (1 － 0) ＋ 30 × (1 － 0) ＝ 90
Points for your counterpart＝ 100 × 0 × 0 ＋ 60 × (1 － 0) ＋ 100 × (1 － 0) ＝ 160
When you choose 0 (X) and your counterpart chooses 1 (Y),Your points ＝ 100 × 0 × 1 ＋ 60 × (1 － 0) ＋ 30 × (1 － 1) ＝ 60
Points for your counterpart ＝ 100 × 0 × 1 ＋ 60 × (1 － 1) ＋ 100 × (1 － 0) ＝ 100
When you choose 1 (Y) and your counterpart chooses 0 (X),Your points ＝ 100 × 1 × 0 ＋ 60 × (1 － 1) ＋ 30 × (1 － 0) ＝ 30
Points for your counterpart ＝ 100 × 1 × 0 ＋ 60 × (1 － 0) ＋ 100 × (1 － 1) ＝ 60
When you choose 1 (Y) and your counterpart chooses 1 (Y),Your points ＝ 100 × 1 × 1 ＋ 60 × (1 － 1) ＋ 30 × (1 － 1) ＝ 100
Points for your counterpart ＝ 100 × 1 × 1 ＋ 60 × (1 － 1) ＋ 100 × (1 － 1) ＝ 100
The point table in this example will be as follows.

Choice of Your Counterpart
XYX

90, 160

60, 100

Y30, 60100, 100Your Choice3
When the choice of your counterpart is 0 (X) and your choice is changed from 0 to 1, the points for you andyour counterpart can be graphed as follows.

PointsPoints for You and Your Counterpart When Your Choice Is
Changed from 0 to 1 (When the Choice of Your Counterpart is 0)

YouYour Counterpart

Your Choice

When the choice of your counterpart is 1 (Y) and your choice is changed from 0 (X) to 1 (Y), the points foryou and your counterpart can be graphed as follows.

PointsPoints for You and Your Counterpart When Your Choice Is
Changed from 0 to 1 (When the Choice of Your Counterpart is 1)

You
Your Counterpart

Your Choice

4
Numerical Value Example 2
Let us say the value of s is 140 and the value of t is 55. In this case, the points will be as follows:

When you choose 0 (X) and your counterpart chooses 0 (X),Your points ＝ 100 × 0 × 0 ＋ 60 × (1 － 0) ＋ 140 × (1 － 0) ＝ 200
Points for your counterpart＝ 100 × 0 × 0 ＋ 60 × (1 － 0) ＋ 55 × (1 － 0) ＝ 115
When you choose 0 (X) and your counterpart chooses 1 (Y),Your points ＝ 100 × 0 × 1 ＋ 60 × (1 － 0) ＋ 140 × (1 － 1) ＝ 60
Points for your counterpart ＝ 100 × 0 × 1 ＋ 60 × (1 － 1) ＋ 55 × (1 － 0) ＝ 55
When you choose 1 (Y) and your counterpart chooses 0 (X),Your points ＝ 100 × 1 × 0 ＋ 60 × (1 － 1) ＋ 140 × (1 － 0) ＝ 140
Points for your counterpart ＝ 100 × 1 × 0 ＋ 60 × (1 － 0) ＋ 55 × (1 － 1) ＝ 60
When you choose 1 (Y) and your counterpart chooses 1 (Y),Your points ＝ 100 × 1 × 1 ＋ 60 × (1 － 1) ＋ 140 × (1 － 1) ＝ 100
Points for your counterpart ＝ 100 × 1 × 1 ＋ 60 × (1 － 1) ＋ 55 × (1 － 1) ＝ 100
In other words, the point table in this example will be as follows.

Choice of Your Counterpart
X

Y

X

200, 115

60, 55

Y

140, 60

100, 100Your Choice5
When the choice of your counterpart is 0 (X) and your choice is changed from 0 to 1, the points for you andyour counterpart can be graphed as follows.

PointsPoints for You and Your Counterpart When Your Choice Is
Changed from 0 to 1 (When the Choice of Your Counterpart is 0)

YouYour Counterpart

Your Choice

When the choice of your counterpart is 1 (Y) and your choice is changed from 0 (X) to 1 (Y), the points foryou and your counterpart can be graphed as follows.

PointsPoints for You and Your Counterpart When Your Choice Is
Changed from 0 to 1 (When the Choice of Your Counterpart is 1)

You
Your Counterpart

Your Choice

6
Explanation of the Computer Screen and the Tasks to Be Performed during the Experiment
Selection screen
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical
数値 value

Value of t

Numerical
数値 value

Please choose X or Y.

The selection screen will display the above. The point table is displayed in the center of the screen. Below it,you will find the values of s and t that are used in the formulae to derive the points. Below that are theselection buttons.

First, please choose X or Y and write it under “Your Choice” on the record sheet. Please also write why you
made that choice in the “Reasons for Your Choice” section.

When you finish writing, please click on the button for the option you wrote in “Your Choice.”

Once everyone clicks a selection button, the next round will begin.

7
Results screen
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical
数値 value

Value of t

数値 value
Numerical

Your choice
Choice of your counterpart
Your points

Numerical
数値 value

Points for your counterpart

Numerical
数値 value

Next

The results screen will display the above. The values of s and t that are used in the formulae to derive thepoints, your choice, the choice of your counterpart, your points, and the points for your counterpart are
displayed below the center of the screen.

First, please write the choice of your counterpart displayed on the screen under “Choice of YourCounterpart” on the record sheet. Please also write your points displayed on the screen in the “Your Points”
section.

When you finish writing, please click on the Next button at the lower right of the screen.

Once all subjects click the Next button, the next round will begin. This will complete the first round of
selection. This process is repeated six times.

You will now have three minutes to review the details of the experiment. If you have a question, please raise
your hand quietly and the experimenter will answer you one-to-one. Please note that you are not allowed tocommunicate with the other participants.

1Part 3
Explanation of the Experiment Details
You will make six rounds of selections as explained below. First, you will be paired with another participant.
The individual you are paired with will be randomly chosen by the computer for each round of selection.
This part is composed of two stages.

Stage 1
You will choose one of two options, X and Y. The points for you and your counterpart will be determined on
the basis of the choices you and your counterpart make.

Choice of Your Counterpart

X

X

Y

Numerical value a,

Numerical value c,

Numerical value b

Numerical value d

Numerical value e,

Numerical value g,

Numerical value f

Numerical value hYour ChoiceY

This point table is read the same way as the previous one. Points a through h will each have a specificnumerical value during the experiment and will change in each round. The numerical values in the point
table are derived by the method explained in Part 2.

Stage 2After verifying each other’s choice and points in Stage 1, you will have an opportunity to give some of yourpoints to your counterpart.

For example, let us say that your choice was X and the choice of your counterpart was Y in Stage 1 and thatyou and your counterpart earned c points and d points, respectively. Furthermore, let us say that you andyour counterpart decided to give 10 points and 15 points to each other, respectively, in Stage 2. In this case,your final points will be c – 10 + 15, while the points for your counterpart will be d – 15 + 10.

Note: please choose an integer of 0 or larger that is smaller than the number of points you earned in Stage 1
to give to your counterpart.

2
Explanation of the Computer Screen and the Tasks to Be Performed during the Experiment
Selection screen in Stage 1
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical value
数値

Value of t

数値
Numerical value

Please choose X or Y.

The selection screen in Stage 1 will display the above. The point table is displayed in the center of the screen.
Below it, you will find the values of s and t that are used in the formulae to derive the points. Below that are
the selection buttons.

First, please choose X or Y and write it under “Your Choice in Stage 1” on the record sheet. Please also write
why you made that choice in the “Reasons for Your Choice in Stage 1” section.

When you finish writing, please click on the button for the option you wrote in “Your Choice in Stage 1.”

Once all subjects click on a selection button, you will proceed to the selection screen in Stage 2.

3
Selection screen in Stage 2
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical
数値
value

Value of t

数値
Numerical
valueYour choice
Choice of your counterpart

Please choose the number of points to give to your counterpart
数値(within the range of 0 and Numerical).value

The selection screen in Stage 2 will display the above. The values of s and t that are used in the formulae toderive the points as well as your choice and the choice of your counterpart in Stage 1 are displayed in thecenter of the screen. Below that is the selection box.

First, please write the choice of your counterpart displayed on the screen under “Choice of Your Counterpart
in Stage 1” on the record sheet.

Next, please write the number of points you are giving to your counterpart under “Your Choice in Stage 2”
on the record sheet. For the number of points to give, please choose an integer that is 0 or larger that does notexceed the number of points you earned in Stage 1. Please also write why you made that choice in the“Reasons for Your Choice in Stage 2” section.

When you finish writing, please enter the numerical value you wrote in “Your Choice in Stage 2” and click
the OK button on the lower right.

Once all subjects click on the OK button, you will proceed to the results screen.

4
Results screen
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical value
数値

Value of t

数値
Numerical value

Points you gave to your counterpart

Numerical value
数値

Points you received from your counterpart

数値
Numerical valueYour final points

Numerical value
数値

Final points for your counterpart

数値
Numerical value

Next

The results screen will display the above. The values of s and t that are used in the formulae to derive thepoints as well as points you gave to your counterpart, points you received from your counterpart, your final
points, and the final points for your counterpart are displayed in the center of the screen.

First, please write the points you received from your counterpart as displayed on the screen under “Choice ofYour Counterpart in Stage 2” on the record sheet. Please also write your final points displayed on the screenin the “Your Point” section in the record sheet.

When you finish writing, please click the Next button on the lower right of the screen.
Once all subjects click on the Next button, the next round will begin. This will complete the first round of
selection. This process is repeated six times.

You will now have three minutes to review the details of the experiment. If you have a question, please raise
your hand quietly and the experimenter will answer you one-to-one. Please note that you are not allowed tocommunicate with the other participants.

5Part 4
Explanation of the Experiment Details
You will make six rounds of selections as explained below. First, you will be paired with another participant.
The individual you are paired with will be randomly chosen by the computer for each round of selection.
Part 4 is composed of three stages.

Stage 1After verifying the point table for Stage 2 (explained later), you will choose whether to proceed to Stage 3(choose Yes; explained later) or not (choose No).

If you or your counterpart (or both) choose Yes, you will proceed to Stage 3. When both of you choose No,
you will not proceed to Stage 3, and the points you earned in Stage 2 will become your final points.

Stage 2After verifying each other’s choice in Stage 1 and determining whether to proceed to Stage 3, you will
choose one of two options, X and Y. The points for you and your counterpart will be determined on the basisof the choices you and your counterpart make.

Choice of Your Counterpart

X

X

Y

Numerical value a,

Numerical value c,

Numerical value b

Numerical value d

Numerical value e,

Numerical value g,

Numerical value f

Numerical value hYour ChoiceY

This point table is read in the same way as the previous ones. Points a through h will have a specificnumerical value during the experiment and will change in each round. The numerical values in the point
table are derived by the method explained in Part 2.

Stage 3After verifying each other’s choice and points in Stage 2, you will have an opportunity to give some of thepoints you have to your counterpart.

Please choose an integer of 0 or larger that is smaller than the number of points you earned in Stage 2 as thenumber of points to give to your counterpart.

6
Explanation of the Computer Screen and the Tasks to Be Performed during the Experiment
Selection screen in Stage 1
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Point Table for Stage 2
Value of s

Numerical value
数値

Value of t

数値
Numerical value

Do you wish to proceed to Stage 3 (the stage where you decide how many points togive to your counterpart)?

The selection screen in Stage 1 will display the above. The point table in Stage 2 is displayed in the center ofthe screen. Below it, you will find the values of s and t that are used in the formulae to derive the points.
Below that are the selection buttons.

First, please choose Yes or No and write it under “Your Choice in Stage 1” on the record sheet. Please also
write why you made that choice in the “Reasons for Your Choice in Stage 1” section.

When you finish writing, please click on the button for the option you wrote in “Your Choice in Stage 1.”

Once everyone clicks a selection button, you will proceed to the selection screen in Stage 2.

7
Selection screen in Stage 2
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical
数値
value

Value of t

数値
Numerical
valueYour choice
Choice of your counterpart
You and your counterpart will proceed to Stage 3 (the stage where you decide how
many points to give to your counterpart).
Please choose X or Y.

The selection screen in Stage 2 will display the above. The values of s and t that are used in the formulae toderive the points, your choice and the choice of your counterpart in Stage 1, and whether to proceed to Stage
3 (the stage where you decide how many points to give to your counterpart) are displayed in the lower centerof the screen.

First, please write down the choice of your counterpart displayed on the screen under “Choice of YourCounterpart in Stage 1” on the record sheet.

Next, please choose X or Y and write it in the “Your Choice in Stage 2” section in the record sheet. Pleasealso write why you made that choice in the “Reasons for Your Choice in Stage 2” section.

When you finish writing, please click on the button for the option you wrote in “Your Choice in Stage 2.”Once all subjects click on a selection button, the selection screen in Stage 3 will be displayed to the pairs
who are proceeding to Stage 3. For those not proceeding to Stage 3, the screen will say, “Other participants
are playing. Please wait for a while.” Please wait until the results screen is displayed.

8
Selection screen in Stage 3
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical value
数値

Value of t

数値
Numerical
valueYour choice
Choice of your counterpart

Please choose the number of points to give to your counterpart
数値(within the range between 0 and Numerical value ).

The above screen will be displayed for the pairs who proceeded to Stage 3. The values of s and t that areused in the formulae to derive the points as well as your choice and the choice of your counterpart in Stage 2
are displayed in the lower center of the screen. Below that is the selection box.

First, please write down the choice of your counterpart displayed on the screen under “Choice of YourCounterpart in Stage 2” in the record sheet.

Next, please write down the number of points you are giving to your counterpart in the “Your Choice inStage 3” section in the record sheet. To give points, please choose an integer that is 0 or larger that does notexceed the number of points you earned in Stage 2. Please also write why you made that choice in “Reasonsfor Your Choice in Stage 3.”

When you finish write, please enter the numerical value you wrote in the “Your Choice in Stage 3” section
and click the OK button on the lower right.

Once all the subjects who proceeded to Stage 3 click on the OK button, you will proceed to the results
screen.

9
Results screen for those proceeding to Stage 3
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical value
数値

Value of t

Numerical value
数値

Points you gave to your counterpart

Numerical value
数値

Points you received from your counterpart

数値
Numerical valueYour final points

Numerical
value
数値

Final points for your counterpart

数値
Numerical
value

Next

When you proceed to Stage 3, the results screen will display the above. The values of s and t that are used in
the formulae to derive the points, the points you gave to your counterpart, the points you received from yourcounterpart, your final points, and the final points for your counterpart are displayed in the lower center ofthe screen.

First, please write down the choice of your counterpart displayed on the screen under “Choice of YourCounterpart in Stage 3” in the record sheet. Please also write down your final points displayed on the screenin the “Your Points” section.

When you finish writing, please click the Next button on the lower right of the screen.

Once all subjects click on the Next button, the next round will begin.

10
Results screen for those not proceeding to Stage 3
Round

Choice of YourCounterpart

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Numerical
数値
value

Your Choice

Value of s

Numerical value
数値

Value of t

数値
Numerical valueYour choice
Choice of your counterpart
Your final points

Numerical value
数値

Final points for your counterpart

数値
Numerical value

Next

If you did not proceed to Stage 3, the results screen will display the above. The values of s and t that are usedin the formulae to derive the points, your choice and the choice of your counterpart in Stage 2, your final
points, and the final points for your counterpart are displayed in the lower center of the screen.

First, please write down the choice of your counterpart displayed on the screen under “Choice of YourCounterpart in Stage 2” in the record sheet. Please also write down your final points displayed on the screenin the “Your Points” section. You do not need to fill out “Your Choice in Stage 3,” “Reason for Making the
Choice You Made in Stage 3,” or “The Choice of Your Counterpart in Stage 3.”

When you finish writing, please click the Next button on the lower right of the screen.

Once all subjects click on the Next button, the next round will begin. This completes one selection. This
process is repeated six times.

You will now have three minutes to review the details of the experiment. If you have a question, please raise
your hand quietly and the experimenter will answer you one-to-one. Please note that you are not allowed tocommunicate with the other subjects.