Sorting in Experiments

with Application to Social Preferences*

Edward P. Lazear Ulrike Malmendier Roberto A. Weber

Stanford University and NBER

UC Berkeley and NBER

Carnegie Mellon University

October 30, 2006

Abstract

In many field settings, participants sort among environments based on their prefer-

ences, beliefs, and skills. Experiments, however, often ignore the potential impact of such

sorting. We demonstrate the importance of sorting for experiments, in the domain of social

preferences. When individuals are constrained to play a dictator game, 61% of the subjects

share. But when subjects are allowed to avoid the situation altogether, only 23% share. This

reversal of proportions illustrates the importance of sorting for drawing inferences from ex-

perimental findings to the field. In a second experiment, we subsidize participation in the dic-

tator game with higher payoffs relative to opting out. We find that the subjects whom the in-

creased payoffs attract back into the sorting environment are primarily those who share the

least. Thus, even with subsidization, the portion shared by participants remains much lower

than without sorting. A second consequence of sorting, then, is that incentives aimed at entic-

ing pro-social behavior can induce adverse selection. Both experiments also shed light on the

motives for sharing. While much sharing is consistent with other-regarding preferences, the

majority of sharers prefer to avoid the sharing environment.

* We thank Colin Camerer, Stefano DellaVigna, Hank Farber, Glenn Harrison, Larry Katz, Georg Weizsäcker, Jordi Brandts as well as seminar participants at the University of Arizona, UC Berkeley, University of Chicago, Cornell University, the European University Institute, Harvard University, Hebrew University of Jerusalem, the London School of Economics, Nottingham University, Stanford University, University of Maryland, University of Wisconsin, the 2004 IMEBE meetings, the 2005 NBER Labor Studies Program Meeting, the 2005 Economic Science and ESSLE meetings for helpful comments. We also thank Jason Dana, Scott Rick, Aniol Llorente and David Rodriguez for help in conducting the experiments and the Pittsburgh Experimental Economics Laboratory (PEEL) and the Laboratori d'Economia Experimental (LEEX) for access to their resources.

1

I. Introduction

Experiments are an important part of every science, including economics. The controlled

laboratory environment provides insights into behavior that cannot be studied easily in the

field. It allows scientists to answer the “what ifs” that are hard to address in the complex and

dynamic world outside the laboratory.

However, such control comes at a cost. Experiments simplify many features of natu-

rally-occurring economic environments. One such feature is the opportunity to sort among

environments. By design, most experiments select a random sample of subjects and lock them

into a specific experimental environment. Non-laboratory environments operate differently –

in the field, individuals can sort into and out of environments based on their preferences, be-

liefs, or skills.1 Thus, the individuals who choose to participate in a market are unlikely to be

a random sample of the population. For example, while a significant portion of randomly se-

lected individuals may suffer from acrophobia, those who build skyscrapers are unlikely to be

among the sufferers. As a result, there will be no wage premium for working at height if there

are a sufficient number of non-acrophobic construction workers. Market wages reflect the

preferences of the marginal individual employed, not those of the average individual in the

population.2 It is equally conceivable that sorting in markets may exacerbate rather than miti-

gate a laboratory phenomenon. Overconfidence, for example, may not be common in the

population. But those who sign up for a health club membership might be prone to overesti-

mating their future self-control, which would explain the low average attendance of members

who pay a high monthly fee.3

1 We use the term “sorting” to describe agents’ voluntary choice of an activity, and the term “selection” to dis-cuss the representativeness of a sample. 2 Cf. the literature on equalizing wage differentials and hedonic prices following Rosen (1974). 3 See DellaVigna and Malmendier (2006), who show, using field data, that subscribers to health clubs do not

2

While some authors see the lack of sorting in the laboratory as a weakness of experi-

mental research (Levitt and List, 2006), we emphasize a different conclusion. We show that

sorting can be usefully introduced within experiments. Allowing laboratory subjects to

endogenously select environments sheds light on the impact of such a choice in the field.

We report two laboratory experiments on social preferences with and without the pos-

sibility of sorting. Our experiments utilize the well-known dictator game, in which one of two

anonymously matched subjects (the dictator) decides how much of a given surplus to send to

the other person (the receiver).4 The standard result is that a significant portion of dictators

give a positive amount to an anonymous receiver, even when their action is not observable by

anyone, including the experimenter (see Camerer, 2003; Hoffman et al., 1994). Such sharing

is usually interpreted as reflecting a stable preference for equitable outcomes or altruism (Fehr

and Schmidt, 1999; Bolton and Ockenfels, 2000; Charness and Rabin, 2002; Andreoni and

Miller, 2002).

Other-regarding preferences are, however, not the only reason to share. Individuals

may feel compelled to give upon request even though they prefer to avoid the sharing situa-

tion in the first place. We introduce such an alternative motivation for sharing – individuals

“dislike not sharing” – in a simple model of social preferences. As shown in the model, agents

who share because they dislike not sharing would be undetectable in the absence of sorting.

Our experiments introduce to the dictator game the option not to participate. This sort-

ing option allows us to tease apart different motivations for sharing. Our results also help rec-

take into account their own behavior to minimize the costs of their subscriptions. 4 We chose the dictator game for two reasons. First, in order to test the effect of sorting on a particular behavior, it is helpful to start with the simplest task that captures that behavior (and little else). The dictator game is the simplest environment in which to demonstrate and test the prevalence of a propensity to share. Second, the shar-ing result of the dictator game is quite robust to most manipulations. Sharing is usually close to 20 percent, and the distributions of the amount shared differ little between most experiments and treatments (see Camerer 2003). Our non-sorting treatments replicate this result.

3

oncile the high altruism parameters estimated in the laboratory with less generous sharing be-

havior observed in the field.

In our first experiment, we show that the sharing behavior in dictator games funda-

mentally changes with the introduction of sorting. That is, we allow dictators not to play the

game – in which case they simply keep the endowment and the recipients never find out that a

game could have been played. We find that in the standard dictator game without a sorting

option most share (61%). With a sorting option, however, only very few do so (23%). The

average percentage of the endowment shared also decreases significantly, from 19% to 6%.

Thus, the majority of individuals who share in a (non-avoidable) dictator game prefer to avoid

the game altogether. These results are consistent with the predictions of our model under the

assumption that some people share only because they feel compelled to do so.

Our second experiment uses a within-subjects design to elicit individuals’ willingness

to pay for avoiding the dictator game. We first present all subjects with a standard dictator

game to measure their propensity to share conditional on being in a sharing environment.

They then play several games with sorting. In these rounds, we increase the amount of surplus

in the dictator game but leave the value of the outside option constant, thus producing a mone-

tary incentive to (re-)enter the dictator game. As in the between-subjects experiment, we find

that the sorting option sharply decreases the percentage of those who share (from 74% to

30%) as well as the average portion of the endowment shared (from 27% to 12%). Moreover,

as also predicted by our model, higher monetary incentives to play the game attract first and

foremost those who share the least. That is, among those who share in a dictator game but

would prefer to avoid the game altogether, those who share the least are the first to re-enter

the dictator game when the endowment increases.

4

The implications of our results are threefold.

First, our analysis demonstrates that sorting affects the applicability of laboratory ex-

periments to market settings. Experiments without sorting can induce significantly different

behavior than observed outside the laboratory, where sorting is possible. However, this con-

clusion does not question the value of experiments for the analysis of economic markets.5

Rather, our analysis provides an example of how a simple adjustment to experimental design

can help account for the potential influence of sorting on economic outcomes.

Second, the observed sorting behavior sheds light on the question of what drives social

behavior. We show that many people who share in a given environment sort out of that envi-

ronment, and are even willing to pay a premium to do so. Therefore, our findings suggest that

much sharing results from a disutility of not giving rather than from a stable preference for

behaving fairly or kindly.6 An interpretation of our results that is more in the spirit of the lit-

erature on social preferences is to assume that subjects care about other players only if they

interact with them, in this case through the dictator game. By sorting out, inequity-averse sub-

jects (Fehr and Schmidt, 1999) avoid the disutility associated with inequality. Under this in-

terpretation, as in our model, social preferences are not stable but depend on the environment

5 Critics have questioned the applicability of experimental results to “real people” performing “real tasks” with “real incentives” (cf. Harrison and List, 2004). Many such criticisms have been successfully addressed in the past, for example by replicating experiments under conditions more similar to field settings – for instance, with higher stakes (Hoffman, McCabe & Smith, 1996; Cameron, 1999; Camerer & Hogarth, 1999; Fehr, Fischbacher & Tougareva, 2002) or with professionals rather than college students (see the overview and discussion in Harri-son and List (2004), Section 4). The point of our paper is different from this debate. Rather than arguing that the samples used in experiments may be too narrow to reflect behavior in the overall population, we ask whether the selection approach is too broad to make inferences about market outcomes. In addition, we point to the potential of laboratory experiments to analyze the role of sorting directly, by the introduction of this naturally-occurring feature into experiments. 6 Our work builds on work in psychology showing that individuals who behave pro-socially are often willing to reverse these choices (at a cost), or that people about to be asked for help by a stranger terminate communication before the request can be made (Dana, Cain, and Dawes, forthcoming; Gaertner, 1973). Our work is also related to other recent work in economics demonstrating that people will rely on the context and (seemingly irrelevant) justifications for acting self-interestedly (Oberholzer-Gee and Eichenberger, 2004, and Dana, Weber, and Kuang, forthcoming).

5

that individuals themselves can choose.

Third, we show that policy interventions or market institutions can exacerbate the dis-

crepancy between the behavior of randomly drawn samples in experiments and self-selected

samples in markets. While targeting the average individual they may affect primarily those

whose behavior is furthest from that of the average. In the context of our experiment, suppose

that, to induce more giving, policy-makers pay people to enter a sharing environment akin to

playing the dictator game. The interaction between sorting and preferences will dramatically

affect the impact of this policy. People who like sharing are giving already. Among the people

currently not giving, the incentives will attract mostly those who share the least. To attract

those who do not derive pleasure from giving, but who would share the most once in an envi-

ronment that allows sharing, the highest payment is required. As a result the policy interven-

tion will be less effective than predicted on the basis of average behavior in the population.7

The paper proceeds as follows. In Section II, we present a model that allows for dif-

ferent motives for sharing and produces several testable predictions for our experiments. The

design and results of Experiment 1 are presented in Section III, while Section IV does so for

Experiment 2. Section V concludes.

II. Model

We present a framework that embeds a broad range of motives for sharing. The distinction

between different motivations is, however, often subtle. For example, is a person who consis-

7 Our analysis mirrors the discussion in the labor literature on the estimation of treatment effects on the “un-treated” rather than the “treated” (e.g. Angrist and Krueger, 1999; Heckman 1997). There, however, the concern is that a sample is too narrow to identify the effect on the untreated. Here, we worry that the sample is too broad to make inferences about the treated. We also add to a small, but important, set of experimental papers that ad-dress the role of selection in other contexts such as the prisoner’s dilemma (Bohnet and Kübler 2005), the choice of reward and punishment (Sutter, Kocher, and Haigner 2006; Botelho, Harrison, Pinto, and Rutström, 2005), incentive contracts (Eriksson and Villeval, 2004; Dohmen and Falk, 2005), auctions (Palfrey and Pevnitskaya, 2003), risky choices (Harrison, Lau and Rutström, 2005), and market entry games (Camerer and Lovallo, 1999).

6

tently shares but is motivated by the pride she derives from giving and does not care about the

receiver “other-regarding”? To avoid such issues of interpretation, we classify agents simply

based on their observed behavior. The model distinguishes three types of preferences: agents

who dislike sharing, agents who like sharing, and agents who dislike not sharing.

The first type, who dislikes sharing, never shares. This type can be thought of as the

standard economic agent. The second type, who likes sharing, always shares, even when there

is an option to sort out of the dictator game. This type of preference captures a number of dif-

ferent motivations for sharing (see Andreoni, 1990). For example, the agent may feel altruistic

toward others, may enjoy the praise and recognition that comes from doing a good deed, or

may take pride in generous behavior. The third type, who dislikes not sharing, shares in the

dictator game but prefers to opt out if sorting is possible. There are various reasons why

agents may dislike not sharing. They may feel shame when others know that they had the op-

portunity to share, but behaved selfishly. Even in the absence of others observing their behav-

ior, they may feel guilty about having been selfish. Or they may feel neither guilt nor shame

but dislike the dirty looks of the passive agent when they do not share.

Two parameters are needed to characterize these preferences. One parameter deter-

mines how much agents share when in a sharing environment. The other parameter dictates

whether or not agents choose to be in the sharing environment. We start with a general formu-

lation of the utility function and will later focus on the concrete example of Cobb-Douglas-

type preferences (detailed in Appendix 1).

Consider an agent who is endowed with an amount w, which she has to divide into a

payoff for herself (x) and a payoff for another agent (y), as in the classic dictator game:

(1) x + y = w.

7

We allow utility to depend on the payoffs x and y as well as on the sharing environment:8

U = U(D, x, y)

where D is a dummy variable equal to 1 if the environment allows sharing and 0 if the alloca-

tion of w is exogenously determined. That is, under D = 1 the agent decides how to split w

with the other person. Under D = 0 the agent has no influence on how w is allocated. We will

analyze the case in which the full endowment w is allocated to the agent under D = 0.

We characterize an individual’s propensity to share in the sharing environment with

the parameter α. The agent allocates x to herself and y to the other person in accordance with

(2) x = αw

(3) y = (1– α)w

Individuals with α = 1 have standard preferences and dislike sharing. Individuals with α < 1

have non-standard preferences. They either like to share or they dislike not sharing. Those

who like to share would pay to be in the sharing environment. Those who dislike not sharing

would pay to avoid the sharing environment. Both kinds of agents behave identically in the

sharing environment if they have the same sharing propensity α; but they differ in their will-

ingness to pay to avoid that environment.

Now, suppose that the endowments in the two environments differ. In the sharing en-

vironment the individual is given w’ to divide, while in the non-sharing environment she re-

ceives a fixed amount w, which cannot be shared. We parameterize an individual’s willing-

ness to pay by the endowment in the sharing environment, ŵ = w’, at which she is indifferent

between entering the sharing environment and opting out, given a fixed endowment w outside

8 By including only “own payoff” and “others’ payoff”, we implicitly assume narrow framing. That is, the agent does not consider payoffs or wealth beyond payoffs from the current decision.

8

the sharing environment. The higher ŵ is, the larger is the individual’s disutility from being in

the sharing environment. Individuals who have ŵ < w like to share and are willing to pay for

the opportunity to share. Individuals who have ŵ > w dislike not sharing. They share when

forced into a sharing environment, but are willing to pay to avoid that environment altogether.

Put differently, they must be compensated with a higher endowed wealth, w′ > w, to voluntar-

ily choose the sharing environment. We assume that individuals who dislike sharing (α = 1)

share nothing and are not willing to pay to avoid the sharing environment (ŵ = w).9

Three propositions follow, which form the basis of the analysis of the experiments.

(All proofs are contained in Appendix 1.)

Proposition 1: Individuals who strictly prefer the sharing to the non-sharing environment

have values ŵ < w. Individuals who strictly prefer the non-sharing environment have ŵ > w.

Proposition 1 allows us to determine the sharing preferences. Given a choice between envi-

ronments with and without sharing and identical endowments (w′ = w), only those who like to

share choose the sharing environment. Thus, a treatment that gives players the choice distin-

guishes between those who like sharing and those who dislike not sharing.

The second proposition characterizes the effect of sorting on the amount y received by

the other person, either under D = 0 or under D = 1, which we denote as the “amount shared.”

Proposition 2: The average amount shared is (weakly) smaller when individuals can sort be-

tween environments than when they cannot sort. 9 This is a simplifying assumption, not a general statement (but also not required for our analysis). The model can be generalized to allow a more subtle distinction of types. For example, agents who share nothing in the sharing environment may still pay something to avoid being put in that environment. Such agents dislike sharing but have ŵ > w. Other agents may get some utility from sharing but feel compelled to share too much in a shar-ing environment. As a result, such agents avoid the sharing situation (and thus share nothing) despite their pref-erence for sharing. These agents like sharing but have ŵ > w. Additionally, an individual might dislike sharing in some ranges of w and like sharing in other ranges. For brevity and simplicity we will distinguish only the three basic types, based on their observable (“net”) sharing decision.

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Giving individuals the option to leave the sharing environment eliminates all of those who

were sharing only because they dislike not sharing. The sharing of those who like to share

remains unchanged; to them, the option to leave the sharing environment has no value. The

sharing of those who dislike sharing also remains unchanged; whether they are in the sharing

environment or not, the other person receives zero. However, those who were sharing only

because they dislike not sharing depart and total sharing declines.

Note that, at the same time, the average amount shared by those who choose to play

when sorting is possible may exceed the conditional average without sorting. This depends on

the distribution of α among those with ŵ < w compared to those with ŵ > w and on the num-

ber of non-sharers with ŵ = w, who decide to opt out.

Our last result describes the dynamic sorting decision of sharers who opt out given

equal endowments: How do they behave if the endowment in the sharing environment in-

creases? Our result here does not hold for any (unspecified) utility function but for a range of

specifications. We consider a modified Cobb-Douglas utility function, described in Appendix

1. This utility function is sufficient for the following proposition:

Proposition 3: The lowest endowment w′, at which individuals who dislike not sharing enter

the sharing environment decreases in α.

Proposition 3 allows us to address the question of who, among the dislike-not-sharing types,

first re-enters the sharing environment as the premium for doing so increases. The proposition

implies that the first to re-enter are those who will keep the most for themselves. Those, in-

stead, who share a lot (when forced into the sharing environment) stay out the longest and re-

quire the highest premium to voluntarily re-enter the sharing environment.

The positive relation between the amount shared and the compensation required for

10

entering the sharing environment implies adverse selection. Suppose that the endowment in

the sharing environment is increased above the outside option (w′ > w) in order to attract more

participants. Two types of people sort back very quickly, even for a small premium (above w):

(i) those who dislike sharing and keep everything for themselves; (ii) the stingiest among

those who dislike not sharing. That is, individuals who do not give much and then opt out are

quickest to re-enter the dictator game as the premium for playing rises. People who like shar-

ing are unaffected by the premium; they never leave the sharing environment. And people

who share a lot but only because they dislike not sharing are the last ones to re-enter.

As an illustration of the above result, consider the situation of encountering a beggar

on the street. Individuals who dislike not sharing will give money if facing the beggar, but

they might choose to cross the street to avoid the encounter. Consider two individuals A and

B with such preferences. If forced to encounter the beggar, individual A gives the beggar a

very small amount, while B gives a large amount. If given the opportunity to cross the street

without cost, both A and B choose to do so because neither likes giving to the beggar. Now

suppose that it is costly to cross the street, as it requires waiting at the street corner for 5 min-

utes until the light changes. The one most likely to wait for the light is individual B, who

would have given the beggar the larger amount of money. He has the most to gain from

avoiding the guilt-producing environment. Individual A gives the beggar only a small amount

and gains less by waiting to crossing the street.

We now have a series of predictions that can be borne out or refuted by experimental

evidence. First, a treatment that does not allow any option to avoid the sharing environment

will see sharing of (1-α)w. The amount shared gives us an estimate of the propensity to share

by subjects, but not of the reason for the sharing (like to share vs. dislike not sharing). It is,

11

however, possible to distinguish the reason for sharing by offering subjects a choice of envi-

ronments: one with an opportunity to share and another without sharing, but both with the

same endowment (w′ = w). The only sharers who choose the sharing environment are those

for whom ŵ < w, i.e., those who share because they like to share. Those who share because

they dislike not sharing (ŵ > w) opt out. Finally, those who dislike not sharing can be induced

into the sharing environment if compensated with a premium (w′ > w). However, the required

premium is higher the more an individual shared initially.

III. Experiment 1 (Between-Subjects Design)

Our first experiment uses a between-subjects design to compare outcomes in treatments with-

out and with sorting (Propositions 1 and 2). In the treatment with sorting, subjects who opt out

receive an amount equal to the full endowment in the dictator game (w = w’).

A. Experimental Design

Experiment 1 was conducted in Barcelona. Subjects were graduate and undergraduate stu-

dents at the Universitat Pompeu Fabra (UPF) and the Universitat Autònoma de Barcelona

(UAB).10 We conducted eight sessions – two of each treatment at each university. In total,

154 subjects participated, 76 subjects (38 dictators) in the No-Sorting treatment and 78 sub-

jects (39 dictators) in the Sorting treatment. Each session consisted of an even number of 12

to 22 participants and lasted 20 to 25 minutes.

Upon arriving at the experiment, subjects were told that they would receive €5 for

their participation and that they might earn additional money.11 Subjects randomly drew par-

ticipant numbers. Those with even numbers were told to follow the experimenter to an area

10 Instructions and materials for both experiments are in Appendices 2 to 4. Experiment 1 was conducted in Spanish (Castilian); the instructions are translated into English. The entire dataset is available from the authors. 11 At the time the sessions were conducted €1 was worth between $1.27 and $1.29.

12

outside the room. While all subjects were still in the room, the experimenter publicly an-

nounced that participants with even numbers would complete a brief questionnaire and would

receive no additional payment for doing so (beyond the €5 participation fee).

Once outside the main room, the even-numbered participants were asked to complete

the questionnaire and to then wait quietly for the experimenter to return. They were also in-

formed that some of them might be asked to return to the room for a brief additional activity.

After the even-numbered participants left the room, the remaining participants re-

ceived instructions, both in writing and aloud. These instructions varied by treatment.

No-Sorting Treatment. In dictator games without sorting, the odd-numbered subjects

were told that they would be randomly and anonymously matched with a participant outside

the room. They would participate in an activity in which they would divide €10 between

themselves and the paired even-numbered subject. At the end of the experiment, the partici-

pants outside the room would be brought back inside. The experimenter would describe the

dictator game publicly to these participants, and then each of the recipients would find out

how much money he or she had been anonymously given. Participants would then be paid and

this would conclude the experiment.

All dictators received an envelope. After the instructions, they were told to open the

envelope. The sheet inside indicated an even number corresponding to the paired recipient.12

On the sheet, each dictator wrote his or her own participant number and indicated a division

of €10 (in ten-cent increments).13 The experimenter then collected the envelopes.

At the end of the session, all of the even-numbered participants were brought back into

12 Random matching was implemented by shuffling the envelopes and allowing the dictators to select from the stack that remained. 13 Subjects were told that if the numbers did not add up to the allocation, then the amount to the recipient would determine the allocation. The dictator would receive the remaining amount. This never occurred.

13

the room. The experimenter read a brief description of the dictator game and then called the

recipients to the front of the room, one at a time. Each recipient was shown the sheet com-

pleted by the paired dictator, saw the division of the €10, and was paid privately and excused

from the experiment. After that, dictators were asked to complete the same one-page ques-

tionnaire that the receivers had completed. Finally, dictators received their payment.

Sorting Treatment. In the other half of the sessions, odd-numbered participants re-

ceived the same instructions, but – in addition – were told they could decide whether to “par-

ticipate” or not in this activity. If they chose to participate, then the participant with whom

they were matched would be brought back into the room and informed of the game. If they

chose not to participate, they would receive a payment of €10 without having the option to

distribute the money. In that case, the potential recipient outside the room would be paid the

€5 participation fee, excused from the experiment, and told nothing about the dictator game.

In this treatment, odd-numbered subjects received two envelopes, one labeled “partici-

pate” (“participar”) and another labeled “don’t participate” (“no participar”). Subjects who

chose to play the game opened the envelope marked “participate,” saw the participant number

of the paired recipient, recorded their own number, and specified a division of the €10. Sub-

ject who chose to not play the game, opened the envelope marked “don’t participate” (which

did not contain an even-numbered participant number) and wrote only their participant num-

ber on the sheet inside.14 After making either choice, subjects returned the envelopes to the

experimenter. At the end, the experimenter brought in only the outside participants who were

matched with a subject who chose to play the game. The remaining (non-paired) participants

were thanked for their participation and paid €5. Upon returning to the main room, the paired 14 This procedure ensured that subjects participating and not participating wrote roughly the same amount on the sheets, thus preserving anonymity.

14

recipients received a description of the dictator game, saw the sheet informing them of how

much they had been anonymously given, and were paid privately. After that, all odd-

numbered participants completed the questionnaire and were paid privately.

The questionnaire, administered in both treatments, asked for detailed demographic in-

formation (age, gender, race or ethnic group, education), including subjects’ family back-

ground (number of siblings, language spoken at home, years of residence in Barcelona, social

class). We also asked about social preferences (donations to charity during the past year) and

risk preferences (like or dislike of risks). Finally, we elicited how many people “in the other

area” a subject knew, i.e. how many receivers dictators knew and vice versa.

B. Results

We analyze the results of Experiment 1 to test the first two propositions: How does the option

to sort out of the dictator game affect the frequency and the amount of sharing? Proposition 1

implies that, if the sorting option reduces the frequency of sharing, then some individuals

must dislike not sharing. In other words, a negative effect indicates that some individuals who

share in the dictator game prefer to avoid the sharing environment altogether. Proposition 2

extends this implication to the amount shared: If some individuals dislike not sharing, then the

amount shared will be lower when sorting is possible.

The summary statistics of self-reported demographics, behaviors, and preferences are

in Table 1. Slightly less than half of our dictators (47%) are female. More than half (56%) are

Catalan and most others (43%) are Spanish.15 Most subjects self-identify their social class as

15 The direct elicitation of “race or ethnic group” (survey question 4, see Appendix 4) was impeded by a widely different understanding of ethnicity. Catalans, for example, indicated partly “Catalan,” partly “Spanish,” and partly “White.” As a remedy, we also elicited the primary language spoken at home (question 5) and asked for how many years participants had lived in Barcelona (question 7). Our ethnicity variable is based on question 5.

15

middle class. The average age is 20.6 years, with a standard deviation of 1.5 year.16 Given the

low variation, we included only one age-related dummy “Age Group,” capturing whether a

subject was a graduate or still an undergraduate student. We also asked students to indicate

their major. The answer was missing in seven cases and ambiguous (“Doctorate”) in one case.

The summary statistics show the number of subjects who unambiguously indicated a specific

major.17 The largest group of subjects major in economics or business administration (44%).

Other majors include other social sciences (21%), Engineering (9%) and Natural Sciences and

Mathematics (12%), Humanities (2.6%) and Law (1.3%). Subjects have between 0 and 4 sib-

lings, with most of them (58%) having one sibling. The dummy variable “Donation” reveals

that 40% of subjects indicate that they made donations to a charitable or human-aid organiza-

tion during the past year. 48% indicated that they “like taking risks.”

The last two rows give the summary statistics of aggregate sharing behavior in Ex-

periment 1, pooling both treatments. Subjects shared between zero and five euros, with an av-

erage of €1.22. The average among those who participated in the dictator game, i.e. who

could not opt out or chose not to opt out, is €1.91, which is similar to results in the previous

literature. Overall 42% shared a positive amount.

The last-mentioned aggregate statistics, however, veil large differences between the

treatments with and without a sorting option. The last row in Table 1 reveals that a majority of

subjects in the sorting treatment (28 of 39) are choosing not to play the game, effectively shar-

ing zero. As displayed in Figure 1, Panel A, the average amount shared is 65% lower in the

treatment with sorting. While the average amounts to €1.87 in the standard dictator treatment

16 Five percent of the dictators indicated that they were 18 years old, 22% were 19 years old, 25% (each) were 20 years and 21 years, and 12% (each) 22 years and 23-25 years. 17 All results remain unchanged if we drop, instead, the 8 observations without specific major. Business and Economics remain the only majors that significantly determine sharing.

16

without sorting (left bar) it is only €0.58 in the treatment with sorting (right bar). In a t-test on

the equality of means, the difference is significant at the p < 0.001 level (t75 = 3.41). Panel B

reveals that this difference is largely driven by an increase in the proportion sharing zero

when sorting is possible. While 61% share a positive amount in the standard dictator game

(without sorting), only 23% do so in the dictator game with sorting. The difference is signifi-

cant at the p < 0.001 level (χ2(1) = 11.11).

Thus, consistent with earlier experimental results, when individuals are put in a shar-

ing environment, the vast majority chooses to share a positive amount. However, when sub-

jects are given the opportunity to opt out of the game, the picture reverses. As predicted by

Propositions 1 and 2 the frequency and amount of sharing decrease significantly when sub-

jects can choose whether or not to enter the sharing environment.

These findings provide evidence that, first, sorting matters in the context of social be-

havior and, second, a large fraction of sharing in an environment without sorting occurs not

because the subjects like to share, but because they dislike not sharing. Most share when

forced into a sharing situation, yet many choose to avoid the situation altogether when given

the option to opportunity to sort.

We gauge the importance and robustness of these findings by relating the effect of

sorting to the impact of other potential determinants of sharing. First, we ask whether any of

the individual characteristics elicited in the questionnaire also predict sharing and, if so, how

their impact compares to the impact of sorting. In Table 2, we compare the effect of sorting on

the amount shared (Column 1) to the effect of the demographics and self-reported preferences

(Column 2). The table presents OLS regressions with robust standard errors.18

18 The low number of sessions prevents clustering, see e.g. Cameron, Miller, and Gelbach (2006).

17

While the effect of Sorting is highly significant and large (subjects share, on average,

€1.30 less when sorting is possible), none of the other dummy variables affect sharing to a

similar extent. All coefficients are smaller in absolute size, ranging between 0.09 and 0.85,

and all but one are statistically insignificant. Only Major has some significant predictive

power: Subjects studying business or economics share about €0.76 less on average, significant

at the p < 0.1 level. None of the other majors have significant predictive power.19

The results are very similar when including both Sorting and the individual character-

istics (Column 3). The estimated coefficient for Sorting increases in absolute value and re-

mains highly significant. The coefficient of a Business/Economics major is roughly the same

(–€0.78) and becomes significant at the p < 0.05 level. The coefficient estimate on the dummy

for “more than 1 sibling” becomes large (€1.26) and marginally significant (p < 0.1).20 Over-

all, the opportunity to sort appears to be significantly more important than any of the individ-

ual characteristics in determining sharing behavior.21

A second way to measure of the importance of Sorting relative to observable individ-

ual characteristics is the portion of explained variance. In the regression with only Sorting as

independent variable (Column 1), the adjusted R2 is 0.12; in the regression with the 11 indi-

vidual characteristics (Column 2), it is only 0.06. That is, the observable characteristics ex-

plain only half as much variance as Sorting alone, once we account for the effect of merely

adding predictors.22 More directly, we calculate the partial coefficients of determination in the

19 The latter result is consistent with previous evidence that economics students are more likely to behave self-interestedly (Frank, Gilovich and Regan, 1993). 20 This is consistent with the finding of Glaeser et al. (2000) that those without siblings return less money in an investment (trust) game. 21 All findings are highly robust to alternative regression specifications such as refinements of the dummies for age, social class, or major (though a higher number of controls risks saturating the model). Only the choice of Business or Economics as major and having 2, 3, or 4 siblings predict sharing in most regression specifications. 22 The adjusted R2 is calculated as 1 – (1 – R2)•[(N – 1)/(N – K – 1)], where N is the number of observations and

18

regression including both Sorting and the individual characteristics (Column 3). The partial

R2’s reflect the strength of association of each particular independent variable23 and are dis-

played to the right of the standard errors in Column 3. Each individual characteristic explains

between 0 and 0.05 of the remaining unexplained variance; Sorting explains 0.19. Thus, the

effect of Sorting is not only larger and has a lower p-value; Sorting is also a more reliable

predictor of Sharing in our data than any other variable.

We also check the robustness of the sorting effect across different subgroups of sub-

jects. For each demographic characteristic (subsamples by gender, ethnicity, socio-economic

status, age, siblings), including educational choices (major, university), and for the elicited

preferences (donations, risk preferences), we calculate the average amount shared in the

treatment without sorting and the treatment with sorting. The results are displayed in Figure 2.

In each of the 20 subgroups, the average amount shared without Sorting (left bars) is lower

than the average amount shared with Sorting (right bars). Thus, our baseline result is not only

robust to the inclusion of individual characteristics as controls; it is also pervasive throughout

all categorizations by such characteristics. The availability of a sorting option induces a re-

duction of sharing in any subgroup of individuals.

A second possible consequence of sorting relates to the amount shared conditional on

not opting out: Are those who share because they like to share on average more generous than

those who share only when they cannot avoid the sharing environment (dislike not sharing)?

In terms of our model, does a low ŵ imply a high sharing parameter α? The between-subject

treatment does not allow us answer this question since we do not know which of the sharers,

K the number of predictors. 23 The partial R2 for predictor i is calculated as (R2 – 2

)(iR )/(1 – 2)(iR ), where 2

)(iR is the R2 with predictor i removed from the equation.

19

in the game without sorting, would opt out. All we can compare is the average amount shared

among those who choose to participate in the treatment with sorting (€2.05) and the overall

average in the treatment without sorting (€1.87), which are not significantly different. The

latter amount combines, however, sharing of all three types. The within-subject design of Ex-

periment 2 allows us to investigate this question, as well as the prediction of Proposition 3.

IV. Experiment 2 (Within-Subject Design)

Experiment 1 provided evidence that the availability of a sorting option lowers sharing

(Propositions 1 and 2) in a between-subjects design. In Experiment 2, we used a within-

subject design to examine the effect of incentives not to opt out (Proposition 3). We analyze

which subjects, among those who opt out when w' = w, are most easily attracted back. That is,

which subjects are the first to return to the dictator game if we increase the endowment in the

game above the outside option (w′ > w). Experiment 2 also explores the robustness of our

findings in a different (albeit also Western) culture and to a different (within-subject) design.

The experiment consisted of three parts. In part 1, the dictator game endowment was

$10 and there was no sorting option. This decision was used to measure the portion a dictator

shares when sorting is not possible (α). In part 2, dictators had the option to sort out of the

game, in which case they received $10 and the (potential) recipient never found out about the

game. Thus, the first two parts replicated the two treatments of Experiment 1 in a within-

subject setting. In part 3, the amount available in the dictator game (w') increased above $10

while the sum dictators received after opting out remained constant (w = $10).24

24 We did not counter-balance the order of the three parts across sessions for several reasons. First, variation in the order of parts 1 and 2 was redundant given the between-subjects comparison in Experiment 1. As we will see, the outcomes in parts 1 and 2 closely replicate the results from the between-subjects experiment. Second, the main purpose of the within-subject design is to compare the rates of re-entry into the dictator game across sub-jects (Proposition 3). Therefore, only subjects exposed to the same initial treatment are comparable. Among dif-

20

In addition, we explored the robustness of our findings to situations in which dictators

are not anonymous – as when one encounters a beggar on the street. In the Anonymity treat-

ment of Experiment 2, dictators and recipients remained anonymous as in Experiment 1 and

as in standard dictator experiments. In the No-Anonymity treatment, however, the identities of

dictators who chose to play the game were revealed to the recipients.

A. Experimental Design

Experiment 2 took place at the Pittsburgh Experimental Economic Laboratory (PEEL) at the

University of Pittsburgh. Subjects were graduate and undergraduate students at the University

of Pittsburgh and Carnegie Mellon University. We conducted 12 sessions, 6 in each anonym-

ity treatment. As shown in Table 3, 188 subjects participated, 92 (46 dictators) in the No-

Anonymity treatment and 96 (48 dictators) in the Anonymity treatment.25

In all three parts, the procedures were very similar to those in Experiment 1. Each ses-

sion consisted of an even number of 10 to 20 participants and lasted 30 minutes. Upon arrival,

subjects were told they would receive $6 and that they might earn additional money. Subjects

drew participant numbers and those with numbers between 11 and 20 were told to follow the

experimenter to an area outside the room.26 While all subjects were still in the main room, the

experimenter publicly announced that participants 11-20 would complete questionnaires for

ferent possible “initial treatments” this order seemed most natural to test how the dynamic decision-making of individuals varies depending on their type revealed in their baseline sharing decision. Third, our design aims at linking the outcome of standard dictator-game experiments to behavior under sorting, requiring us to start with the standard dictator game. While it is possible that experiencing sorting first, i. e. prior to the baseline dictator game, would influence sharing and while such an effect would be interesting, we need to eliminate it from the measurement of sharing in the standard dictator games for the purposes of comparison to other dictator experi-ments. Finally, we do not account, separately, for learning since several recent studies of repeated dictator games have found little change in behavior over time (Duffy and Kornienko, 2005; Hamman et al., 2006), differently from, for example, the case of dominance-solvable games (Weber, 2003; Weber and Rick, 2006). 25 One subject was accidentally allowed to participate twice (both times as dictator). We omitted this subject’s second participation from the data. Since subjects’ choices were never revealed to anyone else until the end of the experiment, it is very unlikely that this subject influenced the choices of other dictators in the second session. 26 In sessions with less than 20 participants, participant numbers ranged from 1 to n/2 and 11 to 10+n/2. Partici-pants with numbers between 11 and 20 always corresponded to half the participants.

21

about 20 to 25 minutes and would not receive additional money for doing so.27 Once outside

the main room, participants 11-20 completed questionnaires (unrelated to this study) for about

20 minutes. If they finished early, they were told to wait quietly for additional instructions.

Once participants 11-20 had left the room, participants 1-10 were informed that they

would make a series of decisions, with new instructions distributed prior to each decision. At

the end of the experiment, one decision would be randomly selected to determine payoffs.

Decision 1. Decision 1 consisted of a dictator game with no sorting option. The en-

dowment was $10, denoted as 40 tokens. Subjects were told that if Decision 1 were selected

to count at the end of the experiment, then participants 11-20 would be brought back into the

room. The experimenter would describe the dictator game publicly and each recipient would

find out how much money he or she had been given. In the No-Anonymity treatment the re-

cipient would also find out the identity of the paired dictator. The remaining procedures were

identical to those in the No-Sorting treatment in Experiment 1, except with dictators indicat-

ing a division of 40 tokens (each worth 25 cents) rather than €10.28

Decision 2. In Decision 2, participants 1-10 had the opportunity to play exactly the

same dictator game as in Decision 1, with a (potentially) new randomly selected participant.

Alternatively, they could choose to “pass” (i.e., not to play the game).

The procedure mirrored the Sorting treatment in Experiment 1. Dictators had to open

one of two envelopes. The envelope labeled “Play” contained the number of a participant out-

side the room. If dictators opened this envelope, they would write their own number and indi-

27 Thus, relative to Experiment 1, participants outside the room were slightly worse off: they had to fill in a se-ries of questionnaires rather than one brief questionnaire. This difference was due to the fact that Experiment 2 consisted of several decisions by dictators (vs. only one decision in Experiment 1) and thus took longer. It may have contributed to the slightly higher propensity to share in Experiment 2 (27% vs. 19% of the endowment when sorting is not possible), though this also involves comparisons across populations and countries.. 28 As in the first experiment, subjects were told that if the numbers did not add up to the allocation, then the amount to the recipient would determine the allocation. Here, this occurred once.

22

cate a division of 40 tokens. The other envelope, labeled “Pass,” did not contain a participant

number. If dictators opened this envelope, they would mark an “X” on the sheet inside.29 The

experimenter told dictators that if they chose to play the dictator game and if Decision 2 were

selected to count, then their paired recipient would be brought back into the room.

Remaining Decisions. The remaining three (Anonymity) or four (No-Anonymity) de-

cisions proceeded exactly as Decision 2, with the exception that the dictator-game endowment

increased. Table 3 presents the endowment (w') for each decision.30

At the end of each session, the experimenter randomly drew one of the decisions to

count. If it was the first decision, then all of the other participants were brought back into the

room. If it was any of the other decisions, then the experimenter brought in only those outside

participants who were paired with a subject who chose to play the game. The remaining par-

ticipants were thanked for their participation and paid $6.

The participants brought back into the room were informed about the game. Each of

them was then shown the sheet filled out by their matched dictator, informing them about

their payoff and the participant number of the dictator. In the No-Anonymity treatment, the

dictators themselves handed the sheets to the recipients, revealing their identity.

B. Results

Aggregate behavior is presented, by treatment, in Figure 3. Each panel presents, by round, the

29 As in Experiment 1, the procedure prevented dictators from inferring the choice of others, since both those playing and those passing had to open an envelope and wrote roughly the same amount on the sheets. 30 There are two reasons why the parameters (number of decisions, endowments) differ between the Anonymity and the No-Anonymity treatments. First, we initially conducted pilot sessions with the same payoffs and struc-ture in the Anonymity and the No-Anonymity sessions. We found that, under Anonymity, a majority of dictators opted out of the game in Decision 2 ($10 allocation), but that the steeper payoffs induced almost all of them to play the game by Decision 4 ($13 allocation). Since part of our goal was to explain the variance in “re-entry” to the game, we modified the payoffs to be able to measure such variance. Second, we also decreased the number of rounds to allow the experiment to run more quickly.

23

total amount shared per subject (bars), the number of subjects opting to play the game (dashed

line), and the percentage of subjects sharing a positive amount (solid line).

The behavior in Decisions 1 and 2 strongly corroborates the findings of our between-

subjects design in Experiment 1. When dictators are forced to play the game (Decision 1),

74% share. When subjects are given the opportunity to opt out of the game (Decision 2), only

30% share. As a result, the total amount shared decreases substantially, from an average of

$2.68 without sorting (Decision 1) to $1.19 when sorting becomes possible (Decision 2).

The figures also reveal that the impact of sorting is robust to the removal of anonym-

ity. In the standard dictator game (Decision 1), 81% share in the No-Anonymity treatment and

67% in the Anonymity treatment. They share average amounts of $2.42 (Anonymity) and

$2.92 (No Anonymity). Thus, as expected, the lack of anonymity produces slightly more shar-

ing. However, this difference is not statistically significant: the significance fails to reach 10%

either using a t-test (t92 = 1.17) or a Kolmogorov-Smirnov test (D46,48 = 0.19). In the dictator

game with sorting (Decision 2), only 25% share in the No-Anonymity treatment and 35% do

so in the Anonymity treatment. The average amounts shared decrease in both treatments, to

$1.22 in Anonymity and to $1.17 in No-Anonymity. Thus, the lack of anonymity makes opt-

ing out more attractive in the No-Anonymity treatment and reduces sharing slightly more than

in the Anonymity treatment. The difference in sharing is, however, again not significant (t92 =

0.14 in the two-sample t-test and D46,48 = 0.10 using the Kolmogorov-Smirnov test).31

In Table 4, we test both the robustness of our sorting result to the within-subject de-

sign and the robustness to different anonymity environments in a regression framework. We

also expand the analysis to the full set of decisions, beyond Decisions 1 and 2. Since the dicta-

31 Also the amounts by which sharing is reduced (by $1.20 in the Anonymity treatment and by $1.76 in the No-Anonymity treatment) are not significantly different.

24

tor-game endowment increases from Decision 3 on (see Table 3), we use the portion rather

than the amount shared as the dependent variable. As in the previous regressions, we calculate

robust standard errors.32 The within-design allows us to include session fixed effects.

Columns (1) to (3) confirm both the significantly negative effect of sorting and the in-

significant effect of anonymity. The availability of a sorting option reduces the portion shared

by more than 50 percent. The same results hold if we analyze the frequency of “sharing any

positive amount” rather than the portion shared. In addition, neither the interaction of ano-

nymity with sorting nor the inclusion of session fixed-effects affects the results.

In Columns (4) and (5) we expand the analysis to all decisions. We include the size of

the dictator-game endowment as it increases from Decision 3 on (see Table 3). The endow-

ment has a statistically significant though economically small effect. The portion shared in-

creases by roughly 1% per additional dollar of endowment. The effect of the sorting option

remains negative and highly significant, amounting to 15-17% of the endowment.

The stability of the coefficient on Sorting across decisions with different endowments

and the small effect of the endowment also suggest that subjects may be using a “proportional

sharing” rule, as implicitly assumed in our econometric specification. Proportional sharing

behavior is not important to the core point of this paper, but it is consistent with the class of

modified Cobb-Douglas preferences we chose to derive Proposition 3 (see Appendix 1). To

test the validity of this assumption directly, we relate the portion a subject shared initially

(Decision 1) to the portion shared in later decisions, conditional on playing the dictator game:

(5) Portion Sharedid = α + β·Initial Portioni + Xi′ Γ + Initial Portioni Xi

′ Δ + ζ·Endowmentd + εid

32 As remarked above, clustering by session is not meaningful given the small number of sessions. Note, though, that all results are robust to clustering; in fact, the clustered standard errors are more precise for all coefficients.

25

where i denotes the individual, d the decision, and Xi are demographic and treatment controls

(gender, anonymity).33 We estimate this model on all observations of subjects participating in

the game except the first decision, which is used to determine the Initial Portion shared by the

subject. If subjects always shared the exact same proportion in every round, in which they

participate, we should find an α of zero and a β equal to 1. The coefficients of all other inde-

pendent variables should be equal to zero as well. The R2 should be equal to 1.

Table 5 displays the results, first setting Γ, Δ, and ζ equal to zero (Column 1) and then

including the controls (Column 2) and Session fixed effects (Column 3). The discrepancy be-

tween the large coefficient of Initial Portion and the minuscule coefficients of Endowment

and the constant is striking, as is the discrepancy in their statistical significance. (The same

holds for the controls.) The coefficient of Initial Portion ranges from 0.75 to 0.92. The coeffi-

cient of the constant lies between 0.01 and 0.04 and is insignificant in all specifications. The

(insignificant) coefficient of Endowment amounts only to -0.003. The R2 is around 60%.

Thus, while not a perfect fit, “proportional sharing” describes the sharing decision of

those choosing to play rather well. Note that the coefficient of Initial Portion increases with

the inclusion of controls. Any misspecification thus appears to attenuate the effect. Downward

bias in the coefficient estimate may also arise from noise in the sharing decision. Since shar-

ing is bounded below (at zero) for those who share little and bounded above (at one) for those

who share a lot, noise diminishes the positive coefficient. When replicating the analysis for

the subset of subjects who choose to play at least two times, three times, or four times, the co-

efficient estimates monotonically increase, likely due to the reduced noise in the measurement

33 Since this experiment required more decisions than Experiment 1, and therefore imposed greater time con-straints, we did not collect the same extensive demographic and background information as in that experiment. (Also, recall that the effect of sorting was robust to all such variables as controls in Experiment 1). We collected gender by simply recording it as subjects’ sheets were collected at the end of the experiment.

26

of sharing. Columns (4) to (6) show the results for the subsample of subjects who participate

at least four times. After including fixed effects, the Endowment coefficient is 1.00.

In summary, average sharing is significantly lower when sorting is possible; but those

who choose not to sort out of the game continue to share roughly a constant portion, regard-

less of the endowment.

The significantly negative effect of Sorting on sharing, both in Experiment 1 and in

Experiment 2, shows that a large fraction of subjects share in environments without a sorting

option not because they like to share, but because they dislike not sharing. Thus, the results of

both experiments are consistent with the predictions of Propositions 1 and 2 of our model.

Classification of subject types

The within-subject design of Experiment 2 allows us to go further and to classify subjects into

the three types laid out in our model, based on their sharing and sorting in the first two deci-

sions. We find that 23% of our subjects dislike sharing since they share nothing in Decision 1

and either opt not to play or share nothing in Decision 2. A group of 29% like sharing as indi-

cated by sharing both in Decision 1 and in Decision 2. The largest group, however, 41% ap-

pear to dislike not sharing; they share in Decision 1 and opt not to play in Decision 2. These

three categories account for 95% of the subjects.34 The distributions of types do not differ sig-

nificantly by anonymity treatment (χ2(2) = 3.49, p = 0.18).35

Thus, the modal behavior is to share some positive amount when no sorting option is 34 Of the remaining five subjects, three shared something in Decision 1 ($0.25, $2.50, $5) and shared nothing in the remainder of the experiment (but frequently opted to play). One shared $2.50 initially, shared $0.50 in Deci-sion 4, and nothing otherwise (but opted to play every time); and one subject shared nothing initially, but then opted to play and share $4 in all subsequent decisions. We might classify the first three subjects as dislike shar-ing and the last subject as like sharing, with trembles or noise in their first decision. After their first decision, each of these four subjects behaved entirely consistently with one of our types. 35 Differentiating by gender, males are more likely to dislike sharing than women (M: 30%; F: 20%) and women are more likely to dislike not sharing (M: 30%; F: 47%). However, the difference in distributions of types by gender is not significant either (χ2(2) = 1.97, p = 0.37).

27

available, but to opt out of the game when sorting is possible. This behavior is consistent with

individuals in our model having a positive willingness to pay to avoid the dictator game (ŵ >

w). That is, they share if they are in the environment that allows sharing, but would pay to

avoid that environment. This means that the majority shared in the first decision because they

dislike not sharing, not because they like sharing.

Given this classification, we can return to the question of which type – likes sharing or

dislikes not sharing – behaves most generously (i.e., has higher values of α). The average

amount shared in Decision 1 by those who like to share is $4.46 and by those who dislike not

sharing is $3.10. The difference is significant at the p < 0.001 level (t64 = 3.95). A second im-

portant implication of sorting, then, is that those who choose to share, even when they can

avoid the sharing environment altogether, are significantly more generous sharers than those

who share only when sorting is unavoidable (i.e., those who dislike not sharing).

Who Is Least Willing to Play?

As the last step in our analysis we ask how increasing dictator-game endowments (w') influ-

ence the sorting decisions of the three types. The logic of the theory section suggests that dis-

like-sharing and like-sharing types should always opt to play the game when its endowment is

higher than the outside option (w' > w). For those who dislike not sharing, instead, there

should be some threshold value that lures them back into the game. Proposition 3 predicts that

this value is decreasing in how much they shared initially. The more dislike-not-sharing indi-

viduals shared initially, the longer they will remain out of the game.

Starting from the aggregate picture in Figures 3a and 3b, we see that individuals who

avoid the dictator game in Decision 2 respond to incentives to play the game as the allocation

increases relative to the fixed $10 for not playing. The proportion choosing to play (dashed

28

line) rises monotonically after Decision 2, though it remains below 100 percent for most deci-

sions.36 Thus, the increased incentives attract subjects back into the sharing environment.37

In order to test Proposition 3 directly, we relate the initial sharing to the incentives

needed to attract an individual back into the dictator game, using two types of analysis. First,

we calculate, for dislike-not-sharing types, how generously they shared initially and how the

initial sharing relates to their sorting decision. That is, for each decision (other than Decision

2 in which, by definition, dislike not sharing types opt not to play the game), we identify

those subjects who chose to participate in the game in that decision and calculate the average

amount those subjects shared initially.

We find that the amount of initial sharing (in Decision 1), averaged over those who

participate in a given round, increases as the endowment in the game (w’) rises and more dis-

like-not-sharing types are attracted back into the game. In the No-Anonymity treatment, we

have 24 dislike-not-sharing types (i.e. subjects who shared in Decision 1 but opted out in De-

cision 2). Six of them re-enter the dictator game in Decision 3. But those 6 are among the

least generous; they initially shared only $2.00. In the next round, 5 more subjects of the dis-

like-not-sharing type reenter, including some more generous ones. Recalculating the amount

shared initially for the 11 subjects gives us $2.36. This trend continues for the next two deci-

sions. We have even more (19) dislike-not-sharing types participating in Decision 5 and their

average amount shared initially is $2.99. Finally, all dislike-not-sharing types have reentered 36 As with Decisions 1 and 2, behavior in Decisions 3 and beyond does not differ between anonymity treatments, when controlling for endowments. For example, we can compare sharing in Decision 3 under No-Anonymity (average amount shared = $1.51) and Decision 4 under Anonymity (average amount shared = $1.42), since in both cases w' = $11. This difference is not significant (t92 = 0.20; D46,48 = 0.13). 37 In spite of the increased re-entry, the average amount shared per subject fails to reach Decision 1 levels until later decisions, if at all. For instance, in Decision 4 of the No-Anonymity treatment, in which the dictator can allocate $13, the amount shared per subject is $2.07, which is well below the amount shared in Decision 1 ($2.92). In the Anonymity treatment, amount shared in Decision 5, where the dictator game is worth $12, is $1.52, which is also below the average allocation in Decision 1 ($2.42). Both of these differences are significant in paired t-tests (No-Anonymity: t47 = 2.73, p < 0.01; Anonymity: t45 = 2.73, p < 0.01).

29

by Decision 6, including the most generous ones, bringing the average initial sharing to $3.04.

The picture is very similar in the Anonymity treatment. Out of the 15 dislike-not-

sharing types, 6 participate in the game in Decision 3, 10 in Decision 4, and 11 in the last de-

cision (Decision 5). The average amounts of initial sharing are $2.67 for those participating in

Decision 3, $2.55 for participants in Decision 4, $3.05 for participants in Decision 5, and

$3.20 for all dislike-not-sharing types. Thus, with the exception of one round, participation is

again more delayed for those who share more generously (when sorting is not possible).

Second, we relate the sorting decision to the amount of initial sharing in a regression

framework, controlling for other determinants of sorting. Table 6 reports the marginal effects

from probit estimations that use a subject’s decision to play (1) or to pass (0) as the dependent

variable. Since all subjects had to play the game in Decision 1 and since the choice to play the

game in Decision 2 is used to construct the types, we exclude these two decisions from the

analysis. In Column (1), we consider the subset of subjects who dislike not sharing as defined

by sharing in Decision 1 and opting out in Decision 2. We find that the portion shared initially

is strongly negatively related to the decision to play the game. For each additional dollar

shared in Decision 1 (corresponding to 10% of the initial endowment), individuals enter the

dictator game 7.8% less often. The result is robust to the inclusion of the usual controls (treat-

ment, gender, their interaction, and endowment). As a placebo test, we re-run the same regres-

sion for subjects who like to share, as defined by sharing both in Decision 1 and in Decision

2. As shown in Column (2), the coefficient has the opposite sign, is small and statistically in-

significant.38 Similarly, we do not find a significant effect using the full sample (Column

38 Since Anonymity perfectly predicts success in the subset of like-sharing types, we drop Anonymity and its interaction with gender as controls.

30

(3)).39 The final specification, in Column (4), uses again the full sample but includes a dummy

for being a Dislike-Not-Sharing type as well as its interaction with the Initial Portion Shared.

We find a significantly positive coefficient of the Initial Portion shared, amounting to 30%

more participation for 100% more sharing, reflecting that those who dislike sharing share less

initially than like-sharing types (zero rather than a positive amount) and then stay out longer.

The coefficient on the interaction of the dummy for initial sharing and the dummy for Dislike-

Not-Sharing, however, is significantly negative and of the same order of magnitude as in the

split-sample regressions. Subjects who dislike not sharing participate about 80% less per

100% more initial sharing.

As in Experiment 1, our findings confirm our predictions. Sorting significantly affects

the extent of sharing. Moreover, increased incentives to re-enter the environment where shar-

ing is possible have the strongest effect on those who are least willing to share.

V. Conclusions

People regularly sort into and out of economic environments such as firms, markets, and insti-

tutions. In the laboratory, instead, subjects are typically placed in one particular situation and

forced to make a choice that they might avoid making outside the laboratory. The goal of our

analysis is to model the influence of a sorting decision and to investigate how it affects con-

clusions drawn from laboratory environments without sorting.

One such laboratory setting where subjects typically do not have the option to sort is

the dictator game, a common laboratory test of sharing and altruism. We introduce the possi-

bility of sorting into this laboratory environment and find that sorting significantly affects be-

havior. When individuals are forced to play a dictator game, the majority share. But when

39 Recall that all dislike sharing types shared 0 in Decision 1, so this group has no variance on this variable.

31

they are allowed to opt out of the game, the majority does not share. Choosing subjects ran-

domly, and forcing them to play the dictator game, might lead us to believe that sharing is

pervasive outside the laboratory. However, allowing people to avoid the sharing situation

leads to the opposite conclusion: a subset of individuals share, but the majority avoids situa-

tions where sharing is possible.

Our paper also introduces a model that allows for an additional motivation for sharing,

relative to those present in most behavioral models. Individuals may share not because they

like to share, but because they dislike not sharing. We find support for the presence of types

who dislike not sharing in both of our experiments.

The model also yields some counter-intuitive predictions about the effects of sorting.

In particular, some of those who appear to be most fairness-minded in the forced-choice ex-

periments are most likely to avoid environments where they can act fairly. Our experiments

find support for this hypothesis. Among those who share because they feel compelled to share

(without really wanting to), larger amounts shared predict more reluctance to enter the sharing

environment altogether. In other words, the more such subjects feel compelled to share the

higher the price they require for entering the sharing environment. Thus, some of those who

might appear the most willing to share are the least likely to do so when sorting is possible.

It is worth noting that our results do not question the existence or relevance of social

preferences. Rather, they indicate that, in addition to altruism or fairness, other types of non-

standard social preferences (e.g. guilt, shame, obligation) strongly influence sharing behavior.

Therefore, our work adds to the understanding of the motivations for social behavior.

Finally, we argue that the possibility of sorting influences the impact of social prefer-

ences outside the laboratory. Sorting options – which are often present outside the laboratory

32

– greatly diminish the amount that people share. Thus, the frequency of sharing is likely to be

lower outside the laboratory than in a laboratory environment without a sorting option. Our

work provides an example of how this influence needs to be accounted for when generalizing

laboratory results to non-laboratory environments.

33

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36

Figure 1. Sharing With and Without Sorting (Between-Subjects Design, Experiment 1) (8 sessions, N = 77)

Panel A. Average Amount Shared The amount is denoted in Euros. The left bar indicates the average amount in the treatment without a sorting option; the right bar the average amount in the treatment with a sorting option. Non-participation in the treat-ment with sorting is included as sharing zero.

0

0.5

1

1.5

2No SortingSorting

Panel B. Frequency of Amounts Shared For each range, the left bar indicates the frequency in the treatment without a sorting option; the right bar the frequency in the treatment with a sorting option. Non-participation in the treatment with sorting is included as sharing zero.

0

0.2

0.4

0.6

0.8

$0 $0.10 -$1.00

$1.10 -$2.00

$2.10 -$3.00

$3.10 -$4.00

$4.10 -$5.00

No SortingSorting

37

Sharing by subsamples based on demographics and elicited preferences. The number in parentheses nextto each subgroup indicates the number of dictators. The left bar in each subgroup indicates the averageamount shared in the treatment without sorting; the right bar the average amount shared with sorting.

Figure 2. Sharing by Subsample (Experiment 1)

Sharing by Gender

0

0.5

1

1.5

2

2.5

3

Female (36) Male (41)

Sharing by Age Group

0

0.5

1

1.5

2

2.5

3

Undergrad. (55) Graduate (22)

Sharing by Number of Siblings

0

0.5

1

1.5

2

2.5

3

0 sibl. (7) 1 sibl. (45) 2-4 sibl. (25)

Sharing by Ethnicity

0

0.5

1

1.5

2

2.5

3

Catalan (43) Non-Catalan (34)

Sharing by Socio-economic Status

0

0.5

1

1.5

2

2.5

3

LoMid (19) Mid (43) MidUp (15)

Sharing by Major

0

0.5

1

1.5

2

2.5

3

BusEcon (34) Other (43)

Sharing by University

0

0.5

1

1.5

2

2.5

3

Pompeu Fabra (44) Autonoma (33)

Sharing by Donation (in past year)

0

0.5

1

1.5

2

2.5

3

Donated (31) Did not donate (46)

Sharing by Risk Attitude

0

0.5

1

1.5

2

2.5

3

Like risk (37) Dislike risk (40)

38

Figure 3. Aggregate Behavior in Experiment 2 (Within-Subject Design) Panel A. No-Anonymity Treatment (6 sessions, N = 48)

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

D1(w'=$10)

No sorting

D2(w'=$10)Sorting

D3(w'=$11)Sorting

D4(w'=$13)Sorting

D5(w'=$16)Sorting

D6(w'=$20)Sorting

0%

20%

40%

60%

80%

100%

Total shared / personPercent sharingPercent choosing play

Panel B. Anonymity Treatment (6 sessions, N = 46)

$0.00

$1.00

$2.00

$3.00

$4.00

$5.00

D1(w'=$10.00)No sorting

D2(w'=$10.00)

Sorting

D3(w'=$10.50)

Sorting

D4(w'=$11.00)

Sorting

D5(w'=$12.00)

Sorting

0%

20%

40%

60%

80%

100%

Total shared / personPercent sharingPercent choosing play

39

Table 1. Summary Statistics (Experiment 1) Ethnicity is identified by the language spoken at home. Socio-Economic Class is based on self-identified association with the upper or upper/middle class (for Upper to Middle), with the mid-dle class (for Middle), and with the middle/lower or lower class (for Middle to Lower). Amount Shared and Positive Amount Shared include non-participation as zero.

Variable Obs. Mean (or %) Std. Dev. Median Gender: Female 77 46.75% 50.22% 0 Ethnicity

Catalan 77 55.84% 49.98% 1 Spanish 77 42.86% 49.81% 0 Other 77 1.30% 11.40% 0

Socio-Economic Class Upper to Middle 77 20.78% 40.84% 0 Middle 77 54.55% 50.12% 1 Middle to Lower 77 24.68% 43.39% 0

Age Group: Graduate Students 77 28.57% 45.47% 0 Major of Studies

Business Administration 77 28.57% 45.47% 0 Economics 77 15.58% 36.51% 0 Other 77 55.84% 49.98% 1

University Universitat Pompeu Fabra 77 57.14% 49.81% 1 Universitat Autònoma de Barcelona 77 42.86% 49.81% 0

Number of siblings 77 1.31 0.77 1 0 siblings 77 9.09% 28.94% 0 1 sibling 77 58.44% 49.61% 1 2-4 siblings 77 32.47% 47.13% 0

Donation during the past year 77 40.26% 49.36% 0 Risk: like taking risks 77 48.05% 50.29% 0 Amount Shared 77 €1.22 €1.78 €0.00 Positive Amount Shared? 77 41.56% 49.61% 0 Chose to participate (Sorting treatment) 39 28.21% 45.58% 0

40

Table 2. Determinants of Sharing (Experiment 1)

(1) (2)Partial Coefficients of Determination

Sorting -1.297 -1.461(0.382)*** (0.384)*** 0.19

Gender: Female -0.335 -0.296(0.416) (0.344) 0.01

Ethnicity: Catalan 0.245 0.423-0.388 -0.382 0.02

Socio-economic status: middle class 0.260 0.677(0.527) (0.470) 0.03

upper to middle class 0.255 0.623(0.670) (0.615) 0.02

Age group: Graduate Student 0.094 0.210(0.475) (0.449) 0.00

Major: Business or Economics -0.758 -0.777(0.401)* (0.388)** 0.05

University: Pompeu Fabra -0.670 -0.770(0.436) (0.422)* 0.05

Siblings: 1 siblings -0.113 0.358-0.745 -0.681 0.00

2-4 siblings 0.845 1.255(0.800) (0.702)* 0.05

Donation (during past year) -0.416 -0.187(0.453) (0.407) 0.00

Risk-seeking -0.207 -0.253(0.422) (0.384) 0.01

Constant 1.874 1.791 1.663(0.331)*** (1.020)* (0.865)*

Observations 77 77 77Adjusted R-Square 0.12 0.06 0.23Robust standard errors in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

(3)

OLS regressions with Total Amount Shared (out of €10.00 endowment) as the dependentvariable .

41

Table 3. Endowment in Dictator Game by Decision and Treatment (Experiment 2)

Dictator Allocation (w') (Anonymity)

Dictator Allocation (w') (No-Anonymity)

Sorting Option (w = $10)

Decision 1 $10.00 (40 tokens) $10.00 (40 tokens) No Decision 2 $10.00 (40 tokens) $10.00 (40 tokens) Yes Decision 3 $10.50 (42 tokens) $11.00 (44 tokens) Yes Decision 4 $11.00 (44 tokens) $13.00 (52 tokens) Yes Decision 5 $12.00 (48 tokens) $16.00 (64 tokens) Yes Decision 6 $20.00 (80 tokens) Yes Number of sessions 6 6 Number of subjects (dictators)

92 (46)

96 (48)

42

Table 4. Determinants of Sharing (Experiment 2)

OLS regressions with Portion Shared (of the endowment) as dependent variable. The Endowment is $10 in Decisions 1 and 2 and increases afterwards (see Table 3). When sorting is possible, Portion Shared is zero for those who opt out.

Decisions 1-2 All Decisions (1) (2) (3) (4) (5) Sorting -0.148 -0.176 -0.176 -0.148 -0.167 (0.029)*** (0.041)*** (0.041)*** (0.025)*** (0.034)***Anonymity -0.05 -0.036 -0.031 (0.043) (0.070) (0.054) Sorting*Anonymity 0.055 0.055 0.041 -0.059 -0.059 -0.047 Endowment 0.011 0.011 (0.003)*** (0.004)***Constant 0.268 0.292 0.259 0.155 0.165 (0.021)*** (0.028)*** (0.043)*** (0.037)*** (0.048)*** Session Fixed Effects X X Observations 188 188 188 518 518 Adjusted R-Square 0.12 0.11 0.12 0.07 0.10

Robust standard errors in parentheses * significant at 10%; ** significant at 5%; *** significant at 1%

43

Table 5. Sharing in Later Rounds as a Function of Initial Sharing (Experiment 2) OLS regressions with Portion Shared as dependent variable. Included are all observations from Deci-sion 2 on, in which a subject chose to participate in the game. Controls include treatment and demo-graphic controls (Anonymity, Gender) and Control Interactions their interaction with the Initial Por-tion shared as well as the triple interaction. Sample:

All Subjects Subjects who played 4x or more

(1) (2) (3) (4) (5) (6) Initial Portion 0.748 0.894 0.921 0.802 0.947 1.002 (0.037)*** (0.039)*** (0.048)*** (0.041)*** (0.032)*** (0.044)***Endowment -0.003 -0.003 0.000 0.000 (0.003) -0.003 (0.003) (0.003) Constant 0.014 0.037 - 0.019 -0.006 - (0.009) (0.043) - (0.014) (0.047) - Controls X X X X X X Control Interactions X X X X Session Fixed Effects X X Observations 288 288 288 178 178 178 Adjusted R-squared 0.58 0.60 0.64 0.64 0.68 0.74 Robust standard errors in parentheses. * significant at 10%; ** significant at 5%; *** significant at 1%

44

Table 6. Relation between Initial Sharing and Participation (Experiment 2)

Subjects who dislike not sharing

Subjects who like sharing

(1) (2) (3) (4)Initial Portion Shared -0.778 0.028 -0.064 0.314

(0.323)*** 0.059 (0.103) (0.126)**Dislike-Not-Sharing -0.016

(0.073)(Initial Portion Shared)*(Dislike-Not-Sharing) -0.824

(0.230)***Controls and Interactions X X X XObservations 141 93 330 330Pseudo-R2 0.30 0.26 0.13 0.26Robust standard errors in parentheses* significant at 10%; ** significant at 5%; *** significant at 1%

All Subjects

Probit estimations, using the sample of all decisions after Decision 2. The dependent variable is binary andequal to 1 if the subject decides to play the dictator game. The sample of Dislike-Not-Sharing types inColumn (1) contains all subjects who shared in Decision 1 and opted out in Decision 2. The sample of Like-Sharing types in Column (2) contains all subjects who shared both in Decision 1 and in Decision 2. Thecoefficients represent the marginal coefficients of the probit in response to a discrete change of the dependent(dummy) variables.

Sample

45

Appendix 1. Theoretical Derivation

We consider a generalized utility function

U = U(D, x, y)

where D is a dummy variable equal to 1 if sharing is possible and 0 if sharing is not possible; x is own payoff; y is other payoff. When D = 0, the individual is precluded from sharing and thus y = 0. It is possible that even with the opportunity to share (i.e. when D = 1), y = 0, but this depends on individual choice. We assume that utility is increasing in the endowment. Us-ing equation (1), the utility function can then be rewritten as

(A1) U = U(D, x, w – x)

We can characterize the different motivations for sharing as follows:

(A2) wxwxUwx <−∈ ),,1(maxarg ],0[ and )0,,0(),,1(max ],0[ wUxwxUwx >−∈ for those who like to share;

wxwxUwx <−∈ ),,1(maxarg ],0[ and )0,,0(),,1(max ],0[ wUxwxUwx <−∈ for those who dislike not sharing.

The premium that an individual is willing to pay to avoid the sharing environment is given by ŵ – w, which is positive for those who dislike not sharing and negative for those who like sharing. Define

(A3) λ(w) = ŵ/w.

Then ŵ and λ are implicitly defined implicitly by (A4) U(1, x', ŵ – x') = U(0, w, 0)

where x' is the own payoff chosen in the sharing environment with allocation w' = ŵ.

Proof of Proposition 1. (A2) and (A4) imply that )ˆ,,1(),,1(max ],0[ xwxUxwxUwx ′−′>−∈ for those who like sharing. Since utility is increasing in wealth, ŵ < w is implied. Conversely, (A2) and (A4) imply )ˆ,,1(),,1(max ],0[ xwxUxwxUwx ′−′<−∈ for those who dislike not shar-ing. Again, because utility increases in wealth, ŵ > w is implied. The relation of λ relative to 1 follows directly from (A3). Q.E.D.

Proof of Proposition 2. Individuals with λ > 1 share in the absence of choice, but sort out of the sharing environment (and thus share zero) when given a choice. Their amount shared falls from a positive amount to zero. Individuals with λ < 1 share in the absence of choice and choose the sharing environment and share the same amount when given a choice. Individuals with λ = 1 share zero in either environment. Thus, total sharing weakly declines when indi-viduals are given a choice. Q.E.D.

Special case: Modified Cobb-Douglas utility function Proposition 3 does not hold in the general set of utility functions employed above. We con-sider a branched Cobb-Douglas utility function which allows for individuals to have the op-portunity to share (or not). Its value depends on x, y, and D as follows:

46

(A5) U D x y x D D y D D D D( , , ) [ ( )/ ][ ][ ( ) ( ) ]= + − − + − + − − − −α α α λ ααα α α1 1 1 1 1 1 1

with ]1;0[∈α . This seemingly complex function is nothing more than the summary of rather simple preferences under D = 1 and under D = 0. When D = 1 (A5) becomes

(A6) αα −= 1),,1( yxyxU ,

which is the standard Cobb-Douglas formulation. The optima of x and y, given this utility function, are x* = wα and y* = w)1( α− so that

(A6′) αα αα −−= 1])1[(][*)*,,1( wwyxU

wαα αα −−= 1)1(

When D = 0, (A5) becomes

(A7) xyxU ααα ααλ −− −= 11 )1(),,0( .

And since x = w and y = 0 under D = 0

(A7′) wwU ααα ααλ −− −= 11 )1()0,,0(

This is also Cobb-Douglas, with one variable where the coefficient on x is 1. In this specifica-tion λ(w) = λ1-α. Individuals prefer D = 1 to D = 0, i. e. they like to share, if λ1-α < 1, and thus λ < 1. Individuals share under D = 1 but prefer D = 0 to D = 1, i. e. they dislike not sharing, if λ > 1. Individuals of this latter group get more utility from the environment that does not per-mit sharing, but have an 1<α and will thus share if in a sharing environment.

Note further that, under D = 1, the allocation of w to x and y does not depend on λ. Agents with equal α share the same amount αw, when placed into a sharing environment, though those with λ > 1 dislike not sharing and those with λ < 1 like sharing.

Proof of Proposition 3. The endowment ŵ at which agents are indifferent between the two environments is defined by (A4). Comparing (A7′) to (A6′), this implies (A8) ŵ = λ(1 - α)w . Differentiating (A8) with respect to α shows that ŵ is decreasing in α.

Q.E.D.

47

Appendix 2. Sample Instructions for Experiment 1 (Between-Subjects Design) The text in brackets and in italics appears only in treatments with sorting option.

General Instructions

Thank you for attending the experiment. The purpose of this session is to study how people make decisions. During the session, you are not permitted to talk or communicate with the other participants. If you have a question, please raise your hand and I will come to answer it.

During the session you will earn money. Everyone will receive €5 for their participa-tion, which will be the minimum compensation for everyone. In addition, there exists a possi-bility that some may earn more money. At the end of the session the quantity that you have earned will be paid to you in cash. The payments are confidential; we will not inform any of the other participants of the quantity that you earn.

In a moment, you will receive an envelope. Once everyone has received an envelope, you may open it and you will see a card with a number. This is your identification number for the experiment. After looking at it, please keep this number since it will be used during the experiment. This number is private and should not be shared with anybody else.

In a moment, I will ask that all of the participants with even numbers, meaning 2, 4, 6, 8, etc., follow me outside this room. These participants will go to an adjacent area, where they will complete a brief questionnaire, and will receive the €5 payment from the experimenter for their participation. When leaving the room, please take all of your belongings.

Instructions for participants with odd numbers

In this experiment, each of you will [decide whether to participate or not] participate in an activity. [That is, participating in the activity is optional]. The activity is the following:

The activity: You will be paired with one of the participants who just left this room. That is, each of you will be paired with one of the participants with an even number (2, 4, 6,…). The pairings will be made randomly and anonymously, which means that no-body will know the identity of the person with whom he or she is paired. You will have to decide how to distribute €10 between yourself and the person with whom you are paired. That is, you will decide how much money, between €0.00 and €10.00, to give to the other person and how much to keep for yourself. For example, you may decide to give €9.00 to the other person and keep €1.00 for yourself, or you may instead decide to give €1.00 to the other person and keep €9.00 for yourself. You may select any distribu-tion of the €10 between yourself and the other person, in increments of €0.10. The as-signed amounts will be paid to you and to the other person (in addition to the €5 for par-ticipation).

Are there questions about the activity?

The participants in the adjacent area do not know anything about this activity. They received a questionnaire and were asked to complete it.

[You must decide whether to participate or not participate in the activity.

• If you opt to participate in the activity, you will be paired with one of the other partici-pants and will distribute the €10 between yourself and this participant.] At the conclusion of the session the participant with whom you are paired will reenter this room and I will

48

explain the activity to him or her. This participant will then discover how much money he or she received from you and how much you kept for yourself. You and the other partici-pant will receive these quantities, plus the €5 for participation.

• [If you opt not to participate in the activity you will not be paired with any other partici-pant and you will not distribute any money. In this case you will receive a fixed amount of €10 (plus the €5 for participation), but you will not have the option to distribute this money. At the conclusion of the session, I will go to the adjacent area and I will pay €5 to the people who are not paired with anyone in this room. These people will not receive any information about the activity.]

This session will now proceed as follows:

1) Each of you has an envelope […two envelopes: one labeled “participate” and another “don’t participate”]. Please do not open this envelope [either envelope] yet.

2) [If you decide to not participate in the activity, you will open the envelope labeled “don’t participate.” Inside this envelope is a sheet. Once you open the envelope, you will remove the sheet and write your participant number in the indicated space. You will receive €10.

3) If you decide to participate in the activity, you will open the envelope labeled “partici-pate.”] Inside the envelope is a sheet with the number of the participant with whom you are paired and on which you will indicate how to distribute the €10 between the other per-son and yourself. Once you open the envelope, you will remove the sheet and will write your participant number in the indicated space. In addition you should look over the sheet to see the number of the participant with whom you are paired. You should then indicate how you wish to distribute the €10 between the other participant and yourself. The total of the two quantities should sum to exactly 10.00. If they do not sum to 10.00, then the other participant will receive the amount that you specify and you will receive the remainder.

4) [In either case,] Once you finish, place the sheet back in the envelope and I will collect the envelopes.

At the end of the session, we will do the following:

5) The experimenter will go to the adjacent area and will bring the other participants. […only those participants who are paired with someone who opted to participate in the activity. The rest of the participants in the adjacent area will not be paired, will receive the €5 for their participation and for them the experiment will have concluded.

6) If you opted to participate in the activity, the participant with whom you are paired will reenter this room and will …] These participants will receive a brief explanation of the ac-tivity. The participant with whom you are paired will receive the sheet that you com-pleted, indicating how much money he or she received from you, out of the €10.

7) The experimenter will then anonymously pay the other participants [who are paired with someone in this room] their total earnings, and will then pay you anonymously. This will conclude the experiment.

Are there questions? Once we answer any questions we will proceed to open the envelopes. [Please open only one of the two envelopes.]

49

Decision sheet

Number of the person with whom you are paired: __________

Your number (please write your number in the space on the right): __________

Amount of money to give to the other person: €_____.____ (in €0.10 increments)

Amount of money to keep for yourself: €_____.____ (in €0.10 increments)

(These two quantities must sum to €10.00)

Decision sheet

You have opted to not participate in the activity. You will not be paired with another partici-pant. At the end of the session, you will receive €10 plus the €5 for participation.

Your number (please write your number in the space on the right): __________

Instructions for participants with even numbers

During the next few minutes, please complete the questionnaire on the attached sheet. After finishing, please wait a few minutes quietly for me to return. At that time, I will pay you the €5. In addition, it is possible that I will require the participation of some of you for a brief ad-ditional activity in the session.

While you wait, you may complete the payment receipt. Please leave the amount blank.

Final information for participants with even numbers

While you were out of this room, [some of] the participants here participated in an activity in which they distributed €10 between themselves and one of you. You are paired with one of these participants. This other participant decided how much money, from €0.00 to €10.00, to give to you and how much to keep for him- or herself. In a moment you will see a sheet on which this participant has indicated how much money to give to you. This amount, along with the €5 for participation, will be your payment for this session.

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Appendix 3. Sample Instructions for Experiment 2 (Within-Subject Design)

Initial Instructions

This is an experiment in decision-making. Several research institutions have provided funds for this research. In addition to a $6 participation bonus, you will be paid any additional amount you accumulate during the experiment privately, in cash, at the end. The exact amount you receive might vary and will be determined during the experiment. If you have any ques-tions during the experiment, please raise your hand and wait for an experimenter to come to you. Please do not talk, exclaim, or try to communicate with other participants during the ex-periment. Participants intentionally violating the rules may be asked to leave the experiment and may not be paid. We will now assign everyone in the room a participant number. Please take an enve-lope from the experimenter. In each of the randomly shuffled envelopes is a card with a num-ber from 1 to 20. The number in your envelope is your participant number for the remainder of the experiment. Your participant number is private and should not be shared with anyone. We would now like to ask all of you who have participant numbers between 11 and 20 to follow the experimenter to an area outside of this room. These participants will complete a series of short questionnaires for about 25 minutes. They will not be paid any money for do-ing so.

Instructions for Participants 1-10

Participants with numbers 1 through 10 will now make a series of decisions. There will be a total of 5/6 decisions. At the end of the experiment, we will randomly select one of these decisions and only this decision will count. We will select the decision that counts by randomly drawing a number from 1 to 5/6. Each participant will be paid based only on this decision (in addition to the $6 participation bonus). Since you do not know which of the deci-sions this will be, you should treat each decision as if it were the only one that counted –it could end up being so.

For each decision, the experimenter will hand you a set of sheets. Please wait until everyone has their sheets before turning them over. After you are done, the experimenter will collect all of the sheets and we will move on to the next decision.

Are there any questions before we proceed?

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Decision 1 (Anonymity)

In the first decision, you will play a game in which you will be matched with one of the participants in the adjacent area (i.e., participants 11-20). The match is anonymous and determined by random draw. In the game, you will allocate 40 tokens between yourself and the participant with whom you are matched. Each of the tokens is worth $0.25 cents. This means that the total value of the tokens is $10.00. Your decision will be to allocate any number of tokens between 0 and 40 to the matched participant and keep the remainder for yourself. For instance, if you keep all 40 tokens then you will receive $10 at the end of the experiment and the person you are anonymously matched with will receive $0. Or, if you give all 40 tokens then you will re-ceive $0 and the person you are matched with will receive $10. The participants in the adjacent area have not been told anything about this game. They were given a set of questionnaires and asked to proceed through them at their own pace. However, if this decision is selected as the one that counts, then the experimenter will bring all participants 11-20 into the room at the end of the experiment. The experimenter will then explain the game you have played to them by reading the basic instructions aloud. Each of these participants will then find out how many tokens he or she received from the participant in this room with whom he or she was anonymously matched. The game will now proceed as follows:

5) Each of you has an envelope in front of you. Please do not open this envelope yet. Inside the envelope is the number of the participant you will be matched with and a sheet on which you will indicate your decision.

6) Once you open the envelope, you should make sure that the other participant’s number is on the sheet. You should then write your participant number in the space where it asks you to do so.

7) You should then indicate how you wish to allocate the 40 tokens between yourself and the other participant. The total of the two amounts should sum to exactly 40. If they do not sum to 40, then the other participant will receive whatever sum you specify and you will receive the remainder.

8) The experimenter will then collect these sheets from you.

If, at the end of the experiment, this decision is selected to count, then the end of the experi-

ment will proceed as follows:

9) The experimenter will bring participants 11-20 back into the room and will briefly explain the game to them. The participant you are matched with will then receive the sheet that you filled out, indicating how many tokens he or she received.

10) The experimenter will then anonymously pay participants 11-20 their total earnings, and will then anonymously pay all of you. This will conclude the experiment.

Are there any questions? If not, then please proceed by opening your envelope.

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Decision 1 (No Anonymity)

In the first decision, you will play a game in which you will be matched with one of the participants in the adjacent area (i.e., participants 11-20). The match is determined by ran-dom draw. In the game, you will allocate 40 tokens between yourself and the participant with whom you are matched. Each of the tokens is worth $0.25 cents. This means that the total value of the tokens is $10.00. Your decision will be to allocate any number of tokens between 0 and 40 to the matched participant and keep the remainder for yourself. For instance, if you keep all 40 tokens then you will receive $10 at the end of the experiment and the person you are matched with will receive $0. Or, if you give all 40 tokens then you will receive $0 and the person you are matched with will receive $10. The participants in the adjacent area have not been told anything about this game. They were given a set of questionnaires and asked to proceed through them at their own pace. However, if this decision is selected as the one that counts, then the experimenter will bring all participants 11-20 into the room at the end of the experiment. The experimenter will then explain the game you have played to them by reading the basic instructions aloud. Each of these participants will then find out how many tokens he or she received from the participant in this room with whom he or she was matched, as well as the identity of the person with whom he or she was matched. The game will now proceed as follows:

11) Each of you has an envelope in front of you. Please do not open this envelope yet. Inside the envelope is the number of the participant you will be matched with and a sheet on which you will indicate your decision.

12) Once you open the envelope, you should make sure that the other participant’s number is on the sheet. You should then write your participant number in the space where it asks you to do so.

13) You should then indicate how you wish to allocate the 40 tokens between yourself and the other participant. The total of the two amounts should sum to exactly 40. If they do not sum to 40, then the other participant will receive whatever sum you specify and you will receive the remainder.

14) The experimenter will then collect these sheets from you.

If, at the end of the experiment, this decision is selected to count, then the end of the experi-

ment will proceed as follows:

15) The experimenter will bring participants 11-20 back into the room and will explain the game to them. You will then hand to the participant with whom you were matched the sheet you filled out, indicating how many tokens he or she received.

16) The experimenter will then anonymously pay participants 11-20 their total earnings, and will then anonymously pay all of you. This will conclude the experiment.

Are there any questions? If not, then please proceed by opening your envelope.

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Decision 2 (Anonymity)

In the second decision, you will have the opportunity to play exactly the same game as in Decision 1. Alternatively, you can decide not to play the game (i.e. you can “pass”), in which case you will receive the fixed sum of $10 (plus the $6 participation bonus). You now have two envelopes in front of you. One is labeled “play” and the other is labeled “pass.” Please do not open either envelope until we are done reading the instructions. If you choose to play the game, open the envelope marked “play.” This envelope will have a sheet like the one in Decision 1. If you open this envelope, then you will be matched with the person whose participant number is on the sheet. The participant number may differ from the one in Decision 1 since the envelopes were randomly distributed each time. You should then write your participant number on the sheet and indicate how you wish to allocate the 40 tokens (each worth 25 cents, i.e. $10 in total). If this decision is selected at the end of the experiment, the matched participant will be brought back into the room and will be told about the game. This matched participant will then receive the sheet you filled out indicating how much he or she received. If you choose not to play the game, open the envelope marked “pass.” Inside this en-velope is a sheet on which you will write your participant number and mark an “X” to indicate that you pass. You will not be matched with one of the participants outside the room and you will not allocate tokens. If this decision is selected at the end of the experiment, you will re-ceive a fixed sum of $10. Notice that if you choose to play the game, then you will be matched with one of the participants outside. If you choose to pass, then you will not be matched with any of the par-ticipants outside. If Decision 2 is selected as the one that counts, then at the end of the experiment the experimenter will go to the area with the other participants and ask: “Will the participants with the following numbers please come back into the room?” If you chose to play the game, then the number of the participant with whom you are matched will be read to the participants outside, and this participant will be brought back into the room. The experimenter will explain the game aloud to the participants who are brought back into the room and will then give them the sheets filled out by the participants in this room with whom they were matched. If you chose not to play the game, then the number of the participant with whom you would have been matched will not be read to the participants outside, and this participant will receive the $6 participation bonus and will leave the experiment without learning anything about the game. Are there any questions? If not, then please proceed by opening only one of the two envelopes.

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Appendix 4. Questionnaire Participant number __________

Questionnaire

Please write your participant number (the number you received in the envelope at the be-ginning of the experiment) in the space at the top of this page. We would like you to answer some questions. Please answer all of the questions truthfully. Your responses will be anonymous and this information will be stored and analyzed only with your participant number as identification.

1. What is your age? _____________ years 2. What is your gender? Male Female 3. What is your race or ethnic group? ________________________________________

(If you are unsure how to answer, please write your city and country of birth.) 4. What language do you primarily speak at home? ________________________ 5. What is the highest level of education you have completed? ___________________ 6. What is your year and major? ______________________________________________________________________ 7. For how many years have you lived in Barcelona? _________ years 8. How many brothers and sisters do you have? __________ 9. During the past year, have you made any donations to an organization that provides charity or human aid? Yes No 10. Would you say that you are someone who likes or dislikes taking risks?

I like taking risks I dislike taking risks 11. Which of the following terms best describes your social class?

Upper class Upper/middle class Middle class Lower middle class Lower class 12. How many people in the other area do you know? _________

Thank you for completing the questionnaire. Once you are done, please wait.