Choices in Two-Person Interactions:
The Effect of Amount and Social Distance on Offers
in the Dictator and Ultimatum Games
Christopher Bechler1
Washington University in St. Louis
March 17, 2013
Abstract
Proposers in the Dictator Game and the Ultimatum Game often do not act as normative
economic theory predicts. Offers are frequently higher than what would be considered income
maximizing. The present study investigates two effects on the amount offered by the proposer.
The first is whether the initial amount provided to the proposer systematically affects the amount
offered (a magnitude effect). The second is whether the social distance between the proposer and
responder influences the amount offered (the social distance effect). Three amounts ($10, $3,000,
and $250,000) at each of three social distances (2, 20, and 100) are studied under the Dictator
Game and the Ultimatum Game. The amount offered is consistently higher under the Ultimatum
Game, and the proportion of the amount offered decreases both as the size of the initial
endowment increases and as the social distance between proposer and responder increases. The
pattern of findings is not differentially affected by demographic factors, including gender, age,
education, income, ethnicity, race, religion, political ideology, political affiliation, geographic
region, or city size, with the exception of a gender difference in the Dictator Game. Offers made
to relatives are higher than those made to non-relatives at a social distance of 2 for the Dictator
Game, but are not significantly different for the Ultimatum Game. These results extend the
generality of findings with two-person economic games and argue for the importance of amount
and social distance in understanding why people fail to conform to normative economic
predictions.
1
I would like to thank Professor Leonard Green, my thesis advisor, for his dedication to this
project. I also would like to thank Professor Joel Myerson, Professor Bruce Petersen, and
Professor Dorothy Petersen for their valuable time and insightful comments.
Bechler
2
Introduction
Two-person economic games have been used widely in experimental and behavioral
economics to increase the explanatory power of economics, test economic theories, and gain
insight into factors that influence people’s everyday actions in an effort to more accurately predict
the decisions they will make in the future (Camerer, Loewenstein, & Rabin, 2011). Two
extremely popular forms of economic games, the Dictator Game and the Ultimatum Game, have
received increasing attention as tests of normative economic theory, particularly as a means of
studying the potential roles of self-interest and altruism in economic decision-making. These two
games also have tangible real-world applications, particularly in contract negotiations. In the
Dictator Game, a first player (the ‘proposer’) is given a hypothetical sum of money. He is told
that he is free to offer as much or as little of this amount to a second player (the ‘responder’), and
that he will receive what is left. The responder has no say in the matter. The rules of the
Ultimatum game are similar except that the responder now has the option to accept or reject the
proposer’s offer. If the offer is accepted, then both players receive the amounts agreed upon; if
the offer is rejected, however, then both players receive nothing.
Normative economic theory predicts that in a non-repeated game, proposers always will
offer the smallest unit of currency to the responder regardless of which form of the game is
played, and that the responder should always accept the offer (if given the choice). However,
participants frequently do not act as theory predicts. Rather, the proposer often offers
considerably more than the minimum amount predicted. Mean offers in the Dictator Game are
around 20 percent of the initial amount (Oxoby & Spraggon, 2008). In the Ultimatum game, the
most common offer is a 50-50 split, and the mean offer usually is between 30-40 percent of the
original amount (Camerer & Thaler, 2009). Responders in the Ultimatum Game also behave
‘irrationally’ from the point of view of normative theory (assuming responders get no utility from
punishing unfairness, which is likely not the case) rejecting offers they should accept. For
example, responders commonly reject offers lower than 20 percent of the initial amount (see e.g.,
Camerer & Thaler, 2009). These findings have been replicated in numerous studies and across
several cultures, including Jerusalem, Ljubljana, Pittsburgh, and Tokyo (Roth, Prasnikar, OkunoFujiwara, & Zamir, 2003).
The notion of fairness is one explanation for why more is offered under both games and
why responders often reject an offer in the Ultimatum Game. For example, proposers offer less
Bechler
3
and responders are willing to accept less when the proposer has done something to earn the
original sum of money. It is assumed in this example that the proposer “deserves” more because
he or she has worked to earn the money (Hoffman, McCabe, Shachat, & Smith, 2008). In another
study, a market of responders was created in which each responder simultaneously decided the
lowest amount he or she would be willing to accept (Roth et al., 2003). The proposer then played
the game with the responder willing to accept the smallest offer. Responders were willing to
accept offers as low as 10% or less of the initial endowment under this situation, a considerably
smaller amount than typically is obtained with responders playing the Ultimatum Game. The
explanation for this finding was that the proposer was taking the best deal available and as such,
there is nothing unfair in this situation (Roth et al., 2003). There also is reason to believe that
one’s desire for fairness is a learned trait: Kindergartners behave most similarly to income
maximizers because they are the most likely to accept minimal offers (Murnighan & Saxon,
1998).
Culture also plays a role in the amount of the allocation and what is deemed “fair.”
Members of the Peruvian Amazon’s Machiguenga people offered a significantly smaller
percentage of the initial amount compared to control groups in cities like Los Angeles (Henrich,
2000). In addition, the rejection frequency among Machiguenga responders was much lower
when compared to control groups, signaling that many responders felt the offer was fair.
Fairness alone, however, cannot explain why observed offers are consistently greater than
predicted offers. If fairness alone were the reason, then offers for the Dictator Game and the
Ultimatum Game should be equivalent. However, proposers offer a significantly lower
percentage when participating in the Dictator Game as compared to when they play the
Ultimatum Game (Forsythe, Horowitz, Savin, & Sefton, 1994). The same findings were obtained
whether the initial amount given to the proposer was $5 or $10.
Few studies have evaluated whether a magnitude effect obtains under the Ultimatum and
Dictator Games. Specifically, little attention has been paid to whether the amount of money
initially given the proposer affects the percentage he or she offers the responder. Magnitude
effects have been studied extensively in other behavioral economic experiments, most notably
those on delay discounting and probability discounting. As the amount of delayed money
increases, the rate of discounting decreases. In contrast, as the amount of probabilistic money
increases, the rate of discounting increases (e.g., Green, Myerson, & Ostaszewski, 1999; for a
review, see Green & Myerson, 2004). The magnitude effect was first studied in the Ultimatum
Game using real amounts of $10 and $100 with inconclusive results: An increase in the initial
endowment resulted in a smaller proportion offered in some trials, but did not in others (Hoffman,
Bechler
4
McCabe, & Smith, 1996). In contrast, a more recent study reported a magnitude effect in the
Ultimatum Game: The percentage of the initial amount offered decreased as the initial amount
increased (Andersen, Ertac, Gneezy, Hoffman, & List, 2011). The study, conducted in India,
used four real amounts: 20, 200, 2,000, and 20,000 Indian rupees, equivalent to $0.41, $4.10,
$41.00, and $410.00 US, respectively.
Economists justify this magnitude effect for the Ultimatum Game by pointing out that the
opportunity cost for rejecting an offer is higher when a larger initial sum of money is used. As
the size of initial endowment increases, the cost of punishment goes up. Thus, a responder is
more likely to accept a lower percentage offer when the initial endowment is large because the
responder’s gain in utility for punishing the proposer for an unfair offer becomes less than the
extra utility obtained from accepting the offer. Due to this switch in preference, responders are
less likely to reject a low percentage offer as the endowment increases. Understanding that the
opportunity cost for rejecting an offer is increasing for responders, proposers rationally allocate a
lower proportion to responders as the size of the initial endowment increases. The following
model lays out the problem faced by the responders. Given the following variables and
assumptions:
S = size of the initial endowment,
F = fraction of the initial endowment allocated by the proposer,
S  F = opportunity cost of rejecting an offer,
B(S, F) = the dollar benefit of punishing a proposer for unfairness,
Assume B ( S , F )  0 whenever F < 0.5,
Assume
B( S , F )
 2 B( S , F )
B(S , F )
 0,
 0,
 0,
F
S
2S
responders will be indifferent between accepting and rejecting an offer whenever:
B(S, F)  S  F,
or
B(S , F )
 F.
S
This model shows the minimum level of F (fraction of initial endowment) a responder
will accept given the dollar benefit they receive from punishing a proposer and the size of the
initial endowment. As long as B(S,F) increases less than proportionately with S, then the
minimum level of F at which the responder accepts falls as S goes up. Proposers who seek to
maximize their utility allocate less to responders when the size of the endowment increases
because they understand that responders will behave in this manner.
Bechler
5
However, responders do not always behave as one would predict when amounts increase.
When the Ultimatum Game was played with a real sum of $100 and against proposers who had
earned the right to move first, 3 of 4 responders rejected offers of $10, 10% of the initial
endowment, and 2 of 5 participants rejected offers of $30, 30% of the initial endowment
(Hoffman et al., 1996). This was a higher rejection rate than the same condition at $10, showing
that proposer intuition may not be a good predictor of responder behavior.
Robert Aumann, the Noble Prize Winner in Economics in 2005, claims that he would still
offer half of the initial sum even for huge amounts (such as $1 million) under the Ultimatum
Game due to risk aversion (Camerer & Thaler, 2009). From the proposer’s point of view, a
responder’s rejection causes the proposer more harm as the initial endowment increases.
Therefore, a risk-averse individual may offer a constant or even an increasing proportion as the
amount of the initial endowment goes up to ensure that their offer will be accepted. It is worth
noting, however, that risk-aversion may not be the norm. When presented with the same initial
endowment of $1 million, the majority of economists claimed that, in contrast to Aumann, they
would offer an amount between $50,000 and $100,000.
Engel (2011) provides some evidence of a magnitude effect in the Dictator Game. His
meta-analysis of more than 100 Dictator Game experiments found that when the stakes were
higher, dictators kept more in both absolute and relative terms (Engel, 2011). These findings are
consistent with a very small magnitude effect, but the results should be interpreted cautiously.
The few amounts studied and the limited range over which amounts varied (from less than $1 to
$130), combined with the theoretical importance of magnitude effects, suggest the need for
systematic replication. One goal of the current study, then, was to investigate the effect of
magnitude over a wide range of initial amounts in both the Ultimatum and Dictator Games.
Another variable of interest that may well influence the proportion of the amount offered
is the social distance between the proposer and the responder. Previous research has
demonstrated that proposers in the Dictator Game are more altruistic (i.e., offer more money)
when they feel closer to the responders (Charness & Gneezy, 2008). Another study of a similar
economic game used a self-determined scale of social distance to show that participants will often
be more altruistic when playing with someone they feel closer with and when playing with
someone who is genetically related to them (Rachlin & Jones, 2008). The present study attempts
to replicate the findings under the Dictator Game. Moreover, there has been little research on the
effect of social distance on Ultimatum Game offers, but initial research suggests the strategy
involved in playing the game may crowd out the desire to give to those with whom the proposer
feels closest. The most pertinent study showed no significant difference in allocations when
Bechler
6
responders’ family names were revealed in the Ultimatum Game (Charness & Gneezy, 2008).
However, this study only looked at two conditions, both of which used fairly far social distance:
one where offers were made to nameless individuals from another university, and one where
offers were made to individuals from another university whose family name was known. The
current effort measures social distance effects over a larger scale and at a much closer social
distance than previous Ultimatum Game experiments.
Analysis of these games using larger initial endowments and under varying degrees of
social distance is especially important due to the real-world applications of these games. The
Ultimatum Game is a simple example of labor union negotiations; a firm makes an offer to the
labor union and the union can accept or reject the offer. If it is accepted, the firm and the labor
union receive the amounts allocated to them. If rejected, both sides receive nothing. Oftentimes,
these negotiations involve huge sums of money and varying social distances. Rejected offers can
result in large deadweight loss. The same behaviors tested in this game also predict decisionmaking in other contract situations, although the deadweight loss that results from a rejected offer
in these circumstances is much smaller since employees can work elsewhere and employers can
find a replacement. A prime example is baseball contract negotiations. Findings from typical
$10 Ultimatum Games are not sufficient for analyzing behavior under such conditions.
In addition to manipulating amount and social distance, this study is the first to test the
effect of social distance on the proportion of amount offered in the Dictator Game and the
Ultimatum Game using a self-determined scale of social distance. The use of a relatively large
sample size also allowed us to evaluate the influence of other demographic variables, including
gender, age, education, income, ethnicity, race, religion, political ideology, political affiliation,
geographic region, and city size, on the proportion offered.
Method
Participants
201 participants nationwide were recruited through the Amazon Mechanical Turk
(MTurk) participant pool for the Dictator Game. 193 participants were recruited in the same
fashion for the Ultimatum Game. Participants were required to have a Human Intelligence Task
(HIT) Approval rate greater than or equal to 85% and to live in the United States to preview the
experiment. The HIT Approval rate meant that for individuals to participate in the study, they
had to have completed 85% of their previous MTurk experiments in a manner acceptable to the
Bechler
7
experimenter. Participants were compensated for their participation by choosing to receive either
25 cents that day or 50 cents in 30 days.
Procedure
After consenting, participants in the Dictator Game read the following Instructions and
Directions:
Thank you for agreeing to participate in this brief study.
You will be asked to make a series of decisions regarding how much
money you might offer another person under various situations that will be
explained shortly. There are no correct or incorrect answers, and the money is
hypothetical – that is, no one will receive the actual money. Nonetheless, we
want you to make your decisions as if the amounts and situations were real.
Before describing the situations, we want you to imagine that you have
made a list of the 100 people closest to you in the world, ranging from your
dearest friend or relative at position #1 to a mere acquaintance at #100. The
person at number one would be someone you know well and is your closest friend
or relative. The person at #100 might be someone you recognize and encounter
but perhaps you may not even know their name. You do not have to physically
create the list - just imagine that you have done so.
Imagine you have been given the amount of money shown in the
following slides. You are to divide the amount of money between yourself and
another person. You are free to give as much or as little of the amount of money
as you wish, and you will receive what is left. Please allocate the amount you
wish to offer the other person by typing it in the space provided.
The procedure for the Ultimatum Game was the same as that for the Dictator Game,
except for the last paragraph of the Instructions and Directions, which read:
Imagine you have been given the amount of money shown in the
following slides. You are to divide the amount of money between yourself and
another person. You are free to give as much or as little of the amount of money
as you wish, and you will receive what is left, but only if the other person accepts
your offer. If the other person rejects your offer, however, then both of you will
receive nothing. Please allocate the amount you wish to offer the other person
by typing it in the space provided.
Bechler
8
Participants were studied with three initial amounts ($10, $3,000, and $250,000) and at
three social distances (2, 20, and 100). Each participant randomly encountered each social
distance at each amount for a total of nine conditions. Participants then were asked to report the
relation of the person they thought of at each social distance (i.e., a relative, a non-relative, or had
no one in mind). Upon completion, the participant completed a brief demographic questionnaire
that asked for gender, age, education, income, ethnicity, race, religion, political ideology, political
affiliation, geographic region, and city size. Finally participants were offered the real choice of
having 25 cents placed in their account that day, or 50 cents placed in their account in 30 days.
The experiment was administered using Qualtrics Survey Software.
Results
Dictator Game
Figure 1 shows the mean relative proportion offered at each amount and at each social
distance for the Dictator Game. Proposers offered a significantly lower percentage to the
responder as the proposer’s initial amount of money increased, F(degrees of freedom between
groups = 2, degrees of freedom within groups = 199) = 69.24, p < 0.001. Offers made when the
initial endowment was $10 averaged 24.1%, whereas offers made when the initial endowment
was $3,000 averaged 14.5%, and offers made when the initial endowment was $250,000 averaged
10.7%. Proposers also offered proportionally less as the social distance between proposer and
responder increased, F(2, 199) = 190.39, p < 0.001. The average offers across all initial amounts
were 31.5%, 11.5%, and 6.5% at social distances 2, 20, and 100, respectively. The decrease in
the proportion of the amount offered as the amount increased represents a magnitude effect, and
the decrease with increasing social distance represents a social distance effect. There also was a
significant interaction between amount and social distance, F(4, 197) = 4.14, p = 0.003.
Ultimatum Game
Figure 2 presents the mean relative proportion offered at each amount and at each social
distance for the Ultimatum Game. As with the Dictator Game, both a significant magnitude and
social distance effect were observed: Proposers offered a significantly lower percentage as the
initial amount increased, F(2, 191) = 71.80, p < 0.001, and as the social distance from the
responder increased, F(2, 191) = 122.59, p < 0.001. The average offer was 35.8% when the
initial endowment was $10, 25.9% when the initial endowment was $3,000, and 22.2% when the
Bechler
9
initial endowment was $250,000. Across all initial amounts, average offers were 39.8%, 25.4%,
and 18.7% at social distances 2, 20, and 100, respectively. In contrast to the Dictator Game
findings, there was no significant interaction between amount and social distance, F(4, 189) =
1.72, p = 0.147. The relative amounts offered by the proposer were consistently higher for the
Ultimatum Game than for the Dictator Game (see Figure 3) in each of the nine conditions.
Demographic Variables
Figure 4 shows the mean proportion offered averaged across all nine conditions as a
function of gender of the proposer for the Dictator Game and the Ultimatum Game. Women
offered significantly more than did men in the Dictator Game, F(1, 199) = 4.15, p = 0.043,
allocating an average offer of approximately 18.1% of the initial amount, compared to an average
offer of 14.7% for men. The gender effect was not obtained in the Ultimatum Game, F(1, 190) =
2.434, p = 0.120. A similar analysis compared mean proportion offered as a function of Political
Affiliation for both games (see Figure 5). Political party affiliation had a marginally significant
effect on mean proportion offered in the Dictator Game, F(2, 169) = 3.02, p = 0.051. Democrats
offered on average 18.9% of the initial amount whereas Republican average offers were 12.9%.
There was no significant effect of political affiliation for the Ultimatum Game, F(1, 163) = 0.272,
p = 0.762.
There was no significant Pearson correlation between mean proportion offered and
participant age in either the Dictator Game, r = -.014, p = 0.848, or the Ultimatum Game, r =
.071, p = 0.325. This can be seen in Figure 6, where age was categorized for illustrative
purposes. Figure 7 shows the correlation of the mean proportion offered and annual income for
both games. The Spearman correlations were not significant: r = -0.026, p = 0.716 for the
Dictator Game, and r = 0.047, p = 0.519 for the Ultimatum Game.
There were no significant differences in the mean proportion of the amount offered for
any of the other demographic variables (level of education, ethnicity, race, religion, political
ideology, geographic region, and city size). There was no significant difference in average offers
between those who chose to receive their 25 cents compensation that day or 50 cents in 30 days
for either the Dictator Game, F(1, 186) = 1.70, p = 0.194, or the Ultimatum Game, F(1, 177) =
1.93, p = 0.167. Summary statistics for these variables are given in Table 1.
Results from the Ultimatum Game showed no significant difference between the mean
proportion offered for participants who had relatives, non-relatives, or no one in mind at a social
distance of 2, F(2, 190) = 0.007, p = 0.993, a social distance of 20, F(2, 190) = 1.886, p = 0.155,
or a social distance of 100, F(2, 190) = 0.759, p = 0.470. In other words, the proportion offered
Bechler 10
in the Ultimatum Game did not depend on the genetic relationship between the proposer and
responder. For the Dictator Game, participants made significantly different mean offers
depending on whom they had in mind at social distance 2, F(2, 198) = 6.401, p = 0.002. At social
distance 2, participants with a relative in mind offered on average 33.5% of the initial
endowment. Those who had non-relatives in mind and those who had no one in mind made
average offers of 30.7% and 16.7%, respectively. Mean offers at social distance 20 were not
significantly affected by who participants had in mind, F(2, 198) = 1.038, p = 0.356. There was a
sufficient number of participants who indicated they had each of the three possible categories of
who the participant had in mind to perform this analysis at a social distance of 2 and 20. Very
few participants (2 playing the Ultimatum Game, and 6 playing the Dictator Game), however,
indicated they were thinking of a relative at a social distance of 100. Therefore, no statistical
analysis was conducted at this social distance. Descriptive statistics of these results are provided
in Table 2.
Discussion
In both forms of economic game at a social distance of 2, the median and modal offers
were $5 when the initial endowment was $10. For the same amount condition, the modal offers
at both social distances 20 and 100 were $0 for the Dictator Game and $5 for the Ultimatum
game. The median offers at these respective social distances for the Dictator Game were $1 and
$0, and for the Ultimatum Game were $4 and $2. The mean offers for the $10 condition under
the Dictator Game were $4.08, $1.92, and $1.21, and under the Ultimatum Game were $4.68,
$3.44, and $2.62, for social distances 2, 20, and 100, respectively. These results compare well
with previous results from both the Dictator Game and the Ultimatum Game (e.g., Camerer &
Thaler, 2009), and suggest that results with Amazon Mechanical Turk are consistent with
previous studies of economic game behavior, although previous studies did not look at quite the
same range of social distances. Other studies also have shown that MTurk produces results
consistent with typical laboratory findings (e.g., Goodman, Cryder, & Cheema, 2013; Raihani &
Bshary, 2012).
Mean offers for the Ultimatum Game fell below 20% in three situations ($3,000 and
social distance 100, $250,000 and social distances 20 and 100; see Figure 2) meaning they fall
below the threshold where offers are commonly rejected in the Ultimatum Game (Camerer &
Thaler, 2009). One possible reason for this is that proposers recognize that the opportunity cost
for rejecting an offer is higher for responders at these larger amounts. Since responders are less
Bechler 11
likely to reject a low percentage offer, proposers allocate proportionally smaller amounts.
However, previous findings show that responders are still likely to reject such offers even at high
amounts (Hoffman et al., 1996). These results suggest that a proposer’s intuition for a future
responder’s actions may not be a good predictor of responder behavior. At the same time, $3,000
and $250,000 are sufficiently larger than amounts previously tested, and it is likely that
responders would often accept offers of lower proportions than 20%. Future study is necessary to
examine responder actions under the Ultimatum Game at larger amounts. One follow-up study
could look at the percentage of offers rejected at 20% of the initial sum as a function of amount.
With more data from responders, one could also analyze whether proposers’ average offers under
the Ultimatum Game are optimal at varying amounts.
Results from both economic games showed both a magnitude and a social distance effect.
To my knowledge, we have shown a magnitude effect over a larger range of amounts than
previously has been tested. As the initial amount of money increased, the proportion of
hypothetical money offered decreased. In addition, participants offered a significantly higher
proportion of the initial amount when they were closer to the responder using Rachlin’s scale of
social distance (Rachlin & Jones, 2008). One difference in the results between the two games
was the significant interaction between amount and social distance in the Dictator Game. This
interaction likely was due to a floor effect, meaning the data could not take values below a lower
limit (in this case $0). For the larger amounts ($3,000 and $250,000), the proportion offered
under the Dictator Game was close to zero. Since participants could not offer negative amounts,
this floor effect resulted in the significant interaction. The low proportion offered under the
Dictator Game at $250,000 may appear to be consistent with normative economic theory, but this
small percentage (2.4%) translates to $6,110, not an insignificant absolute amount. There was no
interaction (and no apparent floor effect) in the Ultimatum Game.
One of the purposes of the current experiment was to investigate the role of a genetic
relationship on offers in the Dictator Game and the Ultimatum Game. Neither game required
participants to think specifically of a relative or a non-relative when making their decisions, and
many participants indicated they had “no one in mind” at each social distance. Of note, the
majority of participants did report having a relative in mind at the closest social distance studied
(70.15% for the Dictator Game and 70.98% for the Ultimatum Game, at social distance 2). At the
intermediate social distance, 14.43% and 15.03% reported having a relative in mind for the
Dictator and Ultimatum Game, respectively, whereas only a small percentage of participants
reported having a relative in mind at social distance 100 (2.99% and 1.04%, respectively, for
Dictator and Ultimatum Games).
Bechler 12
There was no genetic relationship effect on offers in the Ultimatum Game at any social
distance. Our Dictator Game results at social distance 2 are consistent with findings from Rachlin
and Jones (2008) in showing that participants offer greater amounts of money to someone who is
genetically related to them than they offer to non-relatives. At social distance 20, the finding of
no difference in proportion offered as a function of whether the participant had a relative in mind
or not differs from that reported by Rachlin and Jones. It is not clear whether Rachlin and Jones
allowed participants to indicate they had no one in mind at a given social distance, as was
permitted in the current study. But even when we combined participants who indicated they were
thinking of a non-relative with those who had no one in mind at social distance 20, our findings
still did not demonstrate an effect of genetic relationship, F(1, 199) = 0.626, p = 0.430.
Excluding participants who had no one in mind also yields insignificant results, F(1, 159) =
0.259, p = 0.612.
It should be noted that the Rachlin and Jones (2008) study was not a true Dictator Game
situation. Rather, participants were asked the amount of money they would be willing to forgo to
give $75 to someone at a given social distance. A future study might inform proposers of how
genetically similar the responder was (e.g., relative, non-relative) in addition to the initial sum of
money they were given and the responder’s social distance. Such an experiment would be a
between groups design; a participant in one group may have $10 to split between himself and a
relative at social distance 2, whereas a participant in the other group would have $10 to split
between himself and a non-relative at social distance 2. It also would be interesting to see if and
how offers vary based on whether the participant had a specific person in mind. This could be
tested using a similar procedure to the one previously described, but in which one group of
participants would be told to think of a specific person at a given social distance while the other
group would receive no such instructions.
Conclusion
The present study provides another illustration of how individuals’ actions differ from the
predictions of normative economic theory. The study measured behavior over a large range of
amounts and varying social distances, and, as such, these findings may help us to better
understand and predict the behaviors of proposers in tangible applications of these games in
everyday life, such as in contract negotiations. These results extend the generality of findings of
two-person economic games and provide insight into factors that influence people’s everyday
actions, among them, the effect of amount and social distance. Whether the magnitude effect
Bechler 13
observed in the current study is due to similar processes as those involved in the magnitude effect
in delay discounting, or in other magnitude effects, remains to be determined. Regardless of the
reason for the effect, however, these findings can help in making more accurate predictions of
individual decision-making, as well as lead to descriptively richer theoretical models.
Bechler 14
References
Andersen, S., Ertac, S., Gneezy, U., Hoffman, M., & List, J. A. (2011). Stakes matter in
Ultimatum Games. American Economic Review, 101, 3427-3439.
Camerer, C. F., Loewenstein, G., & Rabin, M., (2011). Advances in Behavioral Economics. 2nd
ed. Princeton, NJ: Princeton University Press.
Camerer, C., & Thaler, R. H. (2009). Anomalies: Ultimatums, dictators and manners. In E. L.
Khalil (Ed.), The new behavioral economics. Volume 1. A taste for fairness (pp. 78-88).
Elgar Reference Collection. International Library of Critical Writings in Economics, vol.
238. Cheltenham, U.K. and Northampton, MA.: Elgar.
Charness, G., & Gneezy, U. (2008). What's in a name? Anonymity and social distance in Dictator
and Ultimatum Games. Journal of Economic Behavior and Organization, 68, 29-35.
doi:http://dx.doi.org/10.1016/j.jebo.2008.03.001
Engel, C. (2011). Dictator Games: A meta study. Experimental Economics, 14, 583-610.
doi:http://dx.doi.org/10.1007/s10683-011-9283-7
Forsythe, R., Horowitz, J., Savin, N.E., & Sefton, M. (1994). Fairness in simple bargaining
experiments. Games and Economic Behavior, 6, 347-369.
Goodman, J. K., Cryder, C. E., & Cheema, A. (2013), Data collection in a flat world: The
strengths and weaknesses of mechanical turk samples. Journal of Behavioral Decision
Making, (published electronically April 2, 2012). doi: 10.1002/bdm.1753
Green, L., & Myerson, J. (2004). A discounting framework for choice with delayed and
probabilistic rewards. Psychological Bulletin, 130, 769-792. doi:10.1037/00332909.130.5.769
Green, L., Myerson, J., & Ostaszewski, P. (1999). Amount of reward has opposite effects on the
discounting of delayed and probabilistic outcomes. Journal of Experimental Psychology:
Learning, Memory, and Cognition, 25, 418-427. doi:10.1037/0278-7393.25.2.418
Bechler 15
Hoffman, E., McCabe, K. A., & Smith, V. L. (1996). On expectations and the monetary stakes in
Ultimatum Games. International Journal of Game Theory, 25, 289-301.
Hoffman, E., McCabe, K., Shachat, K., & Smith, V. (2008). Preferences, property rights, and
anonymity in bargaining games. In J. H. Arlen & E. L. Talley (Eds.), Experimental law
and economics (pp. 349-383). Elgar Reference Collection. Economic Approaches to Law,
vol. 20. Cheltenham, U.K. and Northampton, Mass.: Elgar.
Henrich, J. (2000). Does culture matter in economic behavior? Ultimatum Game bargaining
among the Machiguenga of the Peruvian Amazon. American Economic Review, 90, 973979.
Murnighan, J., & Saxon, M. (1998). Ultimatum bargaining by children and adults. Journal of
Economic Psychology, 19, 415-445.
Oxoby, R. J., & Spraggon, J. (2008). Mine and yours: Property rights in dictator games. Journal
of Economic Behavior & Organization, 65, 703-713. doi:10.1016/j.jebo.2005.12.006
Rachlin, H., & Jones, B. A. (2008). Altruism among relatives and non-relatives. Behavioural
Processes, 79, 120-123. doi:10.1016/j.beproc.2008.06.002
Raihani, N. J., & Bshary, R. (2012). A positive effect of flowers rather than eye images in a largescale, cross-cultural dictator game. Proceedings of the Royal Society, 279, 35563564.doi: 10.1098/rspb.2012.0758
Roth, Alvin and Vesna Prasnikar, Masahiro Okuno-Fujiwara, and Shmuel Zamir (1991):
"Bargaining and market behavior in Jerusalem, Ljubljana, Pittsburgh, and Tokyo: An
experimental study", American Economic Review, vol. 81., 1068-95.
Bechler 16
Figures and Tables
0.5
Social Distance
2
20
100
Proportion Offered
0.4
0.3
0.2
0.1
0.0
$10
$3,000
$250,000
Amount
Figure 1. Mean proportion offered as a function of initial amount and social distance in the
Dictator Game. Error bars represent ± 1 standard error of the mean.
Bechler 17
0.5
Proportion Offered
0.4
0.3
0.2
0.1
Social Distance
2
20
100
0.0
$10
$3,000
$250,000
Amount
Figure 2. Mean proportion offered as a function of initial amount and social distance in the
Ultimatum Game. Error bars represent ± 1 standard error of the mean.
Bechler 18
0.5
Proportion Offered
Social Distance = 2
0.4
0.3
0.2
Dictator
Ultimatum
0.1
0.0
$10
$3,000
$250,000
Amount
0.5
Proportion Offered
Social Distance = 20
0.4
0.3
0.2
0.1
0.0
$10
$3,000
$250,000
Amount
0.5
Proportion Offered
Social Distance = 100
0.4
0.3
0.2
0.1
0.0
$10
$3,000
$250,000
Amount
Figure 3. Mean proportion offered as a function of initial amount and economic game. Error
bars represent ± 1 standard error of the mean.
Bechler 19
Proportion Offered
0.5
0.4
Male
Female
0.3
0.2
0.1
0.0
Dictator
Ultimatum
Figure 4. Mean proportion offered as a function of gender in the Dictator and Ultimatum Games.
Error bars represent ± 1 standard error of the mean.
Bechler 20
Proportion Offered
0.5
0.4
Democrat
Republican
Independent
0.3
0.2
0.1
0.0
Dictator
Ultimatum
Figure 5. Mean proportion offered as a function of political party affiliation in the Dictator and
Ultimatum Games. Error bars represent ± 1 standard error of the mean.
Bechler 21
Proportion Offered
0.5
Ultimatum
Dictator
0.4
0.3
0.2
0.1
0.0
18-24
25-29
30-39
40-49
>50
Age (years)
Figure 6. Mean proportion offered as a function of age in the Dictator and Ultimatum Games.
Error bars represent ± 1 standard error of the mean. Age has been categorized for illustrative
purposes.
Bechler 22
Proportion Offered
0.5
Ultimatum
Dictator
0.4
0.3
0.2
0.1
0.0
<25K
25K-35K
35K-50K
50K-75K
>75K
Income ($)
Figure 7. Mean proportion offered as a function of annual income before taxes in the Dictator
and Ultimatum Games. Error bars represent ± 1 standard error of the mean.
Bechler 23
Table 1. The mean proportion offered, standard deviation (in parentheses), and number of
participants for the demographic variables of Gender, Age, Education, Method of Payment,
Annual Income, Political Affiliation, and Geographic Region.
Bechler 24
Table 2. The mean proportion offered, standard deviation (in parentheses), and number of
participants for relatives, non-relatives, and no one in mind at social distances 2, 20, and 100.