Bribery: Greed versus Reciprocity
Uri Gneezy, Silvia Saccardo, and Roel van Veldhuizen
March 12, 2013
Abstract More than an estimated trillion dollars are paid each year in bribes around the world,
distorting justice and economic efficiency. A better understanding of the reasons for bribery can
help the effort to reduce it. We designed an experiment in which two participants compete for a
prize in a real-effort task. A third participant acts as a referee and picks the winner. Participants
are allowed to send a bribe to the referee. When the referee can keep only the bribe of the winner,
we find substantial bribery occurs and, in 86% of the cases, the participant with the larger bribe
wins. However, when the referee keeps all bribes, regardless of her choice of a winner,
participants bribe less, and referees are significantly less likely to ignore quality and award the
prize to the worker with the higher bribe. Hence we show that participants in our lab are easy to
corrupt, and that the mechanism by which bribes work is greed and not reciprocity.
Keywords: Bribery, Reciprocity, Laboratory Experiment
JEL Classification: D73, C91, K42
1. Introduction
Corruption affects economic activity around the world. Because it is illegal in most
places, obtaining good empirical data about corruption is difficult, although the available data
show it is wide spread. The World Bank estimates that more than $1 trillion in bribes exchanges
hands annually (Kaufmann, 2005), and many companies report having to pay bribes to win
business—from 15%-20% in industrialized countries to 40% in China, Russia, and Mexico
(Transparency International, 2011). In some countries, bribes are a major source of income to the
people. For example, bribes amounted to an estimated 20% of Russia’s GDP in 2005 (INDEM,
2005).
Some studies argue bribes are not always bad from an economic perspective, but are
simply used to “grease the wheels” of bureaucracy (e.g., Leff, 1964; Huntington, 1968). Even in
these cases, however, when bureaucrats can endogenously choose the level of corruption, bribes
have a negative effect on economic efficiency (Banerjee, 1997). In the more extreme cases,
bribes can lead to detrimental social outcomes. Consider, for example, the 2008 Sichuan
earthquake in which thousands of school children were killed. Arguably, part of the reason for
the high death toll was the poor construction of the new schools in the region. According to these
allegations, officials received bribes in return for allowing contractors to save on materials and
avoid the government building standards (York, 2008).
From an ethical perspective, corruption, and in particular bribery, is more acceptable in
some places than in others. For example, top executives at Wal-Mart knew the Mexico division
of the company was bribing (a total of $24 million) local officials, a behavior the executives
would probably have stopped had it been occurring, for example, in the United States. In a
survey conducted in Mexico, 48% of businesses said they had lost business because of bribery
(Hardoon, 2012), compared with a lower, but still very high, 30% of businesses that answered
similarly in the United States.
Black’s Law Dictionary defines bribery as “the receiving or offering of any undue reward
by or to any person whomsoever, whose ordinary profession or business related to the
administration of public justice, in order to influence his behavior in office, and to incline him to
act contrary to his duty and the known rules of honesty and integrity.” Bribery can take different
forms, from money in sealed envelopes to gifts, preferential treatment, and so forth.
To reduce bribery, understanding what drives it is important. Experiments are useful in
the process of understanding the motivation for bribery because they can help us isolate key
aspects of the relevant behavior. The existing experimental literature studies different elements
of bribing behavior, from the effect of staff rotation (Abbink, 2004) to culture (Barr and Serra,
2010; Cameron et al., 2009) to wages (Abbink, 2006; Armantier and Boly, 2008; Van
Veldhuizen, 2012). See Abbink (2006) for a comprehensive survey of these experiments. In this
literature, participants are asked to choose between different monetary allocations. These
decisions may include negative externalities on a third party, but they do not include a distortion
of facts or judgment.
Yet a distortion of facts seems to be a key element in bribery. This distortion occurs when
a decision maker uses bribes rather than other objective criteria such as merit, performance, or
quality to determine who receives a particular gain. Hence, to capture this key element, we
introduce a new bribery game in which two participants (“the workers”) compete in a real-effort
task. A third participant, the referee, then determines the winner and awards this winner a prize.
Apart from working on the task, the two workers can also choose to send money to the referee.
We use this basic design to test whether workers actually bribe. When they bribe, we investigate
whether that bribe distorts the referee’s judgment, and when it does, we want to understand why.
2. The bribery game and research questions
2.1 The bribery game
The basic game we study involves three players: two workers and a referee. The workers
compete against each other on a real-effort task, and the referee judges their performance and
determines a winner. The winner receives a prize of p, and the other worker receives zero.
Additionally, workers can send a bribe (0≤bi≤0.5p) to the referee. Referees keep the winning
worker’s bribe and return the other worker’s bribe.
The referee’s monetary payoff-maximizing strategy is to choose the worker who submits
the highest bribe. Assuming the referee chooses this strategy, and given the restriction that
bi≤0.5p, the workers’ monetary payoff-maximizing strategy is to bribe the maximum (or bi=0.5p).
The referee’s equilibrium payoff under these assumptions is Π𝑅 = 𝑏𝑖∗ , where i* is the winner of
the round. The monetary payoff of each worker wi is given by
−𝑏 + 𝑝 𝑖𝑓 𝑤𝑖 𝑤𝑖𝑛𝑠
𝚷𝒘𝒊 = { 𝑖
}.
0
𝑖𝑓 𝑤𝑖 𝑙𝑜𝑠𝑒𝑠
In the experiment we report in this paper, p was equal to $10 and the maximum bribe was
therefore $5. Hence the payoffs in equilibrium under the assumption that all three players are
selfish money maximizing are $5 for the referee and an equal chance of $0 and $5 to the workers.
2.2. Research questions
Given this set-up, the first empirical question we want to investigate regards workers’
bribing behavior. In particular, do workers actually bribe and if so, do they choose the profitmaximizing strategy? Note that even if a worker believes paying a high bribe is beneficial in
terms of monetary rewards, he may choose not to bribe because of some moral costs associated
with unethical behavior. Research shows such motives are important, for example, in deception
behavior (Gneezy, 2005).
The second research question relates to the referee’s behavior. We want to investigate
whether bribing distorts the referee’s judgment. Even though the referee is asked to choose the
winner based on the workers’ performance on the task, a selfish payoff-maximizing referee
would base her decision solely on the size of the bribe bi. Basing her decision on the size of the
bribe rather than on the workers’ performance leads to a distortion of the true ranking between
workers.
If bribery distorts the referee’s judgment, a better understanding of what motivates the
success of bribes becomes important. In particular, two explanations are possible for why bribes
influence judgment: gift exchange and greed. According to the gift-exchange hypothesis, if a
worker sends more money to the referee, the referee might want to reciprocate the favor by
choosing to reward that worker (Akerlof, 1982; Rabin, 1993; Fehr and Gächter, 2000). In this
case, referees will choose the worker who sent the higher bribe, because they want to reciprocate
the nicer behavior, and not just because choosing this worker makes them earn more money. In
contrast with the gift-exchange explanation, greed implies that referees choose the higher bribe
as a winner when doing so benefits them economically. Individuals might have some mental cost
(e.g., lying costs) associated with distorting judgment, and hence in situations in which they can
earn the extra money from the bribes without distorting judgment, bribes will not affect their
choice.
To test these competing explanations of bribery, we compare the base treatment we
discussed above (the “KeepWinner” treatment) with a treatment in which the referee keeps both
bribes (“KeepBoth”). In the KeepBoth treatment, the payoff for the referee in each given round
is therefore given by Π𝑅 = 𝑏𝑖 + 𝑏𝑗 . The monetary payoff of each worker wi is given by
−𝑏 + 𝑝
𝚷𝒘𝒊 = { 𝑖
−𝑏𝑖
𝑖𝑓 𝑤𝑖 𝑤𝑖𝑛𝑠
}.
𝑖𝑓 𝑤𝑖 𝑙𝑜𝑠𝑒𝑠
Because in this treatment the referee’s payoff is not affected by her choice of a winner,
she does not need to distort her judgment to earn more money. However, if gift exchange drives
bribery, the referee should still be more likely to reward the higher bribe, just as in the
KeepWinner treatment. Hence this treatment may allow us to reject the gift-exchange
explanation for the success of bribes.
As a way to compare the importance of the norm of reciprocity with the norm of not
distorting judgment, we conduct an additional test of the gift-exchange explanation in which we
remove the distortion of judgment from the experiment. In this treatment, the workers have no
tasks to perform, and hence no distortion is involved in the choice of the winner (“NoTask”). The
workers simply choose how much money they wish to put in the envelope, and the referee
chooses one of them as the winner. This treatment is more closely related to the existing bribery
games in the literature—starting with Abbink et al. (2002)—that study the role of reciprocity in
bribery relationships. As discussed above, these studies do not include a distortion of judgment
that the real-effort task in our design introduces.
In this treatment, we remove the real-effort task from the KeepBoth treatment: workers
have the opportunity to send money bi to the referee, and the referee simply needs to decide
which worker receives the prize. The referee in this case keeps the monetary transfers from both
workers. Comparing the KeepBoth and the NoTask treatments helps us measure the importance
of the moral costs associated with distortion of judgment versus the reciprocity norm. If
distortion does not affect the referees’ judgment, we should observe similar results between these
two treatments. If distortion generates some costs to the referees, their behavior in the KeepBoth
and NoTask treatments might differ.
Finally, we run a fourth treatment (“Reject”) to test whether referees’ behavior is robust
to giving them the option to reject both bribes. In all the other treatments, the referee is forced to
accept the winner’s bribe. In real life, referees also have the option to reject the bribes. Honest
behavior may imply choosing a worker but rejecting his bribe, and our simplification may hence
induce referees to be greedier. Comparing the Reject treatment with the KeepWinner treatment
allows us to investigate whether (not) allowing referees to reject bribes affects their behavior. In
the Reject treatment, the payoff for the referee in each round is therefore given by
𝑏
𝑖𝑓 𝑡ℎ𝑒 𝑤𝑖𝑛𝑛𝑒𝑟 ′ 𝑠 𝑏𝑟𝑖𝑏𝑒 𝑖𝑠 𝑎𝑐𝑐𝑒𝑝𝑡𝑒𝑑
𝚷𝒓 = { 𝑖∗
}.
0 𝑖𝑓 𝑡ℎ𝑒 𝑤𝑖𝑛𝑛𝑒𝑟 ′ 𝑠 𝑏𝑟𝑖𝑏𝑒 𝑖𝑠 𝑟𝑒𝑗𝑒𝑐𝑡𝑒𝑑
The monetary payoff of each worker wi is given by
−𝑏𝑖 + 𝑝
𝚷𝒘𝒊 = { 𝑝
−𝑏𝑖
3. Experimental design
𝑖𝑓 𝑤𝑖 𝑤𝑖𝑛𝑠 𝑎𝑛𝑑 𝑟 𝑎𝑐𝑐𝑒𝑝𝑡𝑠 𝑡ℎ𝑒 𝑏𝑟𝑖𝑏𝑒
𝑖𝑓 𝑤𝑖 𝑤𝑖𝑛𝑠 𝑎𝑛𝑑 𝑟 𝑎𝑐𝑐𝑒𝑝𝑡𝑠 𝑡ℎ𝑒 𝑏𝑟𝑖𝑏𝑒 }.
𝑖𝑓 𝑤𝑖 𝑙𝑜𝑠𝑒𝑠
3.1 Procedure
The experiment was conducted at the University of California San Diego with a total of
180 participants. Each session lasted approximately 50 minutes.
For the real-effort task, we chose a task that involves creativity, and for which the
evaluation is not fully objective but depends partly on the referee’s subjective taste. In particular,
we asked workers to write a joke about either “economists” (round 1) or “psychologists” (round
2). All instructions can be found in the Appendix.
In each session, we invited six participants to the laboratory. Upon their arrival, we
randomly assigned participants to a computer terminal and asked them to follow the instructions
on screen. Participants were anonymously matched in groups of three, and each of them was
assigned either to the role of workers (called participant A and B in the experiment) or referee.
We then moved the referees to separate rooms (one room for each referee), where they received
the remainder of the instructions, while the workers kept reading their instructions off their
computer terminal. Neither workers nor referees knew which of the other participants were
matched with them.
We then informed participants (except those in the NoTask treatment) about the realeffort task and the referee’s role in determining the winner. In the NoTask treatment, participants
were also informed about the referee’s role in determining the winner, but we did not ask them to
complete any task. In either case, neither the workers nor the referees were yet informed about
the workers’ opportunity to send money to the referee.
On their desk, each worker had an envelope with his show-up fee of $10, in $1 bills. Each
referee had an envelope with a $5 show-up fee. The information about the other participants’
initial show-up fee was made common knowledge.
After all workers had read their instructions and completed some check-up questions, the
topic of the jokes for the first round (“economists”) was announced and workers had 10 minutes
to type a joke (in the NoTask treatment, workers were told to wait 10 minutes before making a
choice).
The experimenters then printed each joke and returned them to the workers. While the
experimenters were printing the jokes, we asked workers to state their expected likelihood of
having a better joke than their opponent (“What do you believe is the probability that you will
have a better joke than your opponent?”).
The workers then received a second set of instructions on the screen, which notified them
of the opportunity to send money to the referee. In particular, workers were asked to put the
printed copy of their joke in a large envelope labeled with their participation ID and were given
the opportunity to take up to $5 from their show-up fee and add it to the envelope. Meanwhile,
the referees also received a second set of instructions telling them about the possibility for
workers to send them money.
After all workers had prepared their envelopes, an experimenter collected them, recorded
the monetary content of each envelope, and gave the envelopes to the referee. Upon receiving the
envelopes, each referee had five minutes to rate on a scale from 0 to 10 the quality of the workers’
jokes, and to select a winner by placing a winner card in the envelope of the worker who won
and a loser card in the envelope of the worker who lost. After five minutes, the referee returned
the envelopes to the experimenter, who opened them to record the referees’ decisions and kept
them until the end of the experiment.
To sum, in the KeepWinner treatment, the referee could keep only the winner’s monetary
transfer, and had to return the loser’s money by putting it back in the envelope. In the KeepBoth
and NoTask treatments, the referee kept all the money sent by both workers. In these treatments,
the referee was not allowed to return any money to the workers. In the Reject treatment, the
referee had to return any money received from the loser, but could also decide to return both
bribes. Table 1 summarizes the experimental treatments. Note that whereas we have 60
participants (20 groups) in the two main treatments, KeepWinner and KeepBoth, we had only 30
participants (10 groups) in each of the two treatments that test alternative explanations (NoTask
and Reject).
Treatment
KeepWinner
KeepBoth
NoTask
Reject
Keep bribe?
Only winner
Both
Both
Chooses whether to keep
the winner’s
Task?
Yes
Yes
No
Yes
# of participants
60
60
30
30
The experiment consisted of two rounds with the same matching of participants. No
feedback was provided between rounds. Workers started the second round while the referees
were evaluating their first round. The topic of the jokes during the second round was
“Psychologists;” the procedure for round 2 was identical to that of round 1. After the second
round, we asked both workers and referees to complete a survey of basic demographic
information. We then allowed referees to leave the experiment, and returned to workers the
envelopes for rounds 1 and 2. Each envelope contained either a winner or a loser card indicating
the referee’s decision. For the KeepWinner and Reject treatments, the envelope also contained
any money the worker who lost sent the referee. For the Reject treatment, the envelope could
also contain any money sent by the winner if the referee decided to reject both bribes.
Participants then exchanged any winner cards for prizes and were subsequently paid.
2.3 Joke quality
After the experiment was completed, we organized additional sessions in which
participants who had not previously participated in the experiment evaluated the quality of
several pairs of jokes. A total of 400 individuals evaluated the quality (on a scale from 0 to 10) of
several pairs of jokes and –for each pair- determined which joke was funnier (please see their
instructions in the appendix), similar to what referees did in the experiment. Raters viewed the
same pairs of jokes that the referees had evaluated during the experiment. Each rater evaluated a
total of six pairs of jokes, chosen at random by an electronic randomizer, among all possible
pairs of jokes. Eighteen to 21 independent raters who were told participants in a previous
experiment had written these jokes evaluated each pair.
3. Results
Table 1 presents some descriptive statistics on our sample. Joke quality and confidence
levels are not statistically different between treatments and rounds (Bonferroni or HolmBonferroni correction for multiple hypothesis testing). In the remainder of this section, we will
use both parametric and non-parametric tests to investigate differences between treatments.
Whenever worker behavior is analyzed, we use one worker as one independent observation;
whenever referee behavior is analyzed, we use one referee as one independent observation.
TABLE 1—DESCRIPTIVE STATISTICS
Joke Quality (Round 1)
Joke Quality (Round 2)
Worker Confidence (Round 1)
Worker Confidence (Round 2)
Psychology Major
Economics Major
Female
Asian
Nonnative speaker
Age
Observations
Overall
KeepWinner
KeepBoth
NoTask
Reject
3.59
(1.21)
3.54
(1.39)
.50
(.27)
.48
(.28)
.09
(.29)
.22
(.41)
.56
(.50)
.72
(.45)
.17
(.37)
20.8
(1.94)
3.59
(1.18)
3.85
(1.29)
.48
(.28)
.44
(.28)
.10
(30)
.20
(.40)
.55
(.50)
.63
(.49)
.15
(.36)
21.1
(2.62)
3.55
(1.17)
3.30
(1.41)
.53
(.27)
.56
(.26)
.08
(.28)
.17
(.38)
.60
(.49)
.82
(.39)
.18
(.39)
20.5
(1.46)
.10
(.31)
.33
(.48)
.57
(.50)
.60
(.50)
.20
(.41)
21.0
(1.30)
3.63
(1.38)
3.41
(1.48)
.49
(.26)
.41
(.30)
.10
(.31)
.23
(.43)
.50
(.51)
.83
(.38)
.13
(.35)
20.6
(1.65)
180
60
60
30
30
Notes: Descriptive Statistics. Joke quality is the average rating of the joke by the independent judges. Confidence is the worker’s
confidence in his own joke. The remaining variables are dummies for psychology majors, economics majors, females, Asians and
nonnative speakers, and a continuous variable for age respectively.
3.1. Do workers bribe?
Figure 1 shows the distribution of bribes in the KeepWinner treatment. First note that
workers do bribe: 41% of bribes are at the maximum $5 and a further 33% are positive. In 26%
of the cases, workers elect not to send a bribe, which suggests the moral costs of corruption also
played a role for some participants. Overall, the average bribe was $2.80.
Result 1: Most of the workers (85%) send a positive bribe in the KeepWinner treatment.
By contrast, as Figure 1 shows, the workers in the KeepBoth treatment mostly do not
bribe (a zero bribe in 66% of the cases). Overall the average bribe in this treatment is $.90. The
difference in the distribution of bribes between the KeepWinner and the KeepBoth treatments is
Fraction of the Data
significant (p<.0001, Mann-Whitney).
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
KeepWinner:
Mean=2.8
KeepBoth: Mean=.9
0
1
2
3
Bribe Amount
4
5
Figure 1. CDF of Worker Bribe Amounts for KeepWinner and KeepBoth
Notes: This figure plots the empirical cumulative distribution function of all bribes sent in the KeepWinner and KeepBoth treatments.
Because participants played the game for two rounds, their behavior might have changed
between the first and second rounds. Table 2 presents average bribes per round for all treatments.
On average, in the KeepWinner treatment, bribes do not change between rounds: the average
bribe is $2.83 in the first round and $2.78 in the second round (the difference is not statistically
significant). In the KeepBoth treatment, the average bribe slightly diminishes in the second
round (Mround 1 =1.125, Mround 2 =.675) and this difference is significant at the 10% level (p=.0562,
Wilcoxon signed rank test). We also investigated whether bribe amounts changed at the
individual worker level. The results are reported in Table 3.
TABLE 2—AVERAGE BRIBE PER ROUND
Overall
KeepWinner
KeepBoth
NoTask
Reject
2.367
(.190)
2.125
(.191)
2.825
(.328)
2.775
(.337)
1.125
(.278)
.675
(.257)
2.95
(.40)
2.25
(.441)
3.35
(.431)
3.6
(.4)
Bribe (Both Rounds)
2.25
(.135)
2.8
(.236)
.9
(.174)
2.6
(.299)
3.475
(.290)
Observations (Per Round)
Observations (Both Rounds)
120
240
40
80
40
80
20
40
20
04
40
Bribe (Round 1)
Bribe (Round 2)
Notes: The table gives average bribe size (over all workers) separately as well as jointly for each treatment and round.
TABLE 3—CHANGES IN BRIBES BETWEEN ROUNDS
Overall
KeepWinner
KeepBoth
NoTask
Reject
Smaller Bribe in Round 2
26.67%
30%
20%
50%
10%
Same Bribe in Round 2
29.17%
32.5%
15%
25%
55%
Larger Bribe in Round 2
Ob
15.83%
22.5%
5%
15%
25%
No Bribe in Either Round
28.33%
15%
60%
10%
10%
Observations
120
40
40
20
20
04
Notes: The table gives average bribe size (over all workers) separately as well as jointly for each treatment and round.
3.2 Does Bribery Distort the Referee’s Judgment?
The KeepWinner treatment
Ob
Our second research question investigates whether bribing results in a distortion of the
referee’s judgment. Figure 2 shows that a large majority of referees (86%) in the KeepWinner
treatment award the winner payment to the worker offering the higher bribe. This number is
significantly larger than chance (p=.001, Wilcoxon). By contrast, the better joke (as judged by
our independent raters) wins only 58% of the time, which is not significantly different from
chance (p=.366, Wilcoxon). Thus these results suggest that when referees can maximize their
payoffs by choosing the higher bribe, bribery distorts referees’ judgment: referees chose the
workers who paid them more, not the ones who wrote the funniest jokes.
Fraction of Winners
Fraction of Winners
1
p=.001
0.9
p=.007
0.8
p=.102
0.7
p=.366
0.6
0.5
Better Bribe
KeepWinner
Better Rating
KeepBoth
FIGURE 2. WIN CHANCE WHEN HAVING THE BETTER BRIBE FOR KEEPWINNER AND KEEPBOTH
Note: the p-values are calculated using a Wilcoxon signed rank test that tests if the fraction is significantly larger than .5.
Result 2: Bribes distort the referees’ choices in the KeepWinner treatment.
Table 2 provides further support for this result. Column (1) shows that for workers who
gave the higher bribe, having a better joke does not significantly increase the chance of winning
the prize. The results of column (2) show that for workers with a superior joke, offering a better
bribe does pay off. Column (3) shows that if we also include cases in which both workers offer
the same bribe amount, having a better-quality joke does make the worker more likely to win,
though offering a better bribe improves the chance of winning to an even greater extent.
TABLE 4—PROBIT REGRESSIONS FOR REFEREES IN KEEPWINNER
Probability (winning)
(1)
(2)
(3)
P(winning)
.87
.63
.30
.15***
(.04)
.10**
(.04)
.15***
(.05)
-.03
(.03)
Quality Difference
.04
(.03)
Bribe Difference
Quality Difference X Bribe Difference
Treatment
KeepWinner
KeepWinner
KeepWinner
Selected Workers
Better Bribe
Better Rating
Random
Observations
29
39
40
Clusters
16
20
20
Notes: Probit estimates (Marginal Effects). Robust standard errors are clustered at the referee level. Quality Difference is the
difference between the average quality of the joke (as judged by the independent raters) of the selected worker and the other worker in
his group. Bribe difference is the difference between the bribe proposed by the selected worker and the other worker in his group. All
marginal effects are evaluated at the means for all independent variables. For specification (1), we select only workers with a better
bribe than the other worker in a given round. For specification (2), we select only workers with a better-quality joke in a given round.
For specification (3), we randomly select one worker per referee in each round.
*** Significant at the 1% level.
** Significant at the 5% level.
* Significant at the 10% level.
The KeepBoth treatment
Figure 2 and Table 5 give an overview of referee behavior in the KeepBoth treatment.
Figure 2 shows that only 64% of referees award the winner payment to the worker offering the
higher bribe. This number is not significantly larger than chance (p=.102, Wilcoxon). By contrast,
the better joke (as judged by our independent raters) wins 72% of the time (p=.007, Wilcoxon).
Thus these results suggest that when the referee’s payoff does not depend on the choice of
winner, bribery does not distort the referee’s judgment: referees choose the workers who write
the funniest joke, not the workers who send them more money.
Result 3: Bribes do not distort the referees’ choices in the KeepBoth treatment.
Table 5 provides further support for this result. Column 1 shows that for workers who
offer a higher bribe, having a better joke increases their chances of winning the prize. Moreover,
column (2) shows that for workers with a superior joke, offering a higher bribe does not pay.
Column (3) shows that if we look at all cases, having a better-quality joke makes the worker
much more likely to win, whereas having a larger bribe does not increase a player’s chance of
winning the prize.
Comparison between KeepWinner and KeepBoth
Comparing the KeepBoth and KeepWinner treatments allows us to disentangle greed
from reciprocity. If reciprocity drives bribery, the results in these treatments should be similar.
By contrast, if reciprocity does not drive bribery, and referees gain some value for reporting their
true judgment, then in the KeepBoth treatment, the (relative) size of the bribes would have less
influence on the referees.
Figure 2 shows that having a better bribe is more effective in the KeepWinner treatment
(64% vs 86%, p=.048; Mann-Whitney), whereas having a better-quality joke is more effective in
the KeepBoth treatment, albeit not significantly so (72% vs 58%, p=.197; Mann-Whitney). As
further support, we can also compare the estimates presented in table 4 and table 5. For workers
with a better bribe, the effect of having a better joke is five times as large in the KeepBoth
treatment. For workers with a better rating, the effect of having a better bribe is almost four times
as large in the KeepWinner treatment. Column 3 shows that if we look at all cases, the effect of
having a better joke is 2.5 times as large for workers in the KeepBoth treatment, whereas the
effect of having a better bribe is 50 percent larger in the KeepWinner treatment . Thus bribery
pays off and distorts judgment in the KeepWinner but not the KeepBoth treatment.
TABLE 5—PROBIT REGRESSIONS FOR REFEREES IN KEEPBOTH
Probability (winning)
(1)
(2)
(3)
(4)
P(winning)
.68
.72
.46
.37
Quality Difference
.21***
(.06)
.04
(.03)
.27***
(.07)
.11
(.07)
-.03
(.02)
.28***
(.08)
.07
(.07)
Bribe Difference
Quality Difference X Bribe Difference
DKeepWinner
.09
Quality Difference (at DKeepWinner=1)
.11**
(.04)
.17***
(.06)
Bribe Difference (at DKeepWinner=1)
Treatment
KeepBoth
KeepBoth
KeepBoth
Selected Workers
Better Bribe
Better Rating
Random
KeepWinner
&
Keep Both
Random
Observations
22
39
40
80
Clusters
12
20
20
40
Notes: Probit estimates (Marginal Effects). Robust standard errors are clustered at the referee level. Quality Difference is the
difference between the average quality of the joke (as judged by the independent raters) of the selected worker and the other worker in
his group. Bribe difference is the difference between the bribe proposed by the selected worker and the other worker in his group. For
specifications (1)-(4), all marginal effects are evaluated at the means for all independent variables. For specification (1), we select only
workers with a better bribe than the other worker in a given round. For specification (2), we select only workers with a better-quality
joke in a given round. For specifications (3) and (4), we randomly select one worker per referee in each round.. For specification (4),
DKeepWinner is a dummy variable for treatment KeepWinner. Specification (4) also includes an interaction term between the treatment
dummy and the quality and bribe variables; the coefficients reported for quality and bribe at D KeepWinner=1 are equal to the sum of the
main effect and the treatment*dummy interaction. All coefficients for specification (4) are always evaluated at the mean values of
Quality Difference and Bribe Difference and at both DKeepWinner=0 and DKeepWinner=1.
*** Significant at the 1% level.
** Significant at the 5% level.
* Significant at the 10% level.
Figures 3a and 3b provide a graphical illustration of column (3) of Table 4 and of column
(3) of Table 5. The figures display the estimated probabilities of winning for different
combinations of difference in quality between the two workers’ jokes and difference in bribes.
Figure 3a underlines the importance of bribes in the KeepWinner treatment: having a higher
bribe increases the worker’s probability of winning. As a case in point, the estimated probability
of winning with a better bribe is close to 90% even when the quality of the joke is considerably
poorer than that of the other worker. Having a better-quality joke matters only when bribes are
equal. Thus, these graphs provide a further illustration that referees’ judgment is distorted: when
bribes are equal, the referees tend to let the best joke win, but when one bribe is higher, they
strongly prefer the higher bribe.
Figure 3b shows a shift in the weight of bribes versus quality in influencing the
likelihood of winning in the KeepBoth treatment. Unlike the KeepWinner treatment, having a
joke of higher quality is more important than having a higher bribe. However, having a higher
bribe does help, particularly when jokes are of approximately equal quality.
FIGURE 3A AND FIGURE 3B. WIN CHANCE AS A FUNCTION OF BRIBE DIFFERENCE AND JOKE-QUALITY DIFFERENCE FOR THE KEEPWINNER AND
KEEPBOTH TREATMENTS
The figures display a heat map of the fraction of winners as a function of bribe difference and joke-quality difference for the KeepWinner (Figure
4) and KeepBoth (Figure 5) treatments. The results are based on probit regressions of win chance on joke-quality difference, bribe difference, and
the interaction of the two (reported as column 3 of Table 5 and Table 6, respectively). For joke-quality difference, we used the difference in the
quality of the joke as rated by independent raters, using the 10th, 30th, 50th, 70th, and 90th percentiles of the distribution.
3.3. The NoTask treatment
As discussed above, reciprocity is a powerful motive. So why are higher bribes
ineffective in the KeepBoth treatment? One hypothesis is that the norm of not distorting
judgment is stronger than the norm of reciprocity, and hence referees will ignore the
bribes. To investigate this hypothesis, we compare referees’ behavior in the KeepBoth
treatment with referees’ behavior in the NoTask treatment.
As predicted by the hypothesis, in the KeepBoth treatment, the referee chooses
the higher bribe in 63% of the cases, whereas in the NoTask treatment, the highest bribe
wins 94% of the time (p=.011, Wilcoxon); the difference in results is significant (p=.044,
MW). Looking at workers’ behavior (Table 2), the average bribe is larger than in the
KeepBoth treatment (p<.0001; Mann-Whitney) and similar to the KeepWinner treatment
(p=.697; Mann-Whitney). Moreover, the average bribe is slightly smaller in round 2 (2.25
vs 2.95, p=.077, Wilcoxon). In this treatment, the fraction of workers who do not send
any bribe is lower than in the KeepBoth treatment (25% vs. 66%), suggesting that
removing distortion also reduced workers’ moral costs associated with bribing.
The comparison between the KeepBoth and the NoTask treatments provides
further evidence that the need to distort judgment presents referees with an additional
moral cost of rewarding the highest bribe. Referees are happy to reward the worker who
sent them more money when this reward does not require them to distort their judgment,
but not when it does require them to distort judgment. In our task, the moral cost of
distorting judgment appears to be stronger than the norm of reciprocity.
Result 4: The norm of not distorting judgment is stronger in our set up than the
norm of reciprocity.
3.4. The Reject treatment
In the KeepWinner treatment, we require the referees to keep the winning bribe.
Comparing the Reject treatment with the KeepWinner treatment allows us to investigate whether
allowing referees to reject bribes affects their behavior. As Figure 5 shows, in the Reject
treatment, the higher bribe won in 100% of the cases, compared with the KeepWinner treatment,
in which the higher bribe won in 86% of the cases (p=.176, MW). Additionally, referees in the
Reject treatment chose the better joke at approximately the same rate as referees in the
KeepWinner treatment (65% vs 58%; p=.377, MW). Finally, note that only two referees in our
sample rejected both bribes. In both cases (both in round 1), the highest bribe won anyway.1
Result 5: Allowing referees to reject bribes does not affect their behavior.
1
The average bribe in the Reject treatment does not differ significantly from the KeepWinner treatment (p=.188); the average bribe also does
not differ between rounds.
Fraction of Winners
Fraction of Winners
p=.003
p=.001
0.9
p=.180
p=.366
0.7
0.5
Better Bribe
KeepWinner
Better Rating
Reject
FIGURE 7. WIN CHANCE WHEN HAVING THE BETTER BRIBE OR BETTER RATING FOR KEEPWINNER AND REJECT
NOTES: THE P-VALUES ARE CALCULATED USING A WILCOXON SIGNED RANK TEST THAT TESTS IF THE FRACTION IS SIGNIFICANTLY LARGER THAN .5.
5. Concluding Remarks
Bribery is widespread and has an important impact on how decisions are made in politics,
business, sports, education, and many other domains, with large economic consequences. The
goal of the current paper is to introduce a new experimental bribery game aimed at capturing an
important element that characterizes bribery: the distortion of judgments or facts that is
generated when bribes, rather than merit or performance, are rewarded.
In our experiment, a considerable number of workers are willing to send a bribe to
influence the referees’ decision, and referees systematically reward the highest bribe when they
can keep only the winner’s bribe. However, in a treatment in which referees kept both bribes,
having a higher bribe was not nearly as effective, and the relative importance of worker
performance greatly increased.
These results suggest that distorting the true ranking generates some moral costs, and
these costs crowd out reciprocity. However, these costs are overcome when the distortion of
judgment maximizes the referees’ payoff, suggesting that greed drives bribery. In a sense, our
experiment allows us to rank the importance of three forces: the norm of reciprocity seems to be
weaker than the norm of not distorting judgment, which in turn is weaker than profit maximizing.
Additionally, our design captures the role of distortion of judgment. We find that
distortion plays an important role in explaining whether referees reciprocate the highest bribe.
When the decision regarding which worker will win a prize does not involve a distortion of
judgment, we find that in line with the previous literature, reciprocity is an important motivator
of bribery (e.g., Abbink et al. 2002).
Taken together, our results have potentially important implications for the understanding
of corruption. For instance, any attempt to fight bribery should take into account the costs
associated with distortion of the truth. Future research could build on this finding and investigate
whether these costs are fixed or whether they depend on the magnitude of the distortion, and
which type of interventions can be successful in reducing bribery. For example, in our study, the
referees had to evaluate a task according to subjective criteria. In situations in which the
evaluation is more objective, the costs associated with distortion could increase, making referees
less likely to go along with the highest bribe. Furthermore, from the perspective of the
individuals who send bribes, situations may exist in which they are more or less likely to bribe.
Identifying the possible moderators of bribing behavior can provide important insights into the
study of corruption and the attempts to reduce it.
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Appendix A
Robustness check
Comparison between rounds
The analysis presented in the paper aggregates observations for round 1 and round 2. However,
as with worker behavior, referees might have changed their behavior between rounds. Table 4
further investigates whether the impact of quality and bribes changed between rounds. Column
(1) shows that in the KeepWinner treatment, bribes matter in both rounds. Further, we find
quality has a larger impact in round 2 rather than round 1. Column (2) shows the effect of
quality seems to be more important than the effect of bribes in both rounds, although this effect
is statistically significant only in round 1, probably due to the small sample size. Hence, similarly
to the pooled data, this analysis suggests a stronger role of bribes in the KeepWinner treatment
and of quality in the KeepBoth treatment.
TABLE 7—PROBIT REGRESSIONS FOR REFEREES IN KEEPWINNER AND KEEPBOTH
Probability (winning)
(1)
(2)
P(winning)
.82
.41
Quality Difference
.06
(.04)
.09*
(.05)
.43
.48***
(.17)
.21**
(.10)
.09
.27**
(.08)
.25***
(.08)
.23
(.21)
-.02*
(.11)
Treatment
KeepWinner
KeepBoth
Selected Workers
Random
Random
40
Random
Random
40
Bribe Difference
DRound2
Quality Difference (at DRound2=1)
Bribe Difference (at DRound2=1)
Observations
Clusters
20
20
Notes: Probit estimates (Marginal Effects). Robust standard errors are clustered at the referee level. Quality Difference is the
difference between the average quality of the joke (as judged by the independent raters) of the selected worker and the other worker in
his group. Bribe difference is the difference between the bribe proposed by the selected worker and the other worker in his group.
Round2 is a dummy variable that is equal to 1 for observations from the second round. Marginal effects are evaluated at the means for
all independent variables. For both specification (1) and (2), we randomly select one worker per referee. Specification (1) and (2)
include an interaction term between the round2 dummy and the quality variable and between the round2 dummy and the bribe
variable.
*** Significant at the 1% level.
** Significant at the 5% level.
* Significant at the 10% level.