Page 1
Games and Economic Behavior 68 (2010) 731–747
Contents lists available at ScienceDirect
Games and Economic Behavior
www.elsevier.com/locate/geb
Experimental comparison of multi-stage and one-stage contests
Roman M. Sheremeta1
The George L. Argyros School of Business and Economics, Chapman University, 1 University Drive, Orange, CA 92866, USA
a r t i c l ei n f o a b s t r a c t
Article history:
Received 12 December 2008
Available online 11 August 2009
JEL classification:
C72
C91
D72
Keywords:
Rent-seeking
Contest
Contest design
Experiments
Risk aversion
Over-dissipation
This article experimentally studies a two-stage elimination contest and compares its
performance with a one-stage contest. Contrary to the theory, the two-stage contest
generates higher revenue than the equivalent one-stage contest. There is significant over-
dissipation in both stages of the two-stage contest and experience diminishes over-
dissipation in the first stage but not in the second stage. Our experiment provides evidence
that winning is a component in a subject’s utility. A simple behavioral model that accounts
for a non-monetary utility of winning can explain significant over-dissipation in both
contests. It can also explain why the two-stage contest generates higher revenue than the
equivalent one-stage contest.
© 2009 Elsevier Inc. All rights reserved.
1. Introduction
Contests are economic, political, or social interactions in which agents expend resources to receive a certain prize. Exam-
ples include marketing and advertising by firms, patent races, and rent-seeking activities. All these contests differ from one
another on multiple dimensions including group size, number of prizes, number of inter-related stages, and rules that reg-
ulate interactions. The most popular theories investigating different aspects of contests are based on the seminal model of
rent-seeking introduced by Tullock (1980). The main focus of rent-seeking literature is the relationship between the extent
of rent dissipation and underlying contest characteristics (Nitzan, 1994).
The majority of rent-seeking studies are based on the assumption that contests consist of only one stage. Many contests
in practice, however, consist of multiple stages. In each stage contestants expend costly efforts in order to advance to the
final stage and win the prize. Two major purposes of our study are to compare the performance of a one-stage contest
versus a two-stage elimination contest and to examine whether over-dissipation is observed in both stages of the two-stage
contest. The experiment is also designed to elicit non-monetary utility of winning from subjects in order to explain potential
over-dissipation in contests.
We find that, contrary to the theory, the two-stage contest generates higher revenue and higher dissipation rates than the
equivalent one-stage contest. Over-dissipation is observed in both stages of the two-stage contest and experience diminishes
over-dissipation in the first stage but not in the second stage. Our experiment also provides evidence that winning is a
E-mail address: sheremet@chapman.edu.
1I am particularly grateful to Tim Cason for excellent guidance and support. I also want to thank two anonymous referees and an associate editor, Jack
Barron, Subhasish Modak Chowdhury, Kai Konrad, Dan Kovenock, and Jingjing Zhang, as well as seminar participants at Purdue University and participants
at the June 2008 Economic Science Association meeting for helpful comments. This research has been supported by National Science Foundation Grant
(SES-0751081). Any remaining errors are mine.
0899-8256/$ – see front matter © 2009 Elsevier Inc. All rights reserved.
doi:10.1016/j.geb.2009.08.001
Page 2
732
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
component in a subject’s utility. A simple behavioral model that accounts for a non-monetary utility of winning can explain
significant over-dissipation in both contests. It can also explain why the two-stage contest generates higher revenue than
the equivalent one-stage contest.
Recent theoretical models of multi-stage elimination contests reveal interesting dynamic aspects. Gradstein and Konrad
(1999) consider a multi-stage elimination contest in which a number of parallel contests take place at each stage and only
winners are promoted to the next stage. The authors show that, depending on the contest success function, a multi-stage
contest may induce higher effort by the participants than a one-stage contest. Under a lottery contest success function,
however, the two structures are equivalent. In the same line of research, Baik and Lee (2000) study a two-stage elimination
contest with effort carryovers. In this contest, players in two groups compete non-cooperatively to win a prize. In the first
stage, each group selects a finalist who competes for the prize in the second stage. First-stage efforts are partially (or fully)
carried over to the second stage. Baik and Lee (2000) demonstrate that, in the case of player-specific carryovers, the rent-
dissipation rate (defined as the ratio of the expended total effort to the value of the prize) increases in the carryover rate
and the rent is fully dissipated with full carryover. Other theoretical studies of multi-stage elimination contests have been
conducted by Rosen (1986), Clark and Riis (1996), Gradstein (1998), Amegashie (1999), Stein and Rapoport (2005), Fu and
Lu (forthcoming), and Groh et al. (forthcoming).2All these studies investigate different aspects of multi-stage contests such
as elimination procedures, interdependency between the stages, asymmetry between contestants, and resource constraints.
Since rent-seeking behavior in the field is difficult to measure, researchers have turned to experimental testing of the
theory, with almost all studies focused on one-stage contests (Millner and Pratt, 1989, 1991; Shogren and Baik, 1991;
Davis and Reilly, 1998; Potters et al., 1998; Anderson and Stafford, 2003).3Despite considerable differences in experimental
design among these studies, most share the major finding that aggregate rent-seeking behavior exceeds the equilibrium pre-
dictions.4Several researchers have offered explanations for such behavior based on non-monetary utility of winning (Parco
et al., 2005), misperception of probabilities (Baharad and Nitzan, 2008), quantal response equilibrium, and heterogeneous
risk preferences (Goeree et al., 2002; Sheremeta, forthcoming).
There are currently only a few experimental studies that investigate the performance of multi-stage contests.5Schmitt
et al. (2004) develop and experimentally test a model in which rent-seeking expenditures in the current stage affect the
probability of winning a contest in both current and future stages. Two other experimental studies are based on a two-
stage rent-seeking model developed by Stein and Rapoport (2005). In this model all players have budget constraints. In
the first stage, players compete within their own groups by expending efforts, and the winner of each group proceeds to
the second stage. In the second stage, players compete with one another to win a prize by expending additional efforts
subject to budget constraints. The experimental studies of Parco et al. (2005) and Amaldoss and Rapoport (2009) reject the
equilibrium model of Stein and Rapoport (2005) because of significant over-dissipation in the first stage. Both experimental
studies conjecture that the non-monetary utility of winning plays a crucial role in explaining excessive over-dissipation in
the first stage. Our experimental design is based on Gradstein’s and Konrad’s (1999) theoretical model, which compares the
performance of a one-stage contest versus a multi-stage elimination contest.
2. Theoretical model
In a simple one-stage contest N identical players compete for a prize of value V . Each risk-neutral player i chooses his
effort level, ei, to win the prize. The probability that a contestant i wins the prize is given by a lottery contest success
function:
ei
?N
The contestant’s probability of winning increases monotonically in own effort and decreases in the opponents’ efforts.
The expected payoff for risk-neutral player i is given by
pi(ei,e−i) =
j=1ej
.
(1)
E(πi) = pi(ei,e−i)V − ei.
That is, the probability of winning the prize, pi(ei,e−i), times the value of the prize, V , minus the effort expended, ei.
Differentiating (2) with respect to eiand accounting for the symmetric Nash equilibrium leads to a classical solution (Tul-
lock, 1980)
(2)
e∗=(N − 1)
N2
V.
(3)
2Another type of multi-stage contests is the multi-battle contests. In a multi-battle contest, players compete in a sequence of simultaneous move contests
to win a prize and the player whose number of victories reaches some given minimum number wins the prize. Such contests have been studied by Harris
and Vickers (1985, 1987), Klumpp and Polborn (2006), and Konrad and Kovenock (2009).
3For empirical results on multi-stage elimination tournaments in sports see Ehrenberg and Bognanno (1990) and Bognanno (2001).
4Shogren and Baik (1991) do not find excessive expenditure.
5Exception is a study by Amegashie et al. (2007) on multi-stage all-pay auction.
Page 3
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
733
Table 3.1
Experimental design and equilibrium effort levels.
TreatmentOSTS
Value of the prize, V
Number of players, N
Number of groups, K
120
4
1
120
4
2
Effort in stage 1, e1
Effort in stage 2, e2
Total revenue
Dissipation rate
22.5
–
90
0.75
7.5
30
90
0.75
The simple model considered above is the building block of contest theory. Gradstein and Konrad (1999) extended this
model to study a multi-stage elimination contest. In their contest, N players expend irreversible efforts in an attempt to
advance to the final stage. In the first stage, all players are divided into several groups. The winner of each group proceeds
to the second stage, where contestants again are divided into competing groups, etc. The winner of the final stage receives
a prize of value V . For our analysis, assume that there are only two stages. In the first stage, all players are divided into
K equal groups (N/K players per each group), with the winner of each group proceeding to the final stage. To analyze the
two-stage contest, we apply backward induction. According to (3), in the second stage each finalist will expend effort of
e∗
2=(K − 1)
The resulting expected payoff in the second stage is E(π∗
each group compete as if the value of the prize was E(π∗
given by
K2
V.
(4)
2) = V/K2. Knowing this, in the first stage N/K players within
2). Therefore, according to (3), the first stage equilibrium effort is
e∗
1=(N − K)
N2K
It is straightforward to show that, under the equilibrium strategy, the second order conditions hold and the resulting
expected payoff is non-negative.6Formulas (4) and (5) demonstrate how the first and second stage equilibrium efforts of
each player depend on the prize value and the number of contestants in each stage.
V.
(5)
3. Experimental design and procedures
3.1. Experimental design
Our experiment consists of two different contests. The outline of the experimental design and theoretical predictions for
each contest are shown in Table 3.1. In each contest there are 4 players and the prize value is 120 experimental francs. In a
baseline treatment, all 4 contestants compete with each other for the prize in a one-stage (OS) contest. In equilibrium the
revenue collected in this contest is 90. The resulting dissipation rate, defined as the total efforts divided by the value of the
prize, is 0.75.
The second treatment is a two-stage (TS) contest which consists of 4 players divided between 2 equal groups. The first
stage winner of each group proceeds to the second stage and the winner of the second stage receives the prize. This contest
resembles many real life situations. For instance, swimming or track tournaments often place competitors in different groups
called “heats” with the winner of each “heat” proceeding to the finale. The major competition in TS arises between the two
players in the second stage (see Table 3.1). Therefore, the revenue collected from the second stage is substantially higher
than the revenue collected from the first stage. The total revenue collected from both stages in the TS treatment is 90,
which is equivalent to the revenue collected in the OS treatment. This equivalence was proved by Gradstein and Konrad
(1999) for a more general multi-stage contest under lottery contest success function.
3.2. Experimental procedures
The experiment was conducted at the Vernon Smith Experimental Economics Laboratory. A total of 84 subjects par-
ticipated in seven sessions (12 subjects per session). All subjects were Purdue University undergraduate students who
participated in only one session of this study. Some students had participated in other economics experiments that were
unrelated to this research.
The computerized experimental sessions were run using z-Tree (Fischbacher, 2007). Each experimental session proceeded
in four parts. Subjects were given the instructions, available in Appendix A, at the beginning of each part and the exper-
imenter read the instructions aloud. Before the actual experiment, subjects completed the quiz on the computer to verify
6For a more detailed derivations, see Amegashie (1999), Gradstein and Konrad (1999), and Baik and Lee (2000).
Page 4
734
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
Table 4.1
Average statistics.
Treatment OS TS
Equilibrium ActualEquilibrium Actual
Effort in stage 1
Effort in stage 2
Net payoff
Total revenue
Dissipation rate
22.5
–
7.5
90
0.75
34.1 (0.7)
–
−4.1 (1.1)
136
1.14
7.5
30
7.5
90
0.75
18.9 (0.6)
47.2 (0.9)
−12.5 (1.2)
170
1.42
Note. Standard error of the mean in parentheses.
their understanding of the instructions. The experiment started only after all subjects had answered all quiz questions. In
the first part subjects made 15 choices in simple lotteries, similar to Holt and Laury (2002).7This method was used to elicit
subjects’ risk preferences. The second and the third parts corresponded to OS and TS treatments ran in different orders. In
three sessions we ran the OS treatment first and in three other sessions we ran the TS treatment first. Each subject played
30 periods in the OS treatment and 30 periods in the TS treatment.
In each period, subjects were randomly and anonymously placed into a group of 4 players and designated as participant
1, 2, 3, or 4. Subjects were randomly re-grouped after each period. In the first stage of the TS treatment, participant 1
was paired with participant 2 and participant 3 was paired with participant 4. In the OS treatment, all 4 participants were
paired against each other. At the beginning of each period, each subject received an endowment of 120 experimental francs.
Subjects could use their endowments to expend efforts (make bids). After all subjects submitted their efforts, the computer
chose the winner by implementing a simple lottery rule. In the TS treatment, the two finalists — one from each pair — again
made their effort choices in the second stage. At the end of the second stage the computer chose the winner of the prize
and displayed the following information to all subjects: the opponent’s effort in the first stage, the other opponent’s effort
in the second stage, the result of the random draw in the first and second stage, and personal period earnings. Subjects
who did not proceed to the second stage in the TS treatment did not receive any information about the decisions made in
the second stage. All subjects were informed that by increasing their efforts, they would increase their chance of winning
and that, regardless of who wins the prize, all subjects would have to pay for their efforts. The instructions explained the
structure of the game in detail.
In the final fourth part of the experiment, subjects were given an endowment of 120 francs and were asked to expend
efforts in a one-stage contest in order to be a winner. The procedure followed closely to the OS treatment. The only differ-
ence was that the prize value was 0 francs. Subjects were told that they would be informed whether they won the contest
or not. We used this procedure to receive an indication of how important it is for subjects to win when winning is costly
and there is no monetary reward for winning.
At the end of the experiment, 1 out of 15 decisions subjects made in part one was randomly selected for payment.
Subjects were also paid for 5 out of 30 periods in part two, for 5 out of 30 periods in part three, and for the 1 decision they
made in part four. The earnings were converted into US dollars at the rate of 60 francs to $1. On average, subjects earned
$25 each which was paid in cash. Each experimental session lasted about 90 minutes.
4. Results
4.1. General results
Table 4.1 summarizes average efforts, average net payoffs, and average dissipation rates over the treatments. The first
striking feature of the data is that, on average, net payoffs in both OS and TS treatments are negative and the actual
dissipation rates are significantly greater than predicted.8Similar findings are also reported in Davis and Reilly (1998) and
Gneezy and Smorodinsky (2006). In both studies, revenues collected repeatedly exceeded the prize and subjects earned, on
average, negative payoffs.
Result 1. There is significant over-dissipation in one-stage and two-stage contests.
There are several possible explanations for significant over-dissipation. First, it is possible that subjects expend signif-
icantly higher efforts because each period they receive a “free” endowment of 120 francs.9Note that this endowment is
7Subjects were asked to state whether they preferred safe option A or risky option B. Option A yielded $1 payoff with certainty, while option B yielded
a payoff of either $3 or $0. The probability of receiving $3 or $0 varied across all 15 lotteries. The first lottery offered a 5% chance of winning $3 and a 95%
chance of winning $0, while the last lottery offered a 70% chance of winning $3 and a 30% chance of winning $0.
8Separately for each treatment, we estimated a random effects model, with individual subject effects, where the dependent variable is effort and the
independent variables are a constant and a period trend. A standard Wald test, conducted on estimates of a model, clearly rejects the hypothesis that the
constant coefficients are equal to the predicted theoretical values as in Table 4.1 (p-value < 0.01).
9The endowment was chosen for several reasons. First, the endowment was chosen to be equal to the prize value to be consistent with other studies
(Anderson and Stafford, 2003; Herrmann and Orzen, 2008). Second, the endowment of 120 francs was also chosen to be substantially higher than the Nash
Page 5
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
735
Fig. 4.1. Average efforts by treatments.
substantially higher than the Nash equilibrium predictions. While the endowment itself has no theoretical impact, it cer-
tainly may have a behavioral impact, causing subjects to over-dissipate. The second explanation, related to the endowment
size effect, is that subjects are likely to make “errors.” Sheremeta (forthcoming) shows how the quantal response equilib-
rium developed by McKelvey and Palfrey (1995), which accounts for errors made by individual subjects, can explain some
over-dissipation in lottery contests. Finally, and probably most importantly, subjects may have a non-monetary utility of
winning. If that is the case, then in addition to the monetary value of 120 francs, subjects also compete to be winners. In
Section 4.3 we provide evidence consistent with subjects having a non-monetary utility of winning which may explain why
there is persistent over-dissipation in both treatments.
It is important to emphasize that the over-dissipation in the TS treatment takes place in both stages of the competition.
In the first stage of TS treatment, subjects expend an average effort of 18.9 which is more than double the equilibrium effort
of 7.5 (Table 4.1). In the second stage, instead of the equilibrium effort of 30, subjects expend an average effort of 47.2. The
first and the second stage efforts in TS treatment are higher than theoretical values in all periods of the experiment (Fig. 4.1).
Result 2. In the two-stage contest, significant over-dissipation is observed in both stages.
This result is very different from previous experimental findings. In a related study, Parco et al. (2005) find significant
over-dissipation only in the first stage of a two-stage contest. Given the first stage over-dissipation, and the fact that subjects
are budget constrained, there is significant under-dissipation in the second stage. Our study shows that, after eliminating
the budget constraints, over-dissipation in a two-stage contest occurs in both stages.
It is often argued that subjects need to get some experience in order to learn how to play the equilibrium. For that
reason, Fig. 4.1 displays the average effort over all 30 periods of the experiment. As players become more experienced, the
average efforts made in the first stage of OS and TS treatments decrease. A simple regression of the first stage effort on a
period trend shows a significant and negative relationship (p-value < 0.01). Although this is true for the first stage, it is not
the case for the subjects’ behavior in the second stage.
Result 3. Experience diminishes over-dissipation in the first stage but not in the second stage.
One possible reason for this finding is that at the beginning of the TS treatment, subjects apply similar strategies to both
stages of the competition. This may occur because the decisions are cognitively difficult, which causes subjects to apply
similar heuristics or “rules of thumb” to both stages (Gigerenzer and Goldstein, 1996). But with the repetition, subjects
learn the strategic aspect of the two-stage contest and correctly redistribute their efforts between the first stage and the
second stage. Note that in the second half of the experiment the magnitude of relative to the equilibrium over-dissipation
in the first stage is very similar to the magnitude of relative over-dissipation in the second stage (efforts are approximately
one and a half times higher than the equilibrium predictions).10
equilibrium predictions in order to make sure that in the two-stage contest subjects are not budget constrained (otherwise, we would have to provide
additional endowment in the second stage of a two-stage contest which would cause substantial differences in earnings between two treatments).
10We estimated a convergence model as in Noussair et al. (1995) and found that the first stage effort in OS and TS treatments does not converge to the
predicted level of 22.5 and 7.5 (p-value < 0.01 for both treatments) and the second stage effort in TS treatment does not converge to the predicted level of
30 (p-value < 0.01).
Page 6
736
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
Fig. 4.2. Distribution of efforts.
Another point that is worth noting is that subjects’ efforts are distributed on the entire strategy space, which is clearly
inconsistent with play at a unique pure strategy Nash equilibrium. Fig. 4.2 displays the full distribution of efforts made in
the first stage of the OS treatment and both stages of the TS treatment. Instead of a single point equilibrium, efforts range
from 0 to 120.
Result 4. There is substantial variance in individual efforts.
High variance in individual efforts is consistent with previous experimental findings of the contest literature (Davis and
Reilly, 1998; Potters et al., 1998). Several explanations have been offered. The first is that subjects play a quantal response
equilibrium by drawing their effort levels from the equilibrium distribution and thus causing some variance.11A second
explanation for effort fluctuations is based on the probabilistic nature of contests, which may affect individual decisions
from period to period. A third explanation is that subjects value winning differently (see Table 4.2), which may explain
why individual efforts are different. Finally, it might be the case that subjects have different preferences towards risk that
affect their behavior. In our experiment we elicited a measure of risk attitudes from a series of lotteries. We find substantial
evidence that the measurement of risk attitude is a good predictor of subject’s behavior in a contest: less risk-averse subjects
expend higher efforts than more risk-averse subjects.12This observation is consistent with theoretical work by Hillman and
Katz (1984) and it can also explain why individual efforts are not identical and instead are distributed on the entire strategy
space.
4.2. One-stage versus multi-stage
The major purpose of this study is to compare the performance of a one-stage contest with a multi-stage contest.
Theoretically, OS and TS treatments should produce the same revenues and the same dissipation rates. However, Table 4.1
reveals a big difference in the revenue collected between the two treatments. The total revenue in the OS treatment is
136, while the total revenue in the TS treatment is 170. Subjects behave more aggressively in the multi-stage contest,
exerting efforts that are 25% higher than efforts in the one-stage contest. The estimation of a random effects model, where
the dependent variable is the effort and the independent variables are a treatment dummy-variable and a period trend,
indicates that the treatment difference is significant (p-value < 0.01). The difference is significant even when we exclude
the first 15 periods of the experiment (p-value < 0.01).
Result 5. The two-stage contest generates higher revenue and higher dissipation rates than an equivalent one-stage contest.
What is causing this substantial treatment difference? A closer look at the distribution of first stage efforts in Fig. 4.2
reveals that there are almost twice as many drop-outs (effort of 0) in the OS treatment than in the TS treatment. From
Fig. 4.3 we see that this difference persists throughout all periods of the experiment. This difference is significant based on
11Another commonly made argument is that players may play an asymmetric equilibrium instead of a symmetric equilibrium. However, this argument
does not apply to rent-seeking contests since the equilibrium in such contests is unique (Szidarovszky and Okuguchi, 1997).
12We estimate several random effects models where the dependent variable is the total effort expended and the independent variables are the mea-
surements of risk-aversion, session, and treatment dummy-variables. All specifications indicate that risk attitudes elicited from lotteries have significant
influence on the effort expended in contests. The results of the estimation are available from the author upon request.
Page 7
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
737
Fig. 4.3. Fraction of drop-outs (0 effort) over 30 periods.
Fig. 4.4. The average effort by outcome of stage in TS treatment.
the estimation of a random effects probit model, where the dependent variable is whether or not the subject expended any
effort and the independent variables are a treatment dummy-variable and a period trend (p-value < 0.01). One immediate
explanation comes from the fact that in the OS treatment each subject always competes with three other subjects at the
same time while in the TS treatment each subject competes with only one other subject at the same time. Therefore, less
competitive subjects drop out of the contest more often in the OS treatment than in the TS treatment. To look for more
evidence on the “drop-out” effect, we conducted an additional session (12 subjects) where two subjects were given the
endowment of 120 francs and were competing in a contest for a prize value of 120 francs. The results fully support the
“drop-out” phenomenon: when the contest is between two players, there are only 2% of drop-outs, and when the contest
is between four players, there are 16% of drop-outs. These differences suggest that “drop-out” phenomenon may partially
explain the higher over-dissipation in TS treatment relative to OS treatment.13
Another explanation for significant over-dissipation in the TS treatment comes from the dynamic nature of the multi-
stage contest. Fig. 4.4 displays the average efforts by both winners and losers in each stage of the TS treatment. In
equilibrium, symmetric players should expend the same effort and therefore should have equal probability of winning the
first and second stage. However, in contrast to the equilibrium predictions, in both stages there is strong heterogeneity in
individual behavior with winners expending significantly higher efforts than losers (the difference is especially large in the
second stage). This important observation can also help to explain why a multi-stage contest generates significantly higher
revenue than a one-stage contest. Subjects who expend higher efforts in the first stage are more likely to proceed to the
second stage. Therefore, the first stage serves as a catalyst that helps to select more competitive subjects into the second
stage. As a result of the selection effect, more competitive subjects compete twice in the same TS treatment.
13Muller and Schotter (forthcoming) also documented the drop-out phenomenon in a contest developed by Moldovanu and Sela (2001).
Page 8
738
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
Table 4.2
Effort in a contest with no prize.
Effort in a contest
with no prize
Percent of subjectsAverage effort in
contests with prize
0
0–10
10–20
20–30
30–40
40–50
50–60
>60
57.7%
17.3%
2.6%
10.3%
1.3%
2.6%
2.6%
5.8%
31.3
33.4
39.9
45.1
50.6
73.2
74.3
54.2
To look for more evidence on the selection effect, we conducted two additional sessions (24 subjects) with a treatment
very similar to the TS treatment. The only difference was that, instead of subjects making their own decisions in the first
stage, subjects had to choose the efforts suggested by the computer. The computer randomly chose the first stage efforts,
drawn independently for each subject from efforts observed in the first stage of original TS treatment. In the second stage,
the two finalists made their own second stage efforts. This treatment was designed to eliminate the selection effect by
exogenously assigning different subjects to the second stage. Consistent with our hypothesis, the average effort in the
second stage significantly dropped from 47.2 originally to 35.3 (p-value < 0.01).14This finding suggests that the selection
effect in fact contributes to the over-dissipation in the TS treatment and it can also explain why the TS treatment generates
higher dissipation than the OS treatment.15
Behavioral economists may recognize yet another possible explanation for significant over-dissipation in TS treatment.
Instead of a selection effect in the first stage, one may argue that significant over-dissipation in the second stage is a result
of a sunk cost fallacy. In economics, sunk costs are costs that have been incurred and which cannot be recovered. Rational
economic agents should not let sunk costs influence their decisions. However, there is some evidence that economic agents
fall prey to a sunk cost fallacy (Arkes and Blumer, 1985; Meyer, 1993; Friedman et al., 2007). In our experiment, subjects
who get to the second stage of the TS treatment are the subjects who expended some positive efforts in the first stage. If
subjects do not discard sunk costs associated with the first stage efforts, they will expend more efforts in the second stage.
This implies that the second stage efforts should decrease when the first stage efforts decrease. The data clearly rejects this
prediction. Although, with experience, subjects decrease the first stage efforts in TS treatment, they do not decrease the
second stage efforts, as the sunk cost fallacy would predict (Result 3, right panel of Fig. 4.1). Moreover, the data from the
session investigating “drop-out” effects indicates that in a two-player contest subjects expend the average effort of 33.5. This
effort is very close to effort expenditures of 35.3 in the session where subjects are exogenously assigned into the second
stage of TS treatment. Note that the difference between these two sessions is that in the first session the selection and
sunk cost effects are eliminated while in the second session only the selection effect is eliminated. Only minor differences
in effort expenditures (33.5 versus 35.3) indicate that additional elimination of the sunk costs effect does change individual
behavior. Therefore, we conclude that the sunk cost fallacy is unlikely to explain the differences in dissipation rates between
TS and OS treatments.16
4.3. Non-monetary utility of winning
The theoretical predictions in Section 2 are based on the assumption that subjects care only about the monetary value
of prize. However, previous experimental research has suggested that subjects may care about winning itself. Schmitt et al.
(2004) argue that the presence of over-dissipation in numerous experimental studies (including their own) suggests that
it is not the result of subjects misunderstanding the experimental environment. They further propose that winning may
be a component in a subject’s utility. Parco et al. (2005) show that a descriptive model, which incorporates non-monetary
utility of winning, better accounts for the behavior observed in the two-stage contest with budget constraints. Other studies
addressing the utility of winning (or “joy of winning”) include Goeree et al. (2002), Amaldoss and Rapoport (2009), and
Herrmann and Orzen (2008). None of these studies, however, experimentally elicit non-monetary utility of winning from
subjects.
14We estimated a random effects model, where the dependent variable is the second stage effort and independent variable is a session dummy. The
session dummy was significant with confidence level of 1%.
15Eriksson et al. (2009) report results from an experiment where subjects could self-select into a tournament. Their results show that when the subjects
choose to enter a tournament, the average effort is higher than when the tournament payment scheme is imposed.
16Note that the sunk cost fallacy works in a different way than the selection effect. The sunk cost fallacy means that subjects who get to the second stage
expend higher efforts because they are not willing to forgo their efforts in the first stage. The selection effect means that more competitive subjects get to
the second stage and therefore they compete more during the second stage. We believe that selection effect and possibly sunk cost fallacy can explain why
TS treatment generates higher dissipation than OS treatment.
Page 9
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
739
Table 4.3
Determinants of effort in contests with prize.
Specification(1) (2)(3) (4)
Dependent variable, total effortOS+TS
−0.27***
(0.05)
0.28***
(0.08)
OS+TS
−0.27***
(0.05)
0.26***
(0.08)
−2.93*
(1.72)
−6.24***
(1.12)
OSTS
Period-trend
(inverse of a period trend, 1/t)
Non-monetary
(effort in a contest with no prize)
Quiz
(number of correct quiz answers)
OS dummy
(1 if OS treatment)
−0.11**
(0.05)
0.22***
(0.08)
−1.97
(1.64)
−0.56***
(0.10)
0.41***
(0.13)
−5.48*
(3.05)
−6.24***
(1.12)
Observations 3960 396025201440
Note. Robust standard errors in parentheses: * significant at 10%, ** significant at 5%, *** significant at 1%. Random effect models account for individual
characteristics of subjects. In each regression we control for session, period, and treatment effects.
In our experiment we elicited a non-monetary value of winning. At the end of each session subjects were given a trivial
task. In a treatment similar to OS treatment, all subjects were given an initial endowment of 120 francs and were asked
to submit their efforts for a prize value 0. Subjects were explicitly told that they would have to pay for their efforts. This
task was used to elicit subject’s non-monetary utility of winning. It is reasonable to assume that subjects who exert higher
efforts in such a task have a higher non-monetary utility of winning. We were very surprised to discover that about 30% of
subjects submitted efforts between 1 and 30, and about 12% of subjects chose efforts higher than 30 (30 francs is equivalent
to $0.5). Table 4.2 shows that the higher efforts subjects expend in a contest with no prize, indicating higher non-monetary
utility of winning, the higher their total effort in contests with prize is.
An obvious question that one may ask is whether the non-monetary utility of winning is a good predictor of subject’s
effort expenditures in a contest. To answer this question we estimate several random effects models where the dependent
variable is the total effort expended and the independent variables are a period trend, a treatment dummy-variable, and
non-monetary expenditures. We also include dummy-variables to control for session effects (not shown in the table). The
results of the estimation are presented in Table 4.3. Specifications (1) and (2) use the data from both treatments, while
specifications (3) and (4) use the data from OS and TS treatments separately.
The estimation of specification (1) in Table 4.3 indicates a very significant and positive correlation between the total
effort and the non-monetary variable. One may argue that non-monetary coefficient is capturing confusion instead of a non-
monetary utility of winning. The problem with such an argument is that subjects participated in the contest with no prize at
the very end of the experiment, after they played other contests for 60 periods. In specification (2) we use the quiz variable
measuring the number of correct quiz answers to further control for confusion.17We find that subjects who understand the
instructions better expend significantly lower efforts in contests. Nevertheless, controlling for confusion, the non-monetary
coefficient is still positive and highly significant. This finding suggests that winning is a component in a subject’s utility
and that higher non-monetary utility of winning causes higher over-dissipation in contests. It is also evident that the non-
monetary coefficient is almost twice as high in the TS treatment as in the OS treatment (specifications 3 versus 4). This
suggests that the non-monetary utility of winning may be more important in a two-stage contest than in a one-stage
contest.
What are the implications of these findings? First, the non-monetary utility of winning can explain why there is persis-
tent over-dissipation in numerous experimental studies, including our own. Second, the non-monetary utility of winning can
explain why the two-stage contest generates higher revenue than an equivalent one-stage contest. To formalize this argu-
ment, consider the following revised version of the theoretical model presented in Section 2. To account for a non-monetary
utility of winning, we assume that each player, in addition to the prize of value V , has a non-monetary value of winning w.
In such a case, the expected payoff of a risk-neutral player i competing in a simple N-player one-stage contest is given by
E(πi) = pi(ei,e−i)[V + w]− ei.
The crucial difference from the original model is that the total value of winning the contest is V + w. Differentiating (6)
with respect to eileads to a Nash equilibrium solution
(6)
e∗=(N − 1)
N2
[V + w].
(7)
17This is a measure of how well subjects understand the instructions. Before the actual experiment, subjects completed the quiz on the computer to
verify their understanding of the instructions. If a subject’s answer was incorrect, the computer provided the correct answer. The experiment started only
after all participants had answered all quiz questions.
Page 10
740
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
Next, consider a two-stage contest, where in the first stage N players are divided into K equal groups. By backward
induction, according to (7), in the second stage each finalist will expend effort of
e∗
2=(K − 1)
The resulting expected payoff in the second stage is [V + w]/K2. Knowing this, in the first stage N/K players within
each group compete as if the value of the prize was [V + w]/K2, and the first stage non-monetary value of winning was w.
Therefore, according to (7), the first stage equilibrium effort is given by
K2
[V + w].
(8)
e∗
1=(N − K)
N2K
Note that this simple behavioral model can explain several phenomena observed in our experiment. First, it can explain
significant over-dissipation in both contests and in both stages of the competition.18It is also straightforward to show that
this model predicts higher effort expenditures in the two-stage contest,
contest,
N
[V + w]. The reason behind this result is that in the two-stage contest some players receive non-monetary
utility of winning twice (in the first stage and then in the second stage), while in the one-stage contest such utility is
received only once. One possible extension to this model is to assume that the non-monetary value of winning depends on
the number of contestants, i.e. w = w(N). For example, one can replicate all qualitative predictions of our behavioral model
under the assumption of linear non-monetary utility of winning, i.e. w(N) = wN. Obviously, the correct specification of the
non-monetary utility of winning is an important question for future research.19
The non-monetary utility of winning w in (7), (8), and (9) is not directly observable. It can be elicited through a simple
experiment in which V = 0, however, as we did in the final stage of our experiment. The data suggests that the average non-
monetary value of winning is about 62.9 experimental francs, which is equivalent to $1.05.20Accounting for such addition
utility of winning, the revised equilibrium effort in the one-stage contest is 34.3. This prediction is almost identical to the
average effort of 34.1 that subjects expended in OS treatment. In the two-stage contest, the revised first stage equilibrium
effort is 27.1 and the second stage effort is 45.7. These predictions are also relatively close to the observed actual efforts of
18.9 and 47.4 in TS treatment. One reason why our behavioral model overestimates the effort expenditures in the first stage
is due to the assumption that subjects correctly account for the future utility of winning in the second stage. However, if
subjects are myopic and they do not recognize the possibility of receiving an additional utility of winning in the second
stage then their expenditures in the first stage will be lower.
?V + w + wK2?.
(9)
(N−1)
N
[V + w] +(N−K)
N
K w, than in the one-stage
(N−1)
5. Conclusions
Many contests in the real world last for multiple stages. In each stage contestants exert costly efforts in order to advance
to the final stage and win the prize. The majority of experimental studies, however, focus on one-stage static contests. In this
article, we depart from conventional practice by studying a multi-stage elimination contest and comparing its performance
with a one-stage contest. We find significant over-dissipation in both contests and in both stages of the competition. This
over-dissipation can be explained by a non-monetary utility of winning.
More importantly, contrary to the theory, the two-stage contest generates higher revenue than the equivalent one-stage
contest. We propose several explanations for this finding. First explanation is based on the observation that there are twice
as many drop-outs in the one-stage contest than there are in the two-stage contest. Another explanation is a selection
effect which implies that more competitive subjects win the first stage and thus proceed to the second stage. As a result,
more competitive subjects compete twice in the same two-stage contest. We find evidence for the selection effect: when
subjects are exogenously assigned into the second stage, subjects on average expend significantly lower second stage efforts
than when the assignment is endogenous. Finally, and probably most importantly, we find that the non-monetary utility of
winning can account for the majority of differences between the one-stage and two-stage contests.
The results of this study have important implications for contest design (Rosen, 1986; Gradstein and Konrad, 1999). By
using a multi-stage contest instead of a one-stage contest, the designer can extract higher total efforts from contestants.
Moreover, by using a multi-stage contest, the designer can increase participation rate. Knowing that the major competition
18The non-monetary utility of winning is not the only explanation for significant over-dissipation. Indeed, such a utility cannot explain why individual
subjects change their effort levels when they receive different endowments (Sheremeta, forthcoming), and thus it may not generalize to other contest
environments. Nevertheless, we believe that a positive utility from winning is an important factor that contributes to individual over-expenditures in
contests.
19One can also provide a more sophisticated analysis, assuming heterogeneous players. For example, consider the case of a simple asymmetric two-player
contest, with only one player having a positive utility from winning. It is straightforward to show that such asymmetry leads to higher equilibrium effort
for the player with a positive utility from winning and lower equilibrium effort for the other player. Moreover, the total effort in such an asymmetric
contest increases relative to a symmetric two-player contest. This basic consideration implies that adding a non-monetary utility from winning to a player
causes his effort to increase, and the other player’s effort to decrease (but by less), thus explaining both over-dissipation (Result 1) and variance in effort
levels (Result 4).
20Eq. (7) implies that w = eN2/(N − 1) − V . In a contest with no prize, V = 0 and N = 4, subjects expend an average effort of e = 11.8. Therefore, the
implied value of w is 62.9.
Page 11
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
741
takes place in the latter stages, the designer can guarantee high performance from contestants in the final stage of a multi-
stage contest.
This study also points out the importance of modeling theoretically a number of behavioral considerations such as
heterogeneity between players and a non-monetary utility of winning. By incorporating these behavioral considerations, we
can understand why individual behavior does not comply with the equilibrium predictions of classical models. Obviously,
this study also opens several interesting questions about how one should model the non-monetary utility of winning,
what are the alternative elicitation mechanisms that can reveal individual preferences towards winning, and what are the
implications of such preferences in different economic environments.
Appendix A
GENERAL INSTRUCTIONS
This is an experiment in the economics of strategic decision making. Various research agencies have provided funds
for this research. The instructions are simple. If you follow them closely and make appropriate decisions, you can earn an
appreciable amount of money.
The experiment will proceed in four parts. Each part contains decision problems that require you to make a series of
economic choices which determine your total earnings. The currency used in Part 1 of the experiment is U.S. dollars. The
currency used in Parts 2, 3 and 4 of the experiment is francs. Francs will be converted to U.S. Dollars at a rate of 60
francs to 1 dollar. At the end of today’s experiment, you will be paid in private and in cash. 12 participants are in today’s
experiment.
It is very important that you remain silent and do not look at other people’s work. If you have any questions, or need
assistance of any kind, please raise your hand and an experimenter will come to you. If you talk, laugh, exclaim out loud,
etc., you will be asked to leave and you will not be paid. We expect and appreciate your cooperation.
At this time we proceed to Part 1 of the experiment.
INSTRUCTIONS FOR PART 1
YOUR DECISION
In this part of the experiment you will be asked to make a series of choices in decision problems. How much you receive
will depend partly on chance and partly on the choices you make. The decision problems are not designed to test you.
What we want to know is what choices you would make in them. The only right answer is what you really would choose.
For each line in the table in the next page, please state whether you prefer option A or option B. Notice that there
are a total of 15 lines in the table but just one line will be randomly selected for payment. You ignore which line will be
paid when you make your choices. Hence you should pay attention to the choice you make in every line. After you have
completed all your choices a token will be randomly drawn out of a bingo cage containing tokens numbered from 1 to 15.
The token number determines which line is going to be paid.
Your earnings for the selected line depend on which option you chose: If you chose option A in that line, you will receive
$1. If you chose option B in that line, you will receive either $3 or $0. To determine your earnings in the case you chose
option B there will be second random draw. A token will be randomly drawn out of the bingo cage now containing twenty
tokens numbered from 1 to 20. The token number is then compared with the numbers in the line selected (see the table).
If the token number shows up in the left column you earn $3. If the token number shows up in the right column you
earn $0.
Any questions?
Participant ID _________
Decision
no.
Option A Option B
Please choose
A or B
1
$1 $3
never
$0
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,
15, 16, 17, 18, 19, 20
2
$1 $3
if 1 comes out of the bingo cage
$0
if 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15,
16, 17, 18, 19, 20
3
$1$3
if 1 or 2 comes out
$0
if 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20
4
$1$3
if 1, 2, or 3
$0
if 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16,
17, 18, 19, 20
5
$1$3
if 1, 2, 3, 4
$0
if 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17,
18, 19, 20
(continued on next page)
Page 12
742
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
Decision
no.
Option A Option B
Please choose
A or B
6
$1$3
if 1, 2, 3, 4, 5
$0
if 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20
7
$1$3
if 1, 2, 3, 4, 5, 6
$0
if 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20
8
$1$3
if 1, 2, 3, 4, 5, 6, 7
$0
if 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
9
$1 $3
if 1, 2, 3, 4, 5, 6, 7, 8
$0
if 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
10
$1$3
if 1, 2, 3, 4, 5, 6, 7, 8, 9
$0
if 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
11
$1 $3
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
$0
if 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
12
$1 $3
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
$0
if 12, 13, 14, 15, 16, 17, 18, 19, 20
13
$1$3
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
$0
if 13, 14, 15, 16, 17, 18, 19, 20
14
$1 $3
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13
$0
if 14, 15, 16, 17, 18, 19, 20
15
$1$3
if 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
$0
if 15, 16, 17, 18, 19, 20
INSTRUCTIONS FOR PART 2
YOUR DECISION
The second part of the experiment consists of 30 decision-making periods and each period consists of two stages. At the
beginning of each period, you will be randomly and anonymously placed into a group of four participants. The composition
of your group will be changed randomly every period. Each period you will be randomly and anonymously assigned as
participant 1, 2, 3, or 4. In Stage 1 participant 1 will be paired with participant 2 and participant 3 will be paired with
participant 4. All four participants will be given an initial endowment of 120 francs. You will use this endowment to bid for
a chance of participating in the final Stage 2. An example of your decision screen is shown below.
Page 13
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
743
The two finalists — one from each pair — will proceed to Stage 2. The other two participants who did not win in Stage 1
will no longer participate in this period. In Stage 2 the two remaining participants will bid for a reward. The reward is
worth 120 francs. The two participants may bid any number of francs between 0 and the amount of francs remaining from
the initial endowment (including 0.5 decimal points). An example of the decision screen is shown below.
YOUR EARNINGS
If you receive the reward your period earnings are equal to your endowment plus the reward minus your bids in Stage 1
and Stage 2. If you do not receive the reward your period earnings are equal to your endowment minus your bids in Stage 1
and Stage 2. Note that if you do not win in Stage 1, your bid in Stage 2 is automatically assigned to zero.
Page 14
744
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
If you receive the reward:
Earnings = Endowment+ Reward− Your Bid in Stage 1− Your Bid in Stage 2
= 120+ 120− Your Bid in Stage 1− Your Bid in Stage 2
If you do not receive the reward:
Earnings = Endowment− Your Bid in Stage 1− Your Bid in Stage 2
= 120− Your Bid in Stage 1− Your Bid in Stage 2
The more you bid in each stage, the more likely you are to win that stage. The more the other participants bid, the less
likely you are to win. Specifically, in Stage 1, for each franc you bid you will receive one lottery ticket. At the end of Stage 1
the computer draws randomly one ticket among all the tickets purchased by you and the other participant. The owner of
the drawn ticket wins Stage 1 and proceeds to Stage 2. Thus, your chance of winning in Stage 1 is given by the number of
francs you bid divided by the total number of francs you and the other participant bids:
Chance of winning
in Stage 1
=
Your Bid
Your Bid+ The other participant’s bid
In case both participants bid zero in Stage 1, the computer randomly chooses one participant who wins Stage 1 and
proceeds to Stage 2. In Stage 2, for each franc you bid you will also receive one lottery ticket. At the end of Stage 2 the
computer draws randomly one ticket among all the tickets purchased by you and the other finalist of Stage 1. The owner
of the drawn ticket wins Stage 2 and receives the reward of 120 francs. Thus, your chance of winning Stage 2 is given by
the number of francs you bid divided by the total number of francs you and the other participant bids:
Chance of winning
in Stage 2
=
Your Bid
Your Bid+ The other participant’s bid
In case both participants bid zero in Stage 2, the winner is determined randomly.
Example of the Random Draw
This is a hypothetical example of how the computer makes a random draw. Let’s say, in Stage 1, participant 1 bids 10
francs, participant 2 bids 5 francs, participant 3 bids 0 francs, and participant 4 bids 40 francs. Therefore, the computer
assigns 10 lottery tickets to participant 1, 5 lottery tickets to participant 2, 0 lottery tickets to participant 3, and 40 lottery
tickets to participant 4. In Stage 1, participant 1 is paired with participant 2. Therefore, for this fist pair the computer
randomly draws one lottery ticket out of 15 (10 lottery tickets for participant 1 and 5 lottery tickets for participant 2). As
you can see, participant 1 has higher chance of winning in Stage 1: 0.67 = 10/15. Participant 2 has 0.33 = 5/15 chance
of winning in Stage 1. Similarly, participant 3 is paired with participant 4 in Stage 1. For this second pair, the computer
randomly draws one lottery ticket out of 40 (0 lottery tickets for participant 3 and 40 lottery tickets for participant 4). As
you can see, in this pair participant 3 has no chance of winning in Stage 1: 0 = 0/40.
Let’s say that computer made a random draw in Stage 1 and the winner of the first pair is participant 2 while the
winner of the second pair is participant 4. Therefore, participant 2 and participant 4 proceed to Stage 2. Let’s say, in Stage 2,
participant 2 bids 60 francs and participant 4 bids 20 francs. Therefore, the computer assigns 60 lottery tickets to participant
2 and 20 lottery tickets to participant 4. Then the computer randomly draws one lottery ticket out of 80 (60 + 20). As you
can see, participant 2 has higher chance of winning in Stage 2: 0.75 = 60/80. Participant 4 has 0.25 = 20/80 chance of
winning in Stage 2.
After four participants make their bids in Stage 1, the computer will make a random draw which will decide who wins
in Stage 1 and thus proceeds to Stage 2. Then after two remaining participants make their bids in Stage 2, the computer
will make a random draw which will decide who wins in Stage 2. Then the computer will calculate your period earnings
based on your bid in Stage 1 and Stage 2 and whether you received the reward or not. These earnings will be converted
to cash and paid at the end of the experiment if the current period is one of the five periods that is randomly chosen for
payment.
At the end of each period, your bid in Stage 1, the other participant’s bid in Stage 1, whether you won in Stage 1 or not,
your bid in Stage 2, the other participant’s bid in Stage 2, whether you received the reward or not, and the earnings for the
period are reported on the outcome screen as shown below. Once the outcome screen is displayed you should record your
results for the period on your Personal Record Sheet under the appropriate heading.
Page 15
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
745
Outcome Screen
IMPORTANT NOTES
You will not be told which of the participants in this room are assigned to which group. At the beginning of each
period you will be randomly re-grouped with three other participants to from a four-person group. You can never guarantee
yourself the reward. However, by increasing your contribution, you can increase your chance of winning in Stage 1 and
Stage 2 and thus increase your chance of receiving the reward. Regardless of who receives the reward, all participants will
have to pay their bids in Stage 1 and Stage 2.
At the end of the experiment we will randomly choose 5 of the 30 periods for actual payment in part 2 using a bingo
cage. You will sum the total earnings for these 5 periods and convert them to a U.S. dollar payment, as shown on the last
page of your record sheet.
Are there any questions?
INSTRUCTIONS FOR PART 3
The third part of the experiment consists of 30 decision-making periods. The rules for part 3 are similar to the rules for
part 2. At the beginning of each period, you will be randomly and anonymously placed into a group of 4 participants. The
composition of your group will be changed randomly every period. Each period you will be given an initial endowment of
120 francs. You will use this endowment to bid for a reward. The reward is worth 120 francs to you and the other three
participants in your group. The only difference is that in part 3, there will be only one stage (instead of two stages). In that
stage all four participants including you will bid for a reward.
After all participants have made their decisions, your earnings for the period are calculated in the similar way as in
part 2.
If you receive the reward:
Earnings = Endowment+ Reward− Your Bid = 120+ 120− Your Bid
If you do not receive the reward:
Earnings = Endowment− Your Bid = 120− Your Bid
The more you bid, the more likely you are to receive the reward. The more the other participants in your group bid, the
less likely you are to receive the reward. Specifically, for each franc you bid you will receive one lottery ticket. At the end
of each period the computer draws randomly one ticket among all the tickets purchased by 4 participants in the group,
Page 16
746
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
including you. The owner of the drawn ticket receives the reward of 120 francs. Thus, your chance of receiving the reward
is given by the number of francs you bid divided by the total number of francs all 4 participants in your group bid:
Chance of receiving
the reward
=
Your Bid
sum of all 4 Bids in your group
In case all participants bid zero, the reward is randomly assigned to one of the four participants in the group.
Example of the Random Draw
This is a hypothetical example used to illustrate how the computer is making a random draw. Let’s say participant 1 bids
10 francs, participant 2 bids 15 francs, participant 3 bids 0 francs, and participant 4 bids 40 francs. Therefore, the computer
assigns 10 lottery tickets to participant 1, 15 lottery tickets to participant 2, 0 lottery tickets to participant 3, and 40 lottery
tickets for participant 4. Then the computer randomly draws one lottery ticket out of 65 (10 + 15 + 0 + 40). As you can
see, participant 4 has the highest chance of receiving the reward: 0.62 = 40/65. Participant 2 has 0.23 = 15/65 chance,
participant 1 has 0.15 = 10/65 chance, and participant 3 has 0 = 0/65 chance of receiving the reward.
After all participants make their bids, the computer will make a random draw which will decide who receives the reward.
Then the computer will calculate your period earnings based on your bid and whether you received the reward or not.
At the end of each period, your bid, the sum of all bids in your group, whether you received the reward or not, and the
earnings for the period are reported on the outcome screen. Once the outcome screen is displayed you should record your
results for the period on your Personal Record Sheet under the appropriate heading.
At the end of the experiment we will randomly choose 5 of the 30 periods for actual payment in part 3 using a bingo
cage. You will sum the total earnings for these 5 periods and convert them to a U.S. dollar payment, as shown on the last
page of your record sheet.
Are there any questions?
INSTRUCTIONS FOR PART 4
The fourth part of the experiment consists of only 1 decision-making period. The rules for part 4 are the same as the
rules for part3. At the beginning of the period, you will be randomly and anonymously placed into a group of 4participants.
You will be given an initial endowment of 120 francs. You will use this endowment to bid in order to be a winner. For each
franc you bid you will receive one lottery ticket. At the end of each period the computer draws randomly one ticket among
all the tickets purchased by 4 participants in the group, including you. The owner of the drawn ticket becomes a winner.
Thus, your chance of becoming a winner is given by the number of francs you bid divided by the total number of francs all
4 participants in your group bid. The only difference is that in part 4 the winner does not receive the reward. Therefore,
the reward is worth 0 francs to you and the other three participants in your group. After all participants have made their
decisions, your earnings are calculated:
Earnings = Endowment− Your Bid = 120− Your Bid
After all participants have made their decisions, your earnings will be displayed on the outcome screen. Your earnings will
be converted to cash and paid at the end of the experiment.
References
Amaldoss, W., Rapoport, A., 2009. Excessive expenditure in two-stage contests: Theory and experimental evidence. In: Columbus, F. (Ed.), Game Theory:
Strategies, Equilibria, and Theorems. Nova Science Publishers, Hauppauge, NY.
Amegashie, J.A., 1999. The design of rent-seeking competitions: Committees preliminary and final contests. Public Choice 99, 63–76.
Amegashie, J.A., Cadsby, C.B., Song, Y., 2007. Competitive burnout: Theory and experimental evidence. Games Econ. Behav. 59, 213–239.
Anderson, L.R., Stafford, S.L., 2003. An experimental analysis of rent seeking under varying competitive conditions. Public Choice 115, 199–216.
Arkes, H.R., Blumer, C., 1985. The psychology of sunk cost. Organizat. Behav. Human Dec. Proces. 35, 124–140.
Baharad, E., Nitzan, S., 2008. Contest efforts in light of behavioural considerations. Econ. J. 118, 2047–2059.
Baik, K.H., Lee, S., 2000. Two-stage rent-seeking contests with carryovers. Public Choice 103, 285–296.
Bognanno, M.L., 2001. Corporate tournaments. J. Lab. Econ. 19, 290–315.
Clark, C., Riis, D.J., 1996. A multi-winner nested rent-seeking contest. Public Choice 87, 177–184.
Davis, D., Reilly, R., 1998. Do many cooks always spoil the stew? An experimental analysis of rent seeking and the role of a strategic buyer. Public Choice 95,
89–115.
Ehrenberg, R.G., Bognanno, M.L., 1990. Do tournaments have incentive effects? J. Polit. Economy 98, 1307–1324.
Eriksson, T., Teyssier, S., Villeval, M.C., 2009. Self-selection and the efficiency of tournaments. Econ. Inquiry 47, 530–548.
Fischbacher, U., 2007. z-Tree: Zurich toolbox for ready-made economic experiments. Exper. Econ. 10, 171–178.
Friedman, D., Pommerenke, K., Lukose, R., Milam, G., Huberman, B., 2007. Searching for the sunk cost fallacy. Exper. Econ. 10, 79–104.
Fu, Q., Lu, J., forthcoming. Optimal multi-stage contest. Econ. Theory.
Gigerenzer, G., Goldstein, D.G., 1996. Reasoning the fast and frugal way: Models of bounded rationality. Psych. Rev. 103, 650–669.
Gneezy, U., Smorodinsky, R., 2006. All-pay auctions — An experimental study. J. Econ. Behav. Organ. 61, 255–275.
Goeree, J., Holt, C., Palfrey, T., 2002. Quantal response equilibrium and overbidding in private-value auctions. J. Econ. Theory, 247–272.
Gradstein, M., 1998. Optimal contest design: Volume and timing of rent seeking in contests. Europ. J. Polit. Economy 14, 575–585.
Gradstein, M., Konrad, K.A., 1999. Orchestrating rent seeking contests. Econ. J. 109, 536–545.
Groh, C., Sela, A., Moldovanu, B., Sunde, U., forthcoming. Optimal seedings in elimination tournaments. Econ. Theory.
Harris, C., Vickers, J., 1985. Perfect equilibrium in a model of a race. Rev. Econ. Stud. 52, 193–209.
Page 17
R.M. Sheremeta / Games and Economic Behavior 68 (2010) 731–747
747
Harris, C., Vickers, J., 1987. Racing with uncertainty. Rev. Econ. Stud. 54, 1–21.
Herrmann, B., Orzen, H., 2008. The appearance of homo rivalis: Social preferences and the nature of rent seeking. University of Nottingham, Working Paper.
Hillman, A.L., Katz, E., 1984. Risk-averse rent seekers and the social cost of monopoly power. Econ. J. 94, 104–110.
Holt, C.A., Laury, S.K., 2002. Risk aversion and incentive effects. Amer. Econ. Rev. 92, 1644–1655.
Klumpp, T., Polborn, M.K., 2006. Primaries and the New Hampshire effect. J. Public Econ. 90, 1073–3114.
Konrad, K.A., Kovenock, D., 2009. Multi-battle contests. Games Econ. Behav. 66, 256–274.
McKelvey, R., Palfrey, T., 1995. Quantal response equilibria for normal form games. Games Econ. Behav. 10, 6–38.
Meyer, D.J., 1993. First price auctions with entry: An experimental investigation. Quart. J. Econ. Finance 33, 107–122.
Millner, E.L., Pratt, M.D., 1989. An experimental investigation of efficient rent-seeking. Public Choice 62, 139–151.
Millner, E.L., Pratt, M.D., 1991. Risk aversion and rent seeking: An extension and some experimental evidence. Public Choice 69, 91–92.
Moldovanu, B., Sela, A., 2001. The optimal allocation of prizes in contests. Amer. Econ. Rev. 91, 542–558.
Muller, W., Schotter, A., forthcoming. Workaholics and drop outs in optimal organizations. J. Europ. Econ. Assoc.
Nitzan, S., 1994. Modelling rent-seeking contests. Europ. J. Polit. Economy 10, 41–60.
Noussair, C., Plott, C., Riezman, R., 1995. An experimental investigation of the patterns of international trade. Amer. Econ. Rev. 85, 462–491.
Parco, J., Rapoport, A., Amaldoss, W., 2005. Two-stage contests with budget constraints: An experimental study. J. Math. Psych. 49, 320–338.
Potters, J.C., De Vries, C.G., Van Linden, F., 1998. An experimental examination of rational rent seeking. Europ. J. Polit. Economy 14, 783–800.
Rosen, S., 1986. Prizes and incentives in elimination tournaments. Amer. Econ. Rev. 76, 701–715.
Schmitt, P., Shupp, R., Swope, K., Cadigan, J., 2004. Multi-period rent-seeking contests with carryover: Theory and experimental evidence. Econ. Gover-
nance 5, 187–211.
Sheremeta, R.M., forthcoming. Contest design: An experimental investigation. Econ. Inquiry.
Shogren, J.F., Baik, K.H., 1991. Reexamining efficient rent-seeking in laboratory markets. Public Choice 69, 69–79.
Stein, W.E., Rapoport, A., 2005. Symmetric multi-stage contests with budget constraints. Public Choice 124, 309–328.
Szidarovszky, F., Okuguchi, K., 1997. On the existence and uniqueness of pure Nash equilibrium in rent-seeking games. Games Econ. Behav. 18, 135–140.
Tullock, G., 1980. Efficient rent seeking. In: Buchanan, J.M., Tollison, R.D., Tullock, G. (Eds.), Toward a Theory of the Rent-Seeking Society. Texas A&M
University Press, College Station, TX, pp. 97–112.