ENHANCING EFFORT SUPPLY WITH PRIZE‐AUGMENTING ENTRY FEES: THEORY AND EXPERIMENTS

• Date: 01 August 2019
• Published date: 01 August 2019
• Author: Jingfeng Lu,Robert G. Hammond,Yohanes E. Riyanto,Bin Liu
• DOI: http://doi.org/10.1111/iere.12379

INTERNATIONAL ECONOMIC REVIEW

Vol. 60, No. 3, August 2019 DOI: 10.1111/iere.12379

ENHANCING EFFORT SUPPLY WITH PRIZE-AUGMENTING ENTRY FEES:

THEORY AND EXPERIMENTS∗

BYROBERT G. HAMMOND,BIN LIU,JINGFENG LU,AND YOHANES E. RIYANTO1

North Carolina State University, U.S.A.; The Chinese University of Hong Kong, Shenzhen,

China; National University of Singapore, Singapore; Nanyang Technological University,

Singapore

Entry fees are widely observed in contests. We study the effect of a prize-augmenting entry fee on expected

total effort in an all-pay auction setting where the contestants’ abilities are private information. An entry fee

reduces equilibrium entry but can enhance the entrants’ effort supply. Our theoretical model demonstrates that

the optimal entry fee is strictly positive and finite. In a laboratory experiment, we empirically test the effect of

entry fees on effort supply. Our results provide strong support for the notion that a principal can elicit higher

effort using an appropriately set entry fee to augment the prize purse.

1. INTRODUCTION

Contests are observed in a wide range of environments such as labor markets, investments

in research and development, political campaigns, advertising, lobbying, conflict, sports, etc. In

many situations, the goal of the contests is to elicit productive effort. For this purpose, the prize

allocation rule has long been recognized as a major instrument that the contest organizer can

use to enhance effort supply. In particular, the principle of “carrot and stick” has been long and

widely followed in practice as a guideline for effective design to provide the right incentives to

agents. In a contest setting, a positive prize can be viewed as a carrot, whereas a negative prize

can be viewed as a stick. In this article, we study a contest design problem—similar to Liu et al.

(2018)—that allows both positive and negative prizes. The contest designer can use an entry fee

as an instrument to create negative prizes for losers. Entry fees are added to the original prize

purse, which will be awarded as a single winning prize to the contestant who exerts the highest

effort. All losing participants win nothing but pay the entry fee, which represents a negative

prize ex post.

Bundling the sum of the revenue collected from awarding negative prizes into the reward

paid as a positive prize has a number of empirical analogs. Sporting contests often require

monetary payments to enter the contest, and these entry fees are used to partly fund the prize

paid to the winner. Examples from sports include registration fees for marathons and “buy-ins”

in poker tournaments, both of which are required entry fees to compete that are then used as

part of the prize purse. Outside the realm of sports, contests in the creative industries often

∗Manuscript received July 2017; revised August 2018.

[Correction added on 19 March 2019, after first online publication: Bin Liu’s affiliation was changed to The Chinese

University of Hong Kong, Shenzhen, China]

1We acknowledge the Isaac Manasseh Meyer Fellowship, which funded Hammond’s visit to the National University

of Singapore, where part of the work on this article was completed. Bin Liu gratefully acknowledges financial support

from the National Natural Science Foundation of China (71703138). Jingfeng Lu gratefully acknowledges the financial

supportfrom the Ministry of Education, Singapore (R-122-000-252-115). We also thank the editor, associate editor, three

referees, Pia Weiss, and seminar participants at the International Industrial Organization Conference for comments

and suggestions. Please address correspondence to: Robert G. Hammond, Department of Economics, North Carolina

State University, 4170 Nelson Hall, Campus Box 8110, Raleigh, NC 27695-8110, U.S.A. Phone: 919-513-2871. Fax:

919-515-7873. E-mail: robert_hammond@ncsu.edu.

1063

C

(2019) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

1064 HAMMOND ET AL.

require prize-augmenting entry fees, including contests giving awards for best works of writing,

photography, architecture, and design.2

We consider an all-pay auction with incomplete information, where the bidders’ abilities are

their private information. The bidders simultaneously decide whether to pay the entry fee to

participate and how to bid if they decide to enter without observing the others’ entry and bidding

decisions. The effect of an entry fee on effort supply is twofold. On one hand, it discourages

the low-ability types from participating in the competition, which lowers their effort supply. On

the other hand, entry fees increase the winner’s prize, which induces more effort from higher

types. The total effect thus relies on the trade-off between these two effects. Our theoretical

study shows that imposing an entry fee indeed enhances the effort supply of agents if it is set

appropriately. We establish that the effort-maximizing entry fee must be strictly positive and

finite. This result helps to explain why entry fees are widely observed in practice.

We verify our theoretical predictions in a laboratory experiment. Our analysis focuses on the

expected total effort of the contestants, which in our context is equivalent to the revenue raised

by the contest designer. We experimentally vary the entry fee and the nature of contestant

heterogeneity in a between-subjects design. The entry fee is set either at 0, the optimal level,

or higher than the optimal level. Contestant heterogeneity is not a treatment variable of our

primary interest but is instead used to present a robust analysis of the optimal entry fee in

different settings of interest. The degree of heterogeneity is measured by the variance of bidders’

marginal cost distribution, where we vary the bounds of the uniform distribution.

Our experimental results strongly support the models’ predictions. We find that revenue is the

highest when the entry fee is set optimally and the prize is augmented with the total entry fees

collected from the entrants. The revenue gains associated with the optimal entry fee is 26.75%

more relative to no entry fee and 46.16% more relative to a high entry fee in these data. Further,

we find strong support for two opposing effects that we demonstrate in our theoretical results. An

entry fee creates a discouragement effect on weaker contestants. However, augmenting the prize

with the sum of entry fees creates an incentive effect on stronger contestants. We indeed find that

an entry fee discourages entry (the discouragement effect) but increases the bids of bidders who

enter with a given marginal cost (the incentive effect). The optimal entry fee raises more revenue

than no entry fee or a higher entry fee because it is successful at balancing these two effects.

The article is organized as follows. Section 2 surveys the related literature. Section 3 presents

our theoretical model and its predictions. We then describe our experimental design and pro-

cedures in Section 4 and discuss our experimental results in Section 5. Section 6 concludes.

2. RELATED LITERATURE

Optimal prize allocation has been studied in various all-pay auction frameworks starting from

the seminal work of Moldovanu and Sela (2001). They establish winner-take-all as the optimal

prize allocation rule when contestants’ effort function is linear or concave while restricting prizes

to be nonnegative. They also establish that convex effort cost can invalidate the optimality of

the winner-take-all. Minor (2013) maintains the assumption of nonnegative prizes and studies

the optimal prize allocation rule when contestants have convex costs of effort or the contest

designer has concave benefit of effort. Moldovanu and Sela (2006) generalize their earlier

investigation to a two-stage all-pay auction framework. Meanwhile, Moldovanu et al. (2007)

analyze the environment where contestants care about their relative status. They further allow

2Several contests explicitly mention that the entry fees are used to supplement the prize paid to the winner.

Fredriksson (1993) discusses rodeos where the “entrance fees were added to the prize money.” In horse racing,

the Thoroughbred Owners and Breeders Association discusses races in which the “sum of owners’ entry fees” are

added to the prize purse (https://www.toba.org/owner-education/entering-races.aspx). Concerning design contests,

http://www.victoriastrauss.com/advice/contests says that contests “charge a fee to fund the prize.” Finally, in the con-

text of writing contests, https://www.freelancer.sg/feesandcharges says that entry fees “will be used to increase the

contest prize,” whereas http://thewritelife.com/27-free-writing-contests/ says that entry fees are used as a “way of

[growing] the prize purse for each contest.”

PRIZE-AUGMENTING ENTRY FEES 1065

for negative prizes in Moldovanu et al. (2012). In Moldovanu et al. (2012), a negative prize is

costly for the organizer to implement. In our article, when negative prizes are implemented for

some contestants, the revenue collected, such as in Fullerton and McAfee (1999) and Liu et al.

(2018), will be used by the organizer to reward other contestants.

Our article is closely related to Liu et al. (2018), who adopt a mechanism design approach

to study the effort-maximizing prize allocation rule allowing both positive and negative prizes.

Imposing an endogenous effort threshold, Liu et al. (2018) characterize the optimal prize

allocation rule and show that such an allocation rule is optimal in a general class of contest

mechanisms. In Liu et al. (2018), a contestant, if he bids, must bid above a threshold. If no

one bids, all bidders equally share the total prize budget, which makes all bidders participate

at the optimum in their setting. The issue of endogenous entry, absent in their paper, however,

definitely arises here in our environment, since only the highest bidder gets a single positive prize

but all pay an entry fee. This issue would potentially reduce the effort supply and complicate

the trade-off. Nevertheless, we find that, at the optimum, entry fee—a special form of negative

prize—still prevails, as the optimal entry fee is always positive.

Thomas and Wang (2013) present a model in which the highest bidding contestant wins a

fixed prize (V) and the lowest bidding contestant pays a fine (P), with P<V. The contest

designer sets the optimal level of fine P. Contestants must decide whether to participate in the

contest. If there is only one bidder who participates in the contest, she will win the prize, but she

also must pay the fine because her bid is both the highest and the lowest. Different from theirs,

in our setup, all contestants must pay an entry fee, regardless of whether their bid is the lowest

bid. The revenues collected from entry fees are then added onto the winning prize. Further,

in our setup, contestants are heterogeneous in their marginal bidding costs. We know from

the literature that greater cost heterogeneity discourages weaker contestants from competing

(Schotter and Weigelt, 1992; Gradstein, 1995; Clark and Riis, 1998). This discouragement effect

may reduce effort.3Counter to this negative effect, Moldovanu and Sela (2001) show that having

multiple prizes encourages weaker contestants to participate. However, this also comes at a cost

of inducing stronger contestants to lower their effort. Moldovanu and Sela (2001) show that

only when bidding costs are sufficiently convex may awarding multiple prizes be optimal.4

Note that the entry fee in our setup essentially works as an endogenous participation con-

straint. Instead of using entry fee to create the participation constraint, Megidish and Sela

(2013) use the minimal effort constraint in which a contestant is only allowed to participate if

her effort exceeds the minimal effort constraint. The minimal effort constraint works in a similar

fashion as the entry fee in our setup. Further, Megidish and Sela (2013) consider two alternative

prize allocation schemes. The first is the winner-take-all scheme and the second is the random

allocation scheme. With the random allocation scheme, all contestants who exert efforts that

exceed the minimal effort constraint have an equal chance to win the prize. They show that the

random prize allocation scheme induces greater participation from contestants. The increase in

the number of participants could offset the reduction in effort due to the discouragement effect.

They show that the random prize allocation scheme is potentially superior to the winner-take-all

allocation scheme.

In our article, we design a lab experiment to test the predictions of our prize-augmenting

entry fee scheme on the total expected effort. The question is whether this scheme creates a

strong enough incentive for stronger contestants to exert high effort, such that it outweighs

the loss from weaker contestants who are less likely to enter the contest because of an entry

fee. To the best of our knowledge, our article is the first to present an experimental analysis of

an all-pay auction with a prize-augmenting entry fee mechanism. Although Dechenaux et al.

3Llorente-Saguer et al. (2016) study the discouragement effect directly and ask whether contests can be designed

in ways that ameliorated it. Their results confirm that the contest designer can reduce the discouragement effect by

favoring weaker contestants (e.g., bid caps and favorable tie-breaking rules), but they find mixed evidence on whether

these designs can increase revenue.

4Several experimental papers have found that a single prize generates higher effort than multiple prizes (Vandegrift

et al., 2007; Sheremeta, 2011; Stracke et al., 2014; Cason et al., 2010).