Sequential choice of sharing rules in collective contests

• Published date: 01 October 2018
• Author: Sabine Flamand,Oliver Gürtler,Pau Balart,Orestis Troumpounis
• Date: 01 October 2018
• DOI: http://doi.org/10.1111/jpet.12303

703

Journal of Public Economic Theory. 2018;20:703–724. wileyonlinelibrary.com/journal/jpet © 2018 Wiley Periodicals, Inc.

Received: 28 February2017 Accepted: 2 April 2018

DOI: 10.1111/jpet.12303

ARTICLE

Sequential choice of sharing rules in collective

contests

Pau Balart1Sabine Flamand2Oliver Gürtler3

Orestis Troumpounis4

1Departmentof Business Economics, Universitat

deles Illes Balears

2Departmentof Economics and CREIP, Universi-

tatRovira i Virgili

3Universityof Cologne, Albertus-Magnus Platz

4Departmentof Economics, Lancaster University

PauBalart, Department of Business Economics,

Universitatde les Illes Balears, Carretera de

Valldemossa,07022 Palma de Mallorca, Spain.

Email:pau.balart@uib.cat

SabineFlamand, Department of Economics

andCREIP,Universitat Rovira i Virgili, Av.de la

Universitat1, 43204 Reus, Spain.

Email:sabine.flamand@urv.cat

OliverGürtler, University of Cologne, Albertus-

MagnusPlatz, D-50923 Cologne, Germany.

Email:oliver.guertler@unikoeln.de

OrestisTroumpounis, Department of Economics,

LancasterUniversity, Bailrigg, Lancaster,LA1

4YX,United Kingdom.

Email:o.troumpounis@lancaster.ac.uk

Fundinginformation

Ministeriode Economía y Competitividad

Grant/AwardNumbers ECO201786305-C4-1-R

(AEI/ERDF,EU), ECO2015-67171-P,ECO2016-

75410-P

Groups competing for a prize need to determine how to distribute

it among their members in case of victory. Considering competition

between two groups of different size, we show that the small group's

sharing rule is a strategic complement to the large group's sharing

rule in the sense that if the small group chooses a more merito-

cratic sharing rule, the large group wishes to choose a more merito-

cratic rule as well. On the contrary,the large group's sharing rule is a

strategic substitute to the small group's sharing rule, hence the tim-

ing of choice is crucial. Forsufficiently private prizes, a switch from a

simultaneous choice to the small group being the leader consists in a

Pareto improvement and reduces aggregate effort. On the contrary,

when the large group is the leader, aggregate effort increases. As a

result, the equilibrium timing is such that the small group chooses its

sharing rule first. If the prize is not private enough, the small group

retires from the competition and switching from a simultaneous to

a sequential timing may reverse the results in terms of aggregate

effort. The sequential timing also guarantees that the small group

never outperforms the large one.

1INTRODUCTION

Contests among organizations and groups of individuals are widespread. Examples include research and development

races, pre-electoral campaigns, procurement contests, or even sport and art contests. In all the above, groups'per-

formance depends on individual contributions of their members, which implies that groups need to coordinate and

establish some rules regarding their internal organization. As the literature on collective contests has pointed out, a

keyelement of groups'organization is related to the allocation of the prize among the winning group members.1

1Starting with Nitzan (1991), the literature has considered both exogenousand endogenous sharing rules. For a recent survey on prize-sharing rules incol-

lectiverent seeking, seeFlamand and Troumpounis (2015). For surveys of the literature on individual contests in general, see among others Corchón (2007),

Corchón and Serena (2018), Konrad (2009), Long(2013), and also Dechenaux, Kovenock, and Sheremeta (2015) for the related experimental evidence. On

collectivecontests, see the recent survey by Kolmar (2013), and also Sheremeta (2017) for a recent review of experimental evidence.

2BALART ETAL.

704

B

While contests among groups are generally thought of as simultaneous, the timing in which contenders organize

and implement their internal rules need not necessarily be so. Indeed, there is no apriorireason to believe that before

the actual competition takes place, the timing in which the involved organizations decide upon their governing rules

coincides. Differences in the size or in the informational advantage of organizations, as well as the existence of some

established organizations challenged by an entrant, may result in the sequential determination of their governing

rules. Consequently, groups involvedin a simultaneous competition may well be deciding upon their internal rules in

a sequential fashion. Similar to previous literature, we find that if the order of movesis determined endogenously, the

equilibrium timing of the game is a sequential one, and this very fact constitutes a strong justification for departing

from the simultaneity assumption (Baik & Shogren, 1992; Leininger,1993; Morgan, 2003).2

In this paper, we contribute to the literature on collectivecontests by showing how different timings with respect

to groups'choice of sharing rules alter individual incentives and thus group performance. In our two-group model,

most of our results arise from the following observations. The small group's sharing rule is a strategic complement

to the large group's sharing rule in the sense that if the small group chooses a more meritocratic sharing rule, the

large group wishes to choose a more meritocratic rule as well, whereas the large group's sharing rule is a strategic

substitute for the small group's sharing rule.3When both groups are active, the large group acting as the leader

behaves in a similar manner as in a standard Stackelberg duopoly model. That is, the large group commits to a more

meritocratic sharing rule than in the simultaneous game (hence effort increases), whereas the small group selects a

less meritocratic rule than in the simultaneous game (hence effort decreases). On the contrary,the small group acting

as the leader follows a very different strategy. It commits to a less meritocratic rule than in the simultaneous game,

thereby weakening competition between groups. In turn, the large group also responds with a less meritocratic rule

than in the simultaneous game. The latter finding is reminiscent of the main result in Kolmar and Wagener (2013).

They consider a group contest and investigate whether groups have an incentiveto implement a costless mechanism

that solves a group's free-rider problem with respect to the group members'effort choices. Surprisingly, they find

that the weaker (e.g., smaller or less productive) group sometimes wishes to abstain from implementing the mecha-

nism. Adopting the mechanism may be problematic for the weaker group because the stronger group may react by

competing more aggressively,implying that the contest may escalate. The main difference between our paper and the

one by Kolmar and Wagener (2013) is the following. We assume that groups decide sequentially about their sharing

rules, whereas the groups in their paper decide simultaneously about the adoption of the mechanism. Furthermore,

by changing the sharing rule in our paper a group can affect the efforts of its members continuously; this is different

from the paper by Kolmar and Wagener (2013)in which the adoption of the mechanism leads to a discrete change in

efforts.

In contrast to the simultaneous timing (Balart, Flamand, & Troumpounis,2016), the small group never outperforms

the large one in terms of winning probabilities. In other words, Olson's (1965) celebrated group size paradox (GSP)

vanishes regardless of the leader's size. The exactnature of the prize is also key to group performance. Indeed, we show

thatwhen the prize is not private enough and the sharing rules allow for transfers, the sequential choice of sharing rules

leads to monopolization, a situation in which one group retires from the competition (Ueda, 2002). Interestingly, the

large group takes advantage of its leadership by preventing the small group from being active for a greater range of

privateness of the prize compared to the simultaneous case (Balart et al., 2016), thereby making monopolization more

likely.However, this is not true when it is the small group that moves first, as in this case monopolization occurs in the

same instances as in the simultaneous game.

Our results clearly have implications regarding aggregate effort expenditures. When the large group is the

leader, and provided that the prize is private enough so that both groups are active, total rent-seeking expendi-

tures increase with respect to the simultaneous case. Conversely, when the small group is the leader, and again

2Hoffmann and Rota-Graziosi (2012) consider a general two-playercontest model and they qualify previous results by showing that a sequential structure

does not always result if the order of moves is endogenized. Most importantly,they assume that the prize to be awarded in the contest may depend on the

chosenefforts. This assumption introduces an additional strategic effect, potentially leading to different results regarding the order of moves.

3Gal-Or (1985) is an early paper studying incentives and payoffs in sequential games. In a model with homogenous players,she already indicated that the

resultscrucially depend on whether reaction functions are upward or downward sloping.

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