Selective incentives and intragroup heterogeneity in collective contests

• Author: Shmuel Nitzan,Kaoru Ueda
• Published date: 01 August 2018
• DOI: http://doi.org/10.1111/jpet.12290
• Date: 01 August 2018

Received: 23 July 2017 Accepted: 16 January 2018

DOI: 10.1111/jpet.12290

ARTICLE

Selective incentives and intragroup heterogeneity

in collective contests

Shmuel Nitzan1Kaoru Ueda2

1Departmentof Economics, Bar Ilan University,

Israeland Hitotsubashi Institute of Advanced

Study,Hitotsubashi University

2Facultyof Economics, Nanzan University

ShmuelNitzan, Department of Economics, Bar

IlanUniversity, Ramat Gan, 52900 Israel and

HitotsubashiInstitute of Advanced Study, Hitot-

subashiUniversity, 186-8601 Tokyo,Kunitachi,

Naka,Japan (nitzans@mail.biu.ac.il). Kaoru Ueda,

Facultyof Economics, Nanzan University, Nagoya,

Aichi466-0824, Japan (k-ueda@nanzan-u.ac.jp)

Theauthors are indebted to three anonymous ref-

ereesfor their useful comments and suggestions.

Uedaacknowledges the financial support of JSPS

KAKENHIGrant Number JP17K03781.

A group taking part in a contest has to confront the collective action

problem among its members, and devices of selective incentives are

possible means of resolution. We argue that heterogeneous prize-

valuations in a competing group normally prevent effective use of

such selective incentives. Tosubstantiate this claim, we adopt cost-

sharing as a means of incentivizing the individual group members.

Weconfirm that homogeneous prize valuations within a group result

in a cost-sharing rule inducing the first-best individual contributions.

As long as the cost-sharing rule is dependent only on the members’

contributions, however, such a first-best rule does not exist for a

group with intragroup heterogeneity. Our main result clarifies how

unequal prize valuations affect the cost-sharing rule and, in partic-

ular, the degree of cost-sharing. If the relative rateof change of the

marginal effort costs is decreasing, it is reduced by intragroup het-

erogeneity.If the rate is increasing, the cost is fully shared, but it can-

not induce the first-best contributions for the group.

1INTRODUCTION

In a collective contest the contestants for a prize are groups. Applications of such contests include confrontations

between labor unions and the employers, ethnic or religious conflicts, military conflict between countries or allies of

countries, promotional competitions by firms with marketing activities, a championship by sports teams, competition

among academic institutes on quality-based recognition or on financial support, and so on.1This paper examines how

heterogeneity of individuals in a group affects the incentive device in such a contest.

Usually a group contains various individuals situated at different positions, politically,economically, and sometimes

ethnically or culturally. Such heterogeneity could prevent them from reaching a consensus on the value of the con-

tested prize, and they naturally havedifferent prize valuations. Their contributions to the contest are diversified then,

which could be inefficient for the group as a whole. Intragroup heterogeneity of competing groups is not an old topic in

the literature of collectivecontests. Baik (2008) examines a model of collective contests for group-specific public-good

prize, assuming linear cost functions, that is, constant marginal costs. Esteban and Ray (2011) study a model of ethnic

conflict with two parameters of intragroup heterogeneity: ethnic radicalism and income. Epstein and Mealem (2009)

and Ryvkin (2011) examine how the composition of individuals in competing groups affects the equilibrium effort

1Formore examples of contests in general, see Konrad (2009). On the basic theory of contests, see Hillman and Riley (1989) and Cornes and Hartley (2005).

Journal of Public Economic Theory.2018;20:477–498. wileyonlinelibrary.com/journal/jpet c

2018 Wiley Periodicals,Inc. 477

478 NITZAN AND UEDA

levels. Nitzan and Ueda (2013) clarify how the form of effort cost functions determines the relation between intra-

group heterogeneity and the equilibrium group effort. Most of the existing literature, however,ignores the possibility

that a competing group introduces an incentive device.

When individuals win or lose the prize as a group, they work as a team sharing a common aim. In such a situa-

tion, the individuals are usually tempted to be free-riders while considering contribution to the teamwork to enhance

the group winning probability.This tendency results in a representative collective action problem, as argued by Olson

(1965,1982).2Collective contests could be viewed as a number of intragroup collective action problems embedded in a

competitive environment. Olson argues that the collectiveaction problem can be amended by “selective incentives,”—

incentives applied selectively to individuals depending on their actions.3In the literature on collective contests, such

an incentive device has been incorporated into the model typically as a prize-sharing rule of a group, which prescribes

how much of the won prize is distributed according to the contributions by the group members.4Choosing an ade-

quate prize-sharing rule prior to the contest, individuals in a group could be effectively motivated to overcome the

free-rider problem. Nitzan and Ueda (2011) consider such a model of a collective contest in which the prize-sharing

rule in each group is endogenously determined to maximize the utilitarian group welfare (i.e., the sum of the expected

utility of the group members), and derive the result that every group can realize the collectivelyoptimal contributions

by its members in a consistent way with the group's objective. The individuals in a group are, however,assumed to be

homogeneous; they havethe same valuation of the prize and the form of their effort cost function is also the same.

Groupsin a real world are characterized by intragroup heterogeneity, to a great or small extent. When competing for

a prize, they face at least two sources of inefficiency,free riding and individual heterogeneity. The selective incentive

devices chosen by the groups must cope with these sources of inefficiency. To make the effect of intragroup hetero-

geneity explicit is therefore important to understand the properties of the appropriate selective incentive devices to

be adopted in collective contests. Forthis purpose, we use a modified model of Nitzan and Ueda (2011) containing two

new important features.

The first is, of course, the existence of intragroup heterogeneity.Unfortunately, however,it is not easy to analyze a

model of prize-sharing with intragroup heterogeneity and, in particular,to characterize the equilibrium prize-sharing

rules. It is especially so when the effort cost of an individual is nonlinear, and such nonlinearity is essential to get

general insights on the collective-contest problem.5Therefore, a second new feature is introduced; instead of prize-

sharing rules, our model assumes that the competing groups use cost-sharing rules as a means of selective incentives.

It has been recently pointed out by Vázquez (2017) that commitment to a transfer rule of the costs among individual

group members can work as a substitute for a prize-sharing rule. Actually,once we notice that cost-sharing makes the

resources of the individuals in a group a common pool resource, it is not surprising that such a device enhances their

activity levels. In general,transfer schemes within a group depending on the sacrifice to enhance the common interest

can work as selective incentives. An individual who contributes more can shift more cost to the others relative to the

2As similar concepts to free-riding, we could count shirking and social loafing (Kidwell and Bennett, 1993). The former is a term used in the context of the

economics of organization, and the latter is mainly used in studies of social psychology.All three concepts concern individuals withholding effort in a group.

Suchoverlapping of concepts in the different areas stresses the substantial role played by the free riding problem in determining the performance of a group.

3Olson's severalconjectures on the collective action problems are neatly arranged and evaluated by Sandler (1992). For two recent surveys on the develop-

mentof research on collective action problems, see Pecorino (2015) and Sandler (2015).

4The idea of a prize-sharing rule is introduced to the research on collective contests by Nitzan (1991). Baik (1994), S. Lee (1995), and Ueda (2002) develop

modelsin which the prize sharing rule is endogenously determined by each of the competing groups. It should be noted that higher selective incentives are not

necessarilybetter for a group. When the members are rewarded for their effort, each member's effort has a negative externality for the others because their

sharesare cut. The result might be an excessive group effort. See Sen (1966).

5Severalimpressive results derived from contest models with linear effort costs are not necessarily preserved under non-linear cost functions. For example,

Estebana nd Ray(2001) reveal that collective contests for a pure private-good prize with linear effort cost functions belong to a special case where the group

size paradoxis always obtained, that is, a smaller group attains a higher win probability. They prove that the paradoxis overturned if the elasticity of marginal

effortcosts is large. Another puzzling possibility is that an individual with a higher prize valuation can get a lower expected payoff in a group (it could be called a

strongversion of the “exploitation of the great by the small”). This is a normal case in contests with linear effort costs, unless the largest value of the valuations

is very prominent. The reason is, as shown by Baik (2008), that in this case only individuals with the largest valuation of the prize in a group put effort,and

all the other group members become pure free riders (see also D.Lee [2012] for interesting related results). But Nitzan and Ueda (2013) point out that such

exploitation is impossible if the elasticity of marginal effort costs is large. We will present another exampleof the peculiarity of the model with linear cost

functionsin Section 5.2. These examples imply that we should be careful regarding the robustness of the results obtained under linear costs.