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Intragroup competition in public good games: The role of relative
performance incentives and risk attitudes
Annarita Colasante
a
, Aurora García-Gallego
a
, Nikolaos Georgantzis
a,b
,
Andrea Morone
a, c
, Tiziana Temerario
c
a
LEE and Department of Economics, Universitat Jaume I, Castellón, Spain
b
Burgundy School of Business, School of Wine and Spirits Business, Dijon, France
c
Dipartimento di Economia, Management e Diritto d’impresa, Università degli Studi di Bari,
Aldo Moro, Italy
Abstract: We analyse a public good game with intragroup competition in which, generally but
not always, the dominant strategy is to not contribute and, therefore, free-riding is the unique
Nash equilibrium, not achieving Pareto efficiency.
We propose a public good game setup where
subjects’ contributions are rewarded with different individual returns following a rank order
voluntary contribution mechanism. It is found that the resulting competition for a better return
significantly increases contributions. This effect is sensitive to the salience of return differences
rewarding higher contributions. Furthermore, the positive effect of return differences on
contribution levels depends on an individual’s return-to-risk sensitivity as elicited through an
independent risk elicitation task.
Keywords: cooperation, public good game, intragroup competition, risk attitude.
JEL codes: D01, D71, H41
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1. Introduction
A public good game (PGG, hereafter) gives rise to a social dilemma insofar it leads to a
conflict between individual and collective incentives. Specifically, in the Nash
equilibrium, individuals may free ride by contributing nothing to the public good,
whereas it would be Pareto optimal if all individual resources were invested in the
public good. An important feature in the emergence of the social dilemma is that
individuals indistinctively access the public good irrespective of their contributions. On
the other extreme, if individuals are granted access to the public good in shares equal to
their participation to the common property, the social dilemma vanishes, provided that
the net return to individual participation is positive. Therefore, appropriation of the
return to one’s own investment eliminates the social dilemma. However, this makes the
essence of a public good disappear, trivially collapsing the context to one of a private
good. We study the intermediate case arising when heterogeneous individual shares of
the public resource, rather than proportional to individual contributions, depend on the
ranking of individual contributions. That is, respectively, higher, intermediate and lower
shares correspond to the highest, intermediate and lowest contributor.
An example in which contributors receive different shares from a public good can
be found in educational systems in which a basic level of the product or service is
shared by all users, while a higher willingness to pay for it gives access to better
education. Another example can be found in social security systems which let you
choose the level of the service, corresponding to different levels of contribution.
We analyse the role of intragroup competition in the sustainability of cooperation
in the context of a PGG. In the repeated PGG implemented, intragroup competition is
introduced by assigning different marginal per capita returns (MPCR, hereafter)
according to each member’s contribution. In particular, subjects in the same group are
ranked according to their contributions, so that all subjects receive a positive share of
the public good but the subject with the highest rank receives the larger share of it.
While, under certain parameterizations, this context preserves the social dilemma nature
of a PGG, our experimental results show that it provides an efficient incentive system
for individual contributions to rise significantly as compared to the standard symmetric-
returns version. As expected, the efficiency of this incentive system in raising individual
contributions is sensitive to the asymmetry of individual returns resulting from the
ranking of contributors. Therefore, this system is shown to be an important candidate
for real-life tax policy measures in which the degree of appropriation of the common
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resource according to the ranking of contributors to the system could constitute an
effective incentive for individuals to contribute more, without revealing the exact
individual contributions to the public good, and, thus, preserving anonymity.
Furthermore, we analyse whether subjects’ responsiveness to this incentive
scheme relates to their risk attitudes. Specifically, we obtain individual data from a risk
elicitation task and analyse whether taking higher risks in the presence of higher risk-
returns predicts higher contributions in the intragroup competitive PGG.
The paper is organized as follows. In Section 2 we briefly review some relevant
related literature. Section 3 motivates the research question and proposes the theoretical
prediction of the game. In Section 4 we explain in detail the experimental design and
state our main research questions. In Section 5 we elaborate the data analysis and show
the main results. Section 6 concludes. The subjects’ experimental instructions are in the
Appendix.
2. State of the art
Cooperation and its sustainability in a social dilemma is a central research question in
the economics research agenda. In the basic version of a PGG, it is individually more
profitable not to contribute and “free ride” on the public good generated by the
contributions of others.
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However, the socially desirable result (Pareto-efficient) in
which all individuals obtain the highest aggregate payoff, is achieved when all subjects
contribute.
Experimental research on repeated PGG has often shown that contributions start
from around 50% of the endowment, declining towards zero as later periods of the
session as reached. Dealing with the free-riding problem has given rise to alternative
strategies like allowing communication among subjects (Isaac and Walker, 1988),
introducing costly punishment (Fehr and Rockenbach, 2003; Fehr and Gatcher, 2000),
allowing for voluntary participation depending on the share of defectors (Semmann et
al., 2003), introducing proportional MPCR factors (Colasante and Russo, 2017; Lange
et al., 2007), and other methods of heterogeneous appropriation of the public good like a
lottery and an all-pay auction (Corazzini et al., 2010; Faravelli and Stanca, 2012).
Julian and Perry (1967) were the first to suggest competition (i.e. rivalry among
players) as a way of solving or at least mitigating the free-rider problem. However, as
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Such is the game-theoretic prediction since ‘not to contribute’ is a dominant strategy in the one-shot and
in the finitely repeated version of the game.
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Gunnthorsdottir and Rapoport (2006) suggest, the distinction of ‘between’ versus
‘within’ group competition is relevant. The literature shows good evidence of the
positive correlation between inter-group competition and cooperation, and this evidence
comes both from the lab (see, for example, Bornstein et al., 2002; Cárdenas and
Mantilla, 2015; Böhm and Rockenbach, 2013; and Markussen et al., 2014) as well as
from the field (Augenblick and Cunha, 2015; and Erev et al., 1993).
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Public good dilemmas with intergroup competition, have been analysed under the
framework of step-level PGG
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(see Rapoport and Bornstein, 1987). The inquiry on the
intergroup competition by using different social dilemma games leads to an important
result: competition is a powerful tool to foster cooperation. Bornstein and Ben-Yossef
(1994) analysed the effect of intergroup conflict in a prisoner’s dilemma game and
found out that cooperation is significantly higher when competition is introduced.
Bornstein et al. (2002) studied the effect of intergroup competition on behaviour in the
minimal-effort game
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and observed that intergroup competition improved collective
efficiency. In the context of a PGG, Tan and Bolle (2007) analysed the effect of
competition with and without monetary incentives and detected a stronger effect of
competition with monetary rewards. Furthermore, Puurtinen and Mappes (2009)
confirmed that competition fosters cooperation even in a simple one-shot game.
Interestingly, the contribution by Markussen et al. (2014) introduces the novelty that
subjects are asked to vote for competition. As a result, the majority of the subjects
showed a preference for competition, which led in turn to a higher level of cooperation.
While the positive effect of intergroup competition on cooperation has been
sufficiently documented, the effect of intragroup competition in enhancing cooperation
still remains rather unexplored. One of the first examples is Falkinger’s (1996)
mechanism for overcoming the free-rider problem, where deviation from the mean
contribution to the public good are taxed and subsidized, depending on the sign of the
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A very interesting theoretical approach deals with cooperation and aspects that are out of the scope of
the present work like the heterogeneity within the group in collective contests (Nitzan and Ueda, 2018),
the size of the group and the coordinated punishment (Hwang, 2017), or the group formation in
heterogeneous societies (Lind, 2017).
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“In step-level […] public goods a funding threshold has to be reached before the good can be provided.
[…] The step-level public good game differs strategically from the linear public good game. In the one-
shot linear public good game, the dominant strategy is not to contribute at all. In the one-shot step-level
public good game multiple Nash equilibria exist. An inefficient Nash equilibrium involves nobody
contributing. There are efficient Nash equilibria in pure strategies where three of the n players contribute
(i.e., there are exactly enough contributions to reach the threshold).” (Schram et al. 2008).
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The group with the higher minimum won the competition and its members were paid according to the
game’s pay-off matrix. The members of the losing group received a zero payoff.
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deviation. Later, Falkinger et al. (2000) conduct a large series of experiment in order to
examine the empirical properties of the mechanism, obtaining immediate and large
efficiency gains, and their result is robust throughout many different experimental
settings. A different type of intragroup competition is considered by Cabrera et al.
(2013), where subjects are endogenously allocated between a major and a minor league
according to their performance during the game. More recently, Angelovski et al.
(2017) test a provision mechanism which utilizes rank competition to mitigate free-
riding where groups compete via observable contributions for a larger share of the
public good. They provide evidence that rank competition enhances efficiency in
situations where discriminatory access to public goods is possible.
Our paper hopefully contributes to further explore intragroup competition in the
context of a PGG, focusing on the size of a subject’s ranking-dependent returns from
the public good and the role of subjects’ risk attitudes on their sensitivity to the
incentive scheme.
3. Theoretical framework
We analyse a PGG with intragroup competition in which, under some
parameterizations, the dominant strategy is to not contribute and, therefore, free-riding
is the unique Nash equilibrium (NE), which diverges from the Pareto efficient outcome.
Alternatively, under other parameterizations, the social dilemma disappears and the NE
with full contribution of individual resources is Pareto efficient.
In order to address our research questions, we implement a standard PGG, where
subjects are compensated with a higher individual marginal return if their contribution
ranks them higher within their group. We consider three different MPCR values (
α
H
,
α
M
and
α
L
) which are endogenously assigned according to subject’s ranking relative to their
levels of contribution. Levels
α
H
,
α
M
, and
α
L
correspond, respectively, to the individual
maximal, average and minimal value of the public good return. In other words, the
subject with the highest contribution will receive the highest individual marginal return,
the intermediately ranked contributor will receive the intermediate return and the lowest
contribution will receive the lowest return.
Consider the resulting generalized PGG. The payoff of individual i in one period
is expressed as:
