Abstract
We experimentally study ways in which social preferences affect individual and group performance under indefinitely repeated relative incentives. We also identify the mediating role that communication and leadership play in generating these effects. We find other-regarding individuals tend to depress efforts by 15% on average. However, selfish individuals are nearly three times more likely to lead players to coordinate on minimal efforts when communication is possible. Hence, the other-regarding composition of a group has complex consequences for organizational performance.
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Notes
There is a fairly large experimental literature on collusion, mostly focused on exploring the effect of monitoring (see e.g. Aoyagi and Fréchette 2009; Duffy and Ochs 2009) and strategic uncertainty (see e.g. Blonski (2004)). Our focus is on the role of group composition in terms of social preferences on cooperation. For an updated survey on cooperation in infinitely repeated games see Dal Bó and Fréchette (2014).
Fisman et al. (2007) uses a slightly different nomenclature to describe distributional preferences. They call preferences for giving the fundamentals that rule the trade-off between individual and others’ payoffs and social preferences the ones that govern the allocation between others. Our study does not focus on that distinction; therefore we employ the following terminology: We use “social preferences” or “other regarding concerns” interchangeably to represent non-selfish behavior.
Since we randomly allocate subjects in the second stage, we do not guarantee an equal distribution of possible treatments. In particular, ex-post we find fewer subjects are Selfish, which results in fewer groups dominated by Selfish subjects. Thus, in Section 1.1 of the online appendix we loosen our definition of Selfish to obtain more balance between treatments, and find results consistent with our original results.
We note also that since the relative performance stage game is played after the dictator game, it is possible that the dictator game could influence choices in the relative performance stage. However, since we are measuring the relative effort choices of Selfish and Other-Regarding players, for this potentially to be a problem it is this relative difference that must be influenced.
Although subjects were not told to do so, almost all entered effort choices as an integer. We had an effort lower bound of 1 to create an upper bound for payoffs. The effort upper bound of 12 came from the periodic endowment of $12.
Note that this is mathematically the same as a Tullock contest played by risk-neutral individuals. That is, the principal has a total pool of 45 Berkeley Bucks to distribute across workers based on their relative performance.
A copy of the instructions given to subjects is available in the online appendix.
While paying for all rounds is consistent with our intended framework of an indefinitely repeated workplace interaction, it is also in line with standard practice in the experimental literature on infinitely repeated games, see e.g. Dal Bó and Fréchette (2014) or Sherstyuk et al. (2013). Furthermore, Sherstyuk et al. (2013) find that cooperation rates in a standard prisoner’s dilemma are not significantly different when paying subjects cumulatively for all periods or paying for the last period only. Paying a random period, on the other hand, leads to lower cooperation rates and thus is consistent with random payment inducing a present bias.
From now on we use the capitalized form of selfish and other-regarding to refer to our categorization.
This assumption only serves to normalize the utility of an Other-Regarding subject to be comparable to a Selfish subject. Assuming weights adding up to an arbitrary number does not entail a qualitative change in the results of this section as long as the other assumptions hold.
This also implies that \(\rho _{s}>1/2,\) which is consistent with the results in Fisman et al. (2007, Figure 6) where the average “giving” parameter is above 1/2 in three person matchings.
A theoretical model that more closely relates to our experimental design is an indefinitely repeated game with incomplete information—because social preferences are private information. Such models, however, have received little attention arguably because of the technical challenge of tracking the evolution of beliefs over time (Bonatti et al. forthcoming). Players may have incentives to manipulate others’ beliefs (e.g., build a reputation) in addition to the incentives to sustain mutually beneficial outcomes through the threat of punishment (Forges 1992; Aumann et al. 1968). Although results for the particular type of competition in the paper do not exist, the extant literature on oligopoly competition with privately known costs shows that first-best collusion can be exactly achieved given sufficiently little discounting (see, e.g., Athey and Bagwell 2008). With cheap talk communication, any payoff profile lying in the Pareto frontier that dominates an appropriately defined minmax value can be approximately attained in a perfect Bayesian equilibrium provided players are sufficiently patient (Escobar and Toikka 2013). In other words, with communication it is possible to have coordination on the Pareto-optimal outcome even with incomplete information.
In principle, coordination can also occur on efforts different from (1, 1, 1). For example, for a group with one Selfish and two very Other-Regarding subjects (\(\rho _{s}\) close to 0.5) the joint utility maximizing outcome is for the Selfish individual to put in an effort slightly larger than 1. We focus on (1, 1, 1) as it is (a) joint profit-maximizing, (b) a Pareto-optimal outcome from the players’ perspective but the worst outcome from the principal’s point of view, (c) arguably very salient. Furthermore, this is also the most prevalent “collusive outcome” observed in our data.
Note that in the group with 1 Selfish, if the two Other-Regarding subjects’ weights on own payoff are close to 0.5, coordination is not an equilibrium even with a continuation probability of 95%.
To see this, note that \(u_{i}\) of an Other-Regarding subject can be written as \(u_{i}=\left(\rho _{s}x_{i}+\rho _{o} \sum _{j\ne i}x_{j}\right)\left(\frac{W}{\sum _{j}x_{j}}-1\right)\) and the utility of a Selfish subject k as \(u_{k}=x_{k}\left(\frac{W}{\sum _{j}x_{j}}-1\right).\) Writing the utility this way is useful because the term on the right is the same across subject types. Thus, comparing \(P_{Ns}^{o}\) and \(P_{Ns}^{s}\) is equivalent to comparing \((\rho _{s}x_{i}+\rho _{o}\sum _{j\ne i}x_{j})\) and \(x_{k}\) in the same group. The result follows from the fact that the effort of an Other-Regarding subject \(x_{i}\) is less than \(x_{k}\), one of the \(x_{j}\) is equal to \(x_{k}\), and Assumption 1. The analytical expressions are in the online appendix.
See the online appendix for examples of group giving and effort choices.
This is consistent with Erkal et al. (2011) in that selfish individuals tend to exert higher levels of effort in tournaments.
Throughout the paper when using a random effects regression, we cluster at the group level. Results are qualitatively unchanged when clustering at the individual level.
We also conduct regressions where the effect of the number of other Selfish may depend on one’s own social preference type as the theoretical model predicts. We did not find that this is the case and thus present the simpler specification here.
We initially collected two other categories of leadership. A “Failed Leader” to denote a subject that called on his group members to decrease efforts but was not listened to/followed. This is a rare event in our study and thus we do not include this variable in our analysis. We also considered a “First Leader,” which was the first subject to propose coordination of efforts. However, this latter category has little explanatory power and so we omit it from our analysis.
We also had both a research assistant from Erasmus University Rotterdam and from Northwestern University independently code the leadership variables. The instructions given to the RAs are provided in the online appendix. The correlations between the alternative leadership dummies and the ones we use in the paper are for Northwestern: 0.88 for whether a Min-Effort Leader exists (on a period/group level) and 0.82 for the subject being a Min-Effort Leader (subject level); and for Rotterdam 0.52 for whether a Min-Effort Leader exists and 0.56 for the subject being a Min-Effort Leader. For both of these classifications, we find similar results in our following analysis.
We note that we do not observe the other possible homogenous group of only Selfish members. Thus our comparison for homogeneous is for those groups only containing Other-Regarding members. We suspect that in practice this unobserved group in our experiment is a rarely occurring group.
Analyzing the chat messages reveals two reasons for the occurrence of this coordinated strategy. Some groups were of the opinion that this was in fact the profit maximizing strategy to take. For other groups taking turns on choosing maximal effort was used to “make things even” after one subject deviated from the collusive outcome of (1, 1, 1).
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Acknowledgements
We would like to thank participants of seminars and conferences in Norwich, Rotterdam, Mannheim, Munich, Trier, Fresno, Budapest, Chicago, Zurich, Amsterdam as well as Juan Atal, Ernesto Dal Bó, Josse Delfgaauw, Robert Dur, Dirk Engelmann, Sacha Kapoor, Martin Kolmar, John Morgan, Felix Vardy, Bauke Visser and two anonymous referees. The authors thank the UC Berkeley Xlab (protocol 2011-04-3183) for financial support. Dana Sisak gratefully acknowledges the financial support of the Swiss National Science Foundation through Grant PBSGP1-130765.
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Hernandez-Lagos, P., Minor, D. & Sisak, D. Do people who care about others cooperate more? Experimental evidence from relative incentive pay. Exp Econ 20, 809–835 (2017). https://doi.org/10.1007/s10683-017-9512-9
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DOI: https://doi.org/10.1007/s10683-017-9512-9