Asymmetric enforcement of cooperation in a social dilemma.

• Author: Nikiforakis, Nikos

[I]f only a few very powerful actors want to promote a certain pattern of behavior, their punishments alone can often be sufficient to establish it, even if the others are not vengeful against defections. (Axelrod 1997; p. 63)

1. Introduction

   A number of daily decisions involve making a choice between the private and the public interest. In these cases, following the private interest reduces efficiency and imposes a negative externality on others. A common way of dealing with negative externalities is the imposition of sanctions on parties that deviate from a widely accepted norm of behavior (Ostrom 1990). Given that the purpose of such sanctions is to lower the return from acting against the social interest, the efficacy of sanctions in enforcing cooperation will depend critically on the punishment power of the sanctioning party. The greater the power of the party abiding to a given norm, the less appealing a deviation from that norm will be for other parties.

   In this article, we present the results from a laboratory experiment investigating the efficacy of decentralized sanctions in fostering cooperation when negative externalities exist and players are asymmetric in their punishment effectiveness. The use of a laboratory experiment permits us to control a number of factors in a way that is difficult to do in the field (e.g. endowments, returns to cooperation, information), and focus on variables of interest, such as the players' punishment power and the extent of the asymmetry in their power.

   To the best of our knowledge, this is the first study to investigate behavior in asymmetric punishment institutions. However, numerous social dilemma experiments have been conducted in which players have the same punishment power (see below). Our goal is to examine how the asymmetry in the players' punishment power affects cooperation rates and efficiency, as well as how behavioral regularities observed in symmetric institutions, such as the determinants of punishment, carry over to asymmetric institutions.

   For our study, we use the two-stage public-good game that was introduced by Fehr and Gachter (2002). In the first stage, each individual is given an endowment in experimental currency units (ECUs). Individuals have to decide how much of their endowment they want to contribute to a public account. The higher the contributions to the public account, the higher the group earnings. However, every individual has also an incentive to free ride and not contribute. In the second stage, individuals are informed of each group member's contribution to the public account and can reduce their earnings by assigning costly punishment points. Each punishment point costs the punisher one ECU and reduces the earnings of the punishment recipient by a factor larger than one. We refer to this factor as punishment effectiveness and use the term interchangeably with punishment and sanctioning power.

   To evaluate the effect of asymmetries in the players' punishment effectiveness, we compare behavior in symmetric and asymmetric punishment institutions. In the symmetric case, as studied in previous articles, group members are given the same punishment effectiveness. That is, they are all equally effective in punishing each other. By contrast, in asymmetric punishment institutions, players differ in their punishment effectiveness: One player has higher punishment effectiveness than the other three players, who all have the same power. To ensure the robustness of our findings, we examined behavior in two symmetric institutions that differ in the players' average punishment effectiveness and four asymmetric punishment institutions. The asymmetric institutions differ in the extent of the asymmetry between strong and weak players.

   Experimental economists have repeatedly used the two-stage public-good game to analyze the resolution of the tension between social good and self interest in symmetric punishment institutions (Fehr and Gachter 2000, 2002; Masclet et al. 2003; Noussair and Tucker 2005; Page, Putterman, and Unel 2005; Anderson and Putterman 2006; Bochet, Page, and Putterman 2006; Carpenter 2007a, b; Carpenter and Matthews 2009; Sefton, Shupp, and Walker 2007; Egas and Riedl 2008; Nikiforakis and Normann 2008; Nikiforakis, forthcoming). The two main goals of this literature have been to understand what triggers punishment and whether the threat of punishment can promote cooperation.

   With respect to the motivation behind punishment, the experimental results show that individuals tend to punish those who free ride by contributing less than the group average even in one-shot interactions (e.g., Fehr and Gachter 2002). This suggests that punishment does not serve the exclusive purpose of increasing one's earnings by raising future contributions to the public account (Falk, Fehr, and Fischbacher 2005). However, despite the non-strategic use of sanctions, punishment is sensitive to economic incentives. Anderson and Putterman (2006), Carpenter (2007a), Egas and Riedl (2008), and Nikiforakis and Normann (2008) find that the higher the cost of punishment (which is the inverse of punishment effectiveness), the less the punishment is inflicted on free riders and the disciplinary power of decentralized punishment. (1)

   With respect to the efficacy of punishment in fostering cooperation, the evidence shows that when individuals interact repeatedly with the same people throughout the experiment (fixed matching), decentralized punishment leads to high cooperation rates as free riders react to punishment by raising their contribution in subsequent periods. When individuals interact with different people in every period (random matching), cooperation rates are higher than they are in the absence of a punishment institution, but lower than under fixed matching. However, the efficacy of punishment depends critically on its effectiveness. Nikiforakis and Normann (2008) find a monotonic relation between punishment effectiveness, cooperation rates, and efficiency. Unless punishment is sufficiently effective, cooperation unravels. (2)

   The main reason for studying behavior in asymmetric punishment institutions is the empirical relevance of such institutions. In most naturally occurring situations, asymmetric players are the norm rather than the exception. (3) Individuals differ in their physical ability to enforce cooperation just as countries differ in their military budgets and technology. Given the documented willingness to punish free riders even in one-shot interactions and the efficacy of symmetric punishment institutions in promoting cooperation, we believe it is interesting to investigate whether asymmetric institutions are as effective in mitigating free riding.

   Another reason for studying the performance of asymmetric punishment institutions is that it seems challenging to predict the effect these asymmetries will have on cooperation. This is because, for our setting, arguments can be made in either direction. On the one hand, an asymmetric institution might have a positive effect on cooperation. First, experimental evidence suggests that higher punishment effectiveness increases the demand for punishment (Anderson and Putterman 2006; Carpenter 2007a; Egas and Riedl 2008; Nikiforakis and Normann 2008). The high punishment effectiveness of strong players suggests that they might be able to unilaterally enforce cooperation. In contrast, in a symmetric punishment institution, more than one individual might be required to discipline free riders (controlling for average punishment effectiveness). This is essentially the reason Axelrod (1997) argues that a "dominant power" will have a positive effect on cooperation. Second, punishment of free riders is (partly) a public good: All group members benefit from the increase in cooperation because of punishment, but all have an incentive to let others carry the cost of punishment. (4) By giving more power to one player, the free rider problem at the punishment stage might be alleviated. Similarly, endowing a single player with more punishment power provides a natural focal point and might help alleviate any coordination problems in punishment.

   On the other hand, the asymmetric nature of the institution might affect cooperation negatively. This can happen through two different channels. First, strong players face a reduced threat relative to players in symmetric institutions because we control for average punishment effectiveness in our experiments. Therefore, they will be more likely to free ride, ceteris paribus, if they are self-regarding. In turn, this jeopardizes the cooperative performance of the whole group because their behavior is likely to be imitated by reciprocal group members (Fischbacher, Gachter, and Fehr 2001). Second, the reliance on fewer individuals to enforce cooperation (or, in our case, the reliance on a single strong player) might make cooperation more fragile compared with a symmetric situation in that the outcome depends on the preferences of the strong player who might not wish to enforce cooperation.

   The effect of asymmetries in public-good games has been studied previously almost exclusively in the absence of punishment opportunities. In general, there seems to be no consensus about the effect of asymmetries on cooperation (see Varughese and Ostrom 2001; Anderson, Mellor, and Milyo 2008). Isaac, McCue, and Plott (1985) were the first to study behavior in a public-good game when agents have asymmetric endowments from which to contribute. The authors argue that the asymmetric environment gives the game-theoretic prediction of zero contributions to the public account its best chance. Cherry, Kroll, and Shogren (2005) provide evidence supporting this conjecture by comparing treatments with symmetric and asymmetric endowments. Another study finding evidence that asymmetries have a negative effect on cooperation is Anderson, Mellor, and Milyo (2008), who examine a public-good game...