Sustaining cooperation in social dilemmas: Comparison of centralized punishment institutions

From the vast amount of research on the public goods game experiment, it became a shared wisdom that a costly punishment of one to others is an effective mechanism to reduce free riders.1 In earlier works of Yamagishi (1986, 1988), a Novel prized work of Ostrom, Walker and Gardner (1992), and seminal works of Fehr and Gächter (2000, 2002), a drastic increase in the average contribution to the public goods is observed with an introduction of a punishment stage after a voluntary provision to public goods where each individual can reduce the payoff of others at his own cost. This observation in the decentralized punishment institution is replicated by several authors with several modifications and we are now in the place to “apply the lesson learned to ‘field’ setting in decentralized institution that deal with social dilemma.” (Chaudhuri 2010) Despite the possible applications including charitable contribution, managing natural resources, labor relations, there exist many fields where the application of the decentralized punishment institution is not valid. One major example is a criminal offense. Also, when participants are in the competitive relationship, this is in problematic (e.g., international relations, regulations of firm’s emission of carbon dioxide, and so on). In addition, there is a finding that when there is a possibility for counterpunishment, cooperators are less willing to punish, resulting in low contribution in the provision stage (Nikiforakis 2008). This implies that even in the decentralized punishment institution, the role of an individual who is entitled not to be punished, like a police officer, is important. Therefore, the importance of the centralized punishment institution should be also emphasized. We can go back to Becker (1968) on economic analyses of crime and penalty when we consider a centralized punishment institution (for a survey, see Polinsky and Shavell 2000). In Becker’s analyses, a potential offender compares the benefit from criminal act with the expected loss–the conviction probability multiplied by the disutility of punishment (fine, imprison, exclusion, etc.). If the former dominates the latter, he commits a crime. In the context of public goods game, a free-rider decides to free-ride when the gain from free-riding is greater than the expected amount of punishment. A difference between the analysis of crime by Becker (1968) and public goods game is that the latter is formulated as a strategic game so that the payoff of an individual depends not only on his own decision but also on the decision of others. This paper investigates the centralized institutions that punish the free-rider in the public goods game. Following the convention of the institutional analysis of economic regulation, the centralized institutions involve two factors: a required level of performance and a fine. An individual whose contribution does not meet the requirement pays a fine. Therefore, all the individuals who violate the “rule”