The second-order probabilistic pool punishment proportional to the payoff difference can solve the punishment problem of previous studies

Abstract

The public goods game is one of the models utilized in theoretical studies of social dilemmas where the pursuit of individual interests does not benefit society as a whole. In the context of the public goods game, the optimal response of participants is defecting (not investing in the public goods). Therefore, the evolution of cooperation in the public goods game generally requires punishment or reward. Out of these two elements, this study deals with punishment. There are two types of punishment: peer punishment and pool punishment. The problem of peer punishment is the high cost of punishment, and the problem of pool punishment is that the cost of punishment is always incurred. Here, extending the previously proposed probabilistic pool punishment, we consider the punishment on cooperators (second-order free riders) as well as defectors. Comparing the pool punishment of this study with pool and peer punishment of existing studies, especially in terms of the average payoff, it is superior to those previous punishment mechanisms. In addition, the various programming techniques in the construction of the simulator in this study are expected to be utilized as teaching materials for specialized education at Kanagawa Institute of Technology.