Evolution of cooperation with peer punishment under prospect theory

Social dilemmas are among the most puzzling issues in the biological and social sciences. Extensive theoretical efforts have been made in various realms such as economics, biology, mathematics, and even physics to figure out solution mechanisms to the dilemma in recent decades. Although punishment is thought to be a key mechanism, evolutionary game theory has revealed that the simplest form of punishment called peer punishment is useless to solve the dilemma, since peer punishment itself is costly. In the literature, more complex types of punishment, such as pool punishment or institutional punishment, have been exploited as effective mechanisms. So far, mechanisms that enable peer punishment to function as a solution to the social dilemma remain unclear. In this paper, we propose a theoretical way for peer punishment to work as a solution mechanism for the dilemma by incorporating prospect theory into evolutionary game theory. Prospect theory models human beings as agents that estimate small probabilities and loss of profit as greater than they actually are; thus, those agents feel that punishments are more frequent and harsher than they really are. We show that this kind of cognitive distortion makes players decide to cooperate to avoid being punished and that the cooperative state achieved by this mechanism is globally stable as well as evolutionarily stable in a wide range of parameter values.