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