O estabelecimento da cooperação no contexto das estratégias reativas

Abstract

Individuals in nature exhibit cooperative behavior. The so called Prisoner's dilemma is a game which is widely used to model this phenomenon. Players in this game have two options: cooperation (C) or desertion (D). If there is only one round, deserting is the best option. But once the individuals meet each other several times, cooperative behavior can emerge. Being p and q the probabilities of cooperating given that the opponent had cooperated and deserted in the last encounter, respectively, an infinity number of strategies is available. The time evolution of the fractions of individuals playing a given strategy is governed by the replicator equation. Since we have distinct versions for this equation and different ways to solve it (using continuous or discrete time approaches) we can obtain discordant outcomes. In this work, it is shown that the usual results which are presented in literature (Generous-tit-for-tat's victory) is found only within some specific conditions. The results were conformed by using an analytical argument related to Nash equilibrium calculations. In order to investigate the establishment of cooperation, the numerical solutions were obtained by using both discrete and continuous versions of the replicator equation (Taylor's and Maynard Smith's). Basically cooperation is able to survive whether the density of strategies is not too large.