Roles of mutation rate and co-existence of multiple strategy updating rules in evolutionary prisoner's dilemma games

Abstract

The emergence and maintenance of cooperation has attracted intensive scholarly interest and has been analysed within the framework of evolutionary game theory. The role of innovation, which introduces novel strategies into the population, is a relatively understudied aspect of evolutionary game theory. Here, we investigate the effects of two sources of innovation---mutation and heterogeneous updating rules. These mechanisms allow agents to adopt strategies that do not rely on the imitation of other individuals. The model introduces---in addition to canonical imitation-based strategy updating---aspiration-based updating, whereby agents switch their strategy by referring solely to the performance of their own strategy; mutation also introduces novel strategies into the population. Our simulation results show that the introduction of aspiration-based rules into a population of imitators leads to the deterioration of cooperation. In addition, mutation, in combination with heterogeneous updating rules, also diminishes cooperators. This phenomenon is prominent when a large proportion of the population consists of imitators rather than adopters of aspiration-based updating. Nevertheless, a high mutation rate, in combination with a low aspiration level, has positive nonlinear effects, and a heterogeneous population achieves a higher level of cooperation than the weighted average of homogeneous populations. Our results demonstrate the profound role of innovation in the evolution of cooperation.