Evolution of cooperation under the coexistence of imitation and aspiration dynamics in structured populations

Abstract

Imitation and aspiration learning rules are frequently observed in humans and animals. The former is an act of copying other’s action, whereas the latter is characterized by the self-evaluation. Here we study the coexistence of these learning mechanisms in structured populations. Both rules have been combined focusing on two different scenarios: (I) adoption of either update rule with a certain probability, and (II) grouping the entire population according to the update rules. We present two pair approximation models, illustrating both scenarios, which yield a nice agreement—under weak selection—with that of agent-based simulations. For weak selection and large population size, we find that the condition for cooperation to dominate defection is similar in both heterogeneous and homogeneous update rules. We examine several variants of the mixed model such as time-evolving aspirations alongside strategies and the coevolution of strategies and update rules. In the former case, our simulation reveals that Prisoner’s dilemma and, in some cases, Stag-hunt experience overall less aspiration levels compared to other games such as Chicken or Trivial. The coevolution of strategies and update rules demonstrates a better cooperation, in contrast to the fixed update rule case, exhibiting the possibility of asymptotic coexistence of both learning mechanisms.