Cooperation guided by the coexistence of imitation dynamics and aspiration dynamics in structured populations

¹ School of Physics, Peking University - Beijing 100871, China
² Center for Systems and Control, College of Engineering, Peking University - Beijing 100871, China
³ Center for Intelligent and Networked Systems, Department of Automation and TNList, Tsinghua University Beijing 100084, China

^(a) longwang@pku.edu.cn

Received: 5 January 2017
Accepted: 27 March 2017

Abstract

In the framework of the evolutionary game theory, two fundamentally different mechanisms, the imitation process and the aspiration-driven dynamics, can be adopted by players to update their strategies. In the former case, individuals imitate the strategy of a more successful peer, while in the latter case individuals change their strategies based on a comparison of payoffs they collect in the game to their own aspiration levels. Here we explore how cooperation evolves for the coexistence of these two dynamics. Intriguingly, cooperation reaches its lowest level when a certain moderate fraction of individuals pick aspiration-level–driven rule while the others choose pairwise comparison rule. Furthermore, when individuals can adjust their update rules besides their strategies, either imitation dynamics or aspiration-driven dynamics will finally take over the entire population, and the stationary cooperation level is determined by the outcome of competition between these two dynamics. We find that appropriate synergetic effects and moderate aspiration level boost the fixation probability of aspiration-driven dynamics most effectively. Our work may be helpful in understanding the cooperative behavior induced by the coexistence of imitation dynamics and aspiration dynamics in the society.