Aspiration-based learning promotes cooperation in spatial prisoner's dilemma games

¹ School of Electronic and Control Engineering, Chang'an University Xi'an 710064, China
² Center for Road Traffic Intelligent Detection and Equipment Engineering, Chang'an University Xi'an 710064, China
³ Evolution and Ecology Program, International Institute for Applied Systems Analysis (IIASA) Schlossplatz 1, 2361 Laxenbury, Austria, EU
⁴ Center for Systems and Control, State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University - Beijing 100871, China

^a yongkuiliu@163.com
^b chenx@iiasa.ac.at

Received: 17 January 2011
Accepted: 7 May 2011

Abstract

We study the evolution of cooperation in spatial prisoner's dilemma by proposing an aspiration-based preference learning, under which individuals switch the learning agents only if the achieved payoffs are lower than their aspirations. Both synchronous and asynchronous updates are considered. We find that the aspiration level can substantially influence the evolution of cooperation, with the moderate aspiration level leading to a plateau of the high cooperation level. There exist phase transitions for proper combinations of parameters and we give an analysis for the phase transition points. We also investigate the stationary configuration patterns and the stationary distributions of cooperators and defectors on the square lattice for a comprehensive understanding. The behavior of the well-mixed system of our model has also been discussed. Our results may provide further insights into understanding the role played by individual aspiration in the emergence of cooperation.