Effects of cost threshold and noise in spatial snowdrift games with fixed multi-person interactions

¹  State Key Laboratory for Turbulence and Complex Systems, Center for Systems and Control, College of Engineering, Peking University - Beijing 100871, China
²  Department of Zoology, University of British Columbia - Vancouver BC V6T 1Z4, Canada

Corresponding authors: xjchen@pku.edu.cn longwang@pku.edu.cn

Received: 30 August 2009
Accepted: 20 April 2010

Abstract

Most previous studies assume that each individual who chooses to cooperate can always afford the cost in multi-person snowdrift games, no matter how much the cost is. However, in real situations each cooperative individual can only afford a limited cost. In other words, there is generally a bearable cost threshold for cooperators. Here we propose a spatial multi-person snowdrift game model with the cost threshold, and study the effects of cost threshold and noise on the evolution of cooperation. Interestingly, simulation results show that the cooperation level varying with the cost threshold exhibits discontinuous phase transitions and step structures, and an intermediate region of cost threshold can lead to the optimal cooperation level. We provide theoretical analysis by pair approximation for the simulation results, and show some typical snapshots of the system. Furthermore, we find that the cooperation level changing with the noise displays several different behaviors for moderate values of cost threshold. We also show how cooperation evolves in a modified way of payoff calculation. Our work reflects the nontrivial roles of cost threshold and noise in the evolution of cooperation in spatial multi-person snowdrift games.