Cooperation emergence in group population with unequal competitions

¹ Department of Automation, Shanghai Jiao Tong University, and Key Laboratory of System Control and Information Processing, Ministry of Education of China - Shanghai 200240, China
² School of Computer Science and Engineering, University of Electronic Science and Technology of China Chengdu 610054, China
³ Shanghai Key Laboratory of Power Station Automation Technology, School of Mechatronic Engineering and Automation, Shanghai University - Shanghai 200240, China

^(a) zhihai.rong@gmail.com
^(b) xfwang@sjtu.edu.cn

Received: 4 May 2020
Accepted: 7 July 2020

Abstract

Groups are the basic unit of organization in our society. It is important to investigate how groups compete and cooperation evolves in the population composed of groups. In this paper, based on the celebrated multi-player public goods game, we propose a general theoretical framework of the stochastic dynamic process to study how inequalities among groups affect the evolution of cooperation in a group population. We find that cooperation can be promoted if enhancement factors of every group are not equivalent and constant, but are dynamic adjusted according to the group reputation which is defined as the fraction of cooperators in the last public goods game. Furthermore, we introduce the inequality in social roles of groups by means of heterogeneous graph and find that, under the influence of dynamic adjustment of enhancement factors, central groups can always own more cooperators compared to peripheral groups during game dynamics. Moreover, a highly heterogeneous group connecting patterns can help cooperators to survive in the population when the enhancement factor is small, but prevents the spread of cooperation more widely even if the enhancement factor increases.