Eur. Phys. J. B (2016) 89: 152
https://doi.org/10.1140/epjb/e2016-60826-y

Regular Article

Understanding cooperative behavior in structurally disordered populations

¹ College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, P.R. China
² Department of Electronics and Communication Engineering, Suzhou Institute of Industrial Technology, Suzhou 215104, P.R. China
³ Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, P.R. China

^a e-mail: pmhui@phy.cuhk.edu.hk

Received: 17 October 2015
Received in final form: 10 April 2016
Published online: 15 June 2016

Abstract

The effects of an inhomogeneous competing environment on the extent of cooperation are studied within the context of a site-diluted evolutionary snowdrift game on a square lattice, with the occupied sites representing the players, both numerically and analytically. The frequency of cooperation ℱ_C generally shows a non-monotonic dependence on the fraction of occupied sites ρ, for different values of the payoff parameter r. Slightly diluting a lattice leads to a lower cooperation for small and high values of r. For a range of r, however, dilution leads to an enhanced cooperation. An analytic treatment is developed for ℱ_C^I + ℱ_C^II, with ℱ_C^I emphasizing the importance of the small clusters of players especially for ℱ_C^II from the other players is shown to be inadequate. A local configuration approximation (LCA) that treats the local competing configurations as the variables and amounts to include spatial correlation up to the neighborhood of a player’s neighbors is developed. Results of ℱ_C (ρ) and the number of different local configurations from LCA are in good agreement with simulation results. A transparent physical picture of the dynamics stemming from LCA is also presented. The theoretical approach provides a framework that can be readily applied to competing agent-based models in structurally ordered and disordered populations.