Understanding cooperative behavior in structurally disordered populations

Authored by C Xu, W Zhang, P Du, C W Choi, P M Hui

Date Published: 2016

DOI: 10.1140/epjb/e2016-60826-y

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

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 rho, 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 = F-C(I) + F-C(II), with F-C(I) emphasizing the importance of the small clusters of players especially for rho << 1 and being treated exactly. A pair approximation for the contribution 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(rho) 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.

Tags

models Dynamics networks social dilemmas Prisoners-dilemma Societies Evolutionary snowdrift game Spatial games