Understanding cooperative behavior in structurally disordered populations

C. Xu, W. Zhang, P. Du, C.W. Choi and P.M. Hui ()
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C. Xu: College of Physics, Optoelectronics and Energy, Soochow University
W. Zhang: Suzhou Institute of Industrial Technology
P. Du: College of Physics, Optoelectronics and Energy, Soochow University
C.W. Choi: The Chinese University of Hong Kong
P.M. Hui: The Chinese University of Hong Kong

The European Physical Journal B: Condensed Matter and Complex Systems, 2016, vol. 89, issue 6, 1-11

Abstract: 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 ℱC I + ℱC II, with ℱC I emphasizing the importance of the small clusters of players especially for ℱC 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.

Keywords: Statistical; and; Nonlinear; Physics (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1140/epjb/e2016-60826-y

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