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Effect of the spatial autocorrelation of empty sites on the evolution of cooperation

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  • Zhang, Hui
  • Wang, Li
  • Hou, Dongshuang

Abstract

An evolutionary game model is constructed to investigate the spatial autocorrelation of empty sites on the evolution of cooperation. Each individual is assumed to imitate the strategy of the one who scores the highest in its neighborhood including itself. Simulation results illustrate that the evolutionary dynamics based on the Prisoner’s Dilemma game (PD) depends severely on the initial conditions, while the Snowdrift game (SD) is hardly affected by that. A high degree of autocorrelation of empty sites is beneficial for the evolution of cooperation in the PD, whereas it shows diversification effects depending on the parameter of temptation to defect in the SD. Moreover, for the repeated game with three strategies, ‘always defect’ (ALLD), ‘tit-for-tat’ (TFT), and ‘always cooperate’ (ALLC), simulations reveal that an amazing evolutionary diversity appears for varying of parameters of the temptation to defect and the probability of playing in the next round of the game. The spatial autocorrelation of empty sites can have profound effects on evolutionary dynamics (equilibrium and oscillation) and spatial distribution.

Suggested Citation

  • Zhang, Hui & Wang, Li & Hou, Dongshuang, 2016. "Effect of the spatial autocorrelation of empty sites on the evolution of cooperation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 296-308.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:296-308
    DOI: 10.1016/j.physa.2015.09.056
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    References listed on IDEAS

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    1. Erez Lieberman & Christoph Hauert & Martin A. Nowak, 2005. "Evolutionary dynamics on graphs," Nature, Nature, vol. 433(7023), pages 312-316, January.
    2. Tsukamoto, Ei & Shirayama, Susumu, 2010. "Influence of the variance of degree distributions on the evolution of cooperation in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 577-586.
    3. Christoph Hauert & Michael Doebeli, 2004. "Spatial structure often inhibits the evolution of cooperation in the snowdrift game," Nature, Nature, vol. 428(6983), pages 643-646, April.
    4. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
    5. Zhang, Hui & Zhang, Feng & Li, Zizhen & Gao, Meng & Li, Wenlong, 2009. "Evolutionary diversity and spatiotemporal dynamics of a spatial game," Ecological Modelling, Elsevier, vol. 220(19), pages 2353-2364.
    6. Francisco C Santos & Jorge M Pacheco & Tom Lenaerts, 2006. "Cooperation Prevails When Individuals Adjust Their Social Ties," PLOS Computational Biology, Public Library of Science, vol. 2(10), pages 1-8, October.
    7. F. Fu & L.-H. Liu & L. Wang, 2007. "Evolutionary Prisoner's Dilemma on heterogeneous Newman-Watts small-world network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(4), pages 367-372, April.
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