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The use of a data envelopment analysis efficient rule to produce a steady and high cooperation frequency in a spatial evolvement game

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  • Peng, Yu
  • Wang, Bing-Hong
  • Zeng, Qing-Ke
  • Lu, Qian
  • Wang, Hong

Abstract

We use the data envelopment analysis (DEA) method to estimate the relative efficiency of the current strategy for each player in a game by taking the spatial distribution of strategies as input and the total payoff as output. Based on the optimal value of the DEA model, we present a DEA efficient rule to update the strategy in evolutionary games. Simulations of the prisoner’s dilemma game (PDG) [4] and the snowdrift game (SG) on two-dimensional regular lattices of four, six, and eight neighbors with periodic boundary conditions, are carried out; the results show the emergence of high and stable cooperator frequency. The heuristic analysis of the DEA efficient rule are discussed in detail. Our work may be helpful in exploring the promotion of cooperator behavior.

Suggested Citation

  • Peng, Yu & Wang, Bing-Hong & Zeng, Qing-Ke & Lu, Qian & Wang, Hong, 2012. "The use of a data envelopment analysis efficient rule to produce a steady and high cooperation frequency in a spatial evolvement game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2000-2006.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:5:p:2000-2006
    DOI: 10.1016/j.physa.2011.10.029
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    References listed on IDEAS

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    1. Blume Lawrence E., 1995. "The Statistical Mechanics of Best-Response Strategy Revision," Games and Economic Behavior, Elsevier, vol. 11(2), pages 111-145, November.
    2. 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.
    3. Charnes, A. & Cooper, W. W. & Rhodes, E., 1978. "Measuring the efficiency of decision making units," European Journal of Operational Research, Elsevier, vol. 2(6), pages 429-444, November.
    4. Hopkins, Ed, 1999. "A Note on Best Response Dynamics," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 138-150, October.
    5. Hisashi Ohtsuki & Christoph Hauert & Erez Lieberman & Martin A. Nowak, 2006. "A simple rule for the evolution of cooperation on graphs and social networks," Nature, Nature, vol. 441(7092), pages 502-505, May.
    6. Gao, Kun & Wang, Wen-Xu & Wang, Bing-Hong, 2007. "Self-questioning games and ping-pong effect in the BA network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 528-538.
    7. Cook, Wade D. & Seiford, Larry M., 2009. "Data envelopment analysis (DEA) - Thirty years on," European Journal of Operational Research, Elsevier, vol. 192(1), pages 1-17, January.
    8. Charnes, A. & Cooper, W. W. & Golany, B. & Seiford, L. & Stutz, J., 1985. "Foundations of data envelopment analysis for Pareto-Koopmans efficient empirical production functions," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 91-107.
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    Cited by:

    1. Peng, Yu & Lu, Qian & Wu, Xue & Zhao, Yueru & Xiao, Yue, 2020. "Dynamics of Hotelling triopoly model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 373(C).

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