• Prisoners' Dilemma Supergame on Rectangle Lattice
  • DOI: 10.4236/ojapps.2013.31B1002   PP.7 - 11
  • Author(s)
  • Zhongxing Ye, Jingshu Chen
  • In this paper a class of large supergames, i.e., infinitely repeated games played by many players are studied. The players located on the vertex set of planar rectangle lattice play several basic games with his neighbors. The basic game is two-person prisoners’ dilemma game with asymmetric payoffs. Under the conditions of the pre-specified updating rules and the transition probabilities, the relevant stochastic process of strategy evolution forms a Markovian process. The simulation results about the long-run behavior are provided.

  • Prisoners' Dilemma; Supergame; Planar Rectangle Lattice; Markov Process; Invariant Measure; Equilibrium
  • References
  • [1] A. J. Wang, Z. X. Ye and Y. C. Liu, “On the Long-run Equilibria of a Class of Large Super Game on Z^d,” Journal of Mathematical Sciences: Advances and Applications, Vol. 12, No. 1, 2012, pp. 21-46.

    [2] H. Ou and Z. X. Ye, “Dynamic Supergames on Trees,” Proceeding of 2010 International Conference on Progress in Informatics and Computing(PIC-2010), Shanghai, December 10-12, 2010.

    [3] G. Kendall, X. Yao, S. Y. Chong, “The Iterated Prisoners’ Dilemma: 20 Years On,” World Scientific Publishing Co Pte Ltd, 2007.

    [4] Y. K. Liu, Z. Li, X. J. Chen and L. Wang, “Evolutionary Prisoners’ Dilemma Game on Highly Clustered Community Networks,” Chinese Physics, Vol. 18, No. 7, 2009, pp. 2623-2628. doi:10.1088/1674-1056/18/7/001

    [5] M. A. Saif and P. M. Gade, “Prisoner’s Dilemma with Semi- synchronous Updates: Evidence for a First Order Phase Transition,” Vol. 6, 2009.

    [6] R. Kinderman and J. L. Snell, “Markov Random Fields and Their Applicarions,” American Mathematical Society (AMS), Providence Rhode Island, 1980. doi:10.1090/conm/001

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Important Dates
Submission Due:
    December 11, 2013>>  February 16, 2014
Acceptance notification:
    February 26, 2014
Camera-ready due:
    February 10, 2014
    April 16-18, 2014
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