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The role of mixed strategies in spatial evolutionary games

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  • Szabó, György
  • Hódsági, Kristóf

Abstract

We study three-strategy evolutionary games on a square lattice when the third strategy is a mixed strategy of the first and second ones. It is shown that the resultant three-strategy game is a potential game as well as its two-strategy version. Evaluating the potential we derive a phase diagram on a two-dimensional plane of rescaled payoff parameters that is valid in the zero noise limit of the logit dynamical rule. The mixed strategy is missing in this phase diagram. The effects of two different dynamical rules are analyzed by Monte Carlo simulations and the results of imitation dynamics indicate the dominance of the mixed strategy within the region of the hawk–dove game where it is an evolutionarily stable strategy. The effects and consequences of the different dynamical rules on the final stationary states and phase transitions are discussed.

Suggested Citation

  • Szabó, György & Hódsági, Kristóf, 2016. "The role of mixed strategies in spatial evolutionary games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 198-206.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:198-206
    DOI: 10.1016/j.physa.2016.06.076
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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. Weisbuch, Gérard & Stauffer, Dietrich, 2007. "“Antiferromagnetism” in social relations and Bonabeau model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 542-548.
    3. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 68(2), pages 235-260.
    4. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    5. Ross Cressman, 2003. "Evolutionary Dynamics and Extensive Form Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033054, April.
    6. Sebastian Grauwin & Dominic Hunt & Eric Bertin & Pablo Jensen, 2011. "Effective Free Energy For Individual Dynamics," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 529-536.
    7. 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.
    8. Galam, Serge & Walliser, Bernard, 2010. "Ising model versus normal form game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 481-489.
    9. Kokubo, Satoshi & Wang, Zhen & Tanimoto, Jun, 2015. "Spatial reciprocity for discrete, continuous and mixed strategy setups," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 552-568.
    10. M. Sysi-Aho & J. Saramäki & J. Kertész & K. Kaski, 2005. "Spatial snowdrift game with myopic agents," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 44(1), pages 129-135, March.
    11. Wardil, Lucas & da Silva, Jafferson K.L., 2013. "The evolution of cooperation in mixed games," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 160-165.
    12. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
    13. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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    Keywords

    Evolutionary games; Mixed strategies;

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