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Delayed response in the Hawk Dove game

Abstract

We consider a group of agents playing the Hawk-Dove game. These agents have a finite memory of past interactions which they use to optimize their play. By both analytical and numerical approaches, we show that an instability occurs at a critical memory length, and we provide its characterization. We show also that when the game is stable, having a long memory is beneficial but that instability, which may be produced by excessively long memory, hands the advantage to those with shorter memories.

References

  1. J. Maynard Smith, G.R. Price, Nature 246, 15 (1973)

    Article  Google Scholar 

  2. J. Hofbauer, K. Sigmund, Evolutionary games and population dynamics (Cambridge University Press, Cambridge, 1998)

  3. J.M. McNamara, F.J. Weissing, Evolutionary game theory (Cambridge University Press, Cambridge, 2010)

  4. J. Maynard Smith, Am. Sci. 64, 41 (1976)

    ADS  Google Scholar 

  5. J. Maynard Smith, Proc. Roy. Soc. London 205, 475 (1979)

    ADS  Article  Google Scholar 

  6. H. Kokko, S.C. Griffith, S.R. Pryke, Proc. Biol. Sci. 281, 20141794 (2014)

    Article  Google Scholar 

  7. M. Hanauske et al., Physica A 389, 5084 (2010)

    ADS  Article  Google Scholar 

  8. Y.H. Hsieh et al., Inf. Syst. Front. 16, 697 (2014)

    Article  Google Scholar 

  9. R. Sugden, The Economics of Rights, Co-operation and Welfare (Palgrave Macmillan, London, 2005)

  10. T. Galla, Phys. Rev. Lett. 103, 198702 (2009)

    ADS  Article  Google Scholar 

  11. T. Galla, J. Doyne Farmer, Proc. Natl. Acad. Sci. USA 110, 1232 (2013)

    ADS  MathSciNet  Article  Google Scholar 

  12. Y. Sato, J.P. Crutchfield, Phys. Rev. E 67, 015206 (2003)

    ADS  Article  Google Scholar 

  13. D. Challet, Y.-C. Zhang, Physica A 246, 407 (1997)

    ADS  Article  Google Scholar 

  14. T. Erneux, Applied Delay Differential Equations (Springer, New York, 2009)

  15. J. Miekisz, S. Wesolowski, Dyn. Games. Appl. 1, 440 (2011)

    MathSciNet  Article  Google Scholar 

  16. J. Alboszta, J. Miekisz, J. Theor. Biol. 231, 157 (2004)

    Article  Google Scholar 

  17. T. Yi, W. Zuwang, J. Theor. Biol. 187, 111 (1997)

    Article  Google Scholar 

  18. L. Averell, A. Heathcote, J. Math. Psych. 55, 25 (2010)

    Article  Google Scholar 

  19. P. Crowley, Behav. Ecol. 12, 735 (2001)

    Article  Google Scholar 

  20. J. Burridge, Y. Gao, Y. Mao, Phys. Rev. E 92, 032119 (2015)

    ADS  MathSciNet  Article  Google Scholar 

  21. J. Burridge, Phys. Rev. E 92, 042111 (2015)

    ADS  Article  Google Scholar 

  22. E. Wesson, R. Rand, D. Rand, Int. J. Bifurc. Chaos 26, 1650006 (2016)

    Article  Google Scholar 

  23. J. Maynard Smith, Evolutionary and the theory of games (Cambridge University Press, Cambridge, 1982)

  24. G. Grimmett, D. Stirzaker, Probability and Random Processes (Oxford University Press, Oxford, 2001)

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Correspondence to James Burridge.

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Burridge, J., Gao, Y. & Mao, Y. Delayed response in the Hawk Dove game. Eur. Phys. J. B 90, 13 (2017). https://doi.org/10.1140/epjb/e2016-70471-1

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  • DOI: https://doi.org/10.1140/epjb/e2016-70471-1

Keywords

  • Statistical and Nonlinear Physics