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Evolutionary minority games with memory

Author

Listed:
  • Gian Italo Bischi

    (Università di Urbino “Carlo Bo”)

  • Ugo Merlone

    (Università di Torino)

Abstract

We propose a simple dynamic adjustment mechanism, equivalent to the standard replicator dynamics in discrete time, to study the time evolution of a population of players facing a binary choice game, and apply this mechanism to minority games in order to investigate the effects of memory on the stability of the unique Nash equilibrium. Two different kinds of memory are considered, one where the players take into account the current and the previous payoffs in order to decide the strategy chosen in the next period, and the other one where the players consider the whole series of payoffs observed in the past through a discounted sum with exponentially fading weights. Both the memory representations proposed lead to an analytically tractable two-dimensional dynamical system, so that analytical results can be given for the stability of the Nash equilibrium. However, a global analysis of the models – performed by numerical methods and guided by the analytical results – shows that some complexities arise for intermediate values of the memory parameter, even if the stabilization effect of uniform memory is stated in both cases.

Suggested Citation

  • Gian Italo Bischi & Ugo Merlone, 2017. "Evolutionary minority games with memory," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 859-875, November.
    • Handle: RePEc:spr:joevec:v:27:y:2017:i:5:d:10.1007_s00191-017-0526-4
    DOI: 10.1007/s00191-017-0526-4
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    References listed on IDEAS

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    1. Cabrales, Antonio & Sobel, Joel, 1992. "On the limit points of discrete selection dynamics," Journal of Economic Theory, Elsevier, vol. 57(2), pages 407-419, August.
    2. Holmes, James M. & Manning, Richard, 1988. "Memory and market stability : The case of the cobweb," Economics Letters, Elsevier, vol. 28(1), pages 1-7.
    3. Franke, Reiner, 2003. "Reinforcement learning in the El Farol model," Journal of Economic Behavior & Organization, Elsevier, vol. 51(3), pages 367-388, July.
    4. Bischi, Gian-Italo & Merlone, Ugo, 2010. "Binary choices in small and large groups: A unified model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 843-853.
    5. W. Brian Arthur, 1994. "Inductive Reasoning, Bounded Rationality and the Bar Problem," Working Papers 94-03-014, Santa Fe Institute.
    6. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521558747, January.
    7. Arthur, W Brian, 1994. "Inductive Reasoning and Bounded Rationality," American Economic Review, American Economic Association, vol. 84(2), pages 406-411, May.
    8. Dindo, Pietro, 2005. "A tractable evolutionary model for the Minority Game with asymmetric payoffs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 110-118.
    9. Stahl, Dale O. & Haruvy, Ernan, 2008. "Level-n bounded rationality and dominated strategies in normal-form games," Journal of Economic Behavior & Organization, Elsevier, vol. 66(2), pages 226-232, May.
    10. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, January.
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    Cited by:

    1. Bischi, Gian Italo & Merlone, Ugo & Pruscini, Eros, 2018. "Evolutionary dynamics in club goods binary games," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 104-119.
    2. Davide Radi & Fabio Lamantia & Tomáš Tichý, 2021. "Hybrid dynamics of multi-species resource exploitation," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 559-577, December.
    3. Arianna Dal Forno & Ugo Merlone, 2018. "Reference group influence on binary choices dynamics," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 427-445, November.
    4. Arianna Dal Forno & Ugo Merlone, 2019. "Heterogeneous Society in Binary Choices with Externalities," Dynamic Games and Applications, Springer, vol. 9(2), pages 433-457, June.

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    More about this item

    Keywords

    Binary games; Minority games; Replicator dynamics; Memory; Stability;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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