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Ordinal Imitative Dynamics

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  • George Loginov

Abstract

This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, agents in a population game imitate the strategy of a randomly chosen opponent whenever the opponent`s realized payoff is higher than their own. Such behavior generates an ordinal mean dynamics which is polynomial in strategy utilization frequencies. We demonstrate that while the dynamics does not possess Nash stationarity or payoff monotonicity, under it pure strategies iteratively strictly dominated by pure strategies are eliminated and strict equilibria are locally stable. We investigate the relationship between the dynamics based on the IBR rule and the replicator dynamics. In trivial cases, the two dynamics are topologically equivalent. In Rock-Paper-Scissors games we conjecture that both dynamics exhibit the same types of behavior, but the partitions of the game set do not coincide. In other cases, the IBR dynamics exhibits behaviors that are impossible under the replicator dynamics.

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  • George Loginov, 2019. "Ordinal Imitative Dynamics," Papers 1907.04272, arXiv.org.
    • Handle: RePEc:arx:papers:1907.04272
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    1. Yannick Viossat, 2015. "Evolutionary dynamics and dominated strategies," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 3(1), pages 91-113, April.
    2. Schlag, Karl H., 1998. "Why Imitate, and If So, How?, : A Boundedly Rational Approach to Multi-armed Bandits," Journal of Economic Theory, Elsevier, vol. 78(1), pages 130-156, January.
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    4. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
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    6. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    7. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    8. Nachbar, J H, 1990. ""Evolutionary" Selection Dynamics in Games: Convergence and Limit Properties," International Journal of Game Theory, Springer;Game Theory Society, vol. 19(1), pages 59-89.
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    Cited by:

    1. Clemens Buchen, 2023. "Institutional reform paths," Economics and Politics, Wiley Blackwell, vol. 35(3), pages 1099-1121, November.
    2. Izquierdo, Luis R. & Izquierdo, Segismundo S. & Sandholm, William H., 2019. "An introduction to ABED: Agent-based simulation of evolutionary game dynamics," Games and Economic Behavior, Elsevier, vol. 118(C), pages 434-462.

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