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Ordinal imitative dynamics

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  • George Loginov

    (Augustana University)

Abstract

This paper introduces an evolutionary dynamics based on imitate the better realization (IBR) rule. Under this rule, an agent in a population game imitates the strategy of a randomly chosen opponent whenever the opponent’s realized payoff is higher than his or her own. Such behavior generates a mean dynamics which depends on the order of payoffs, but not their magnitudes, and 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.

Suggested Citation

  • George Loginov, 2022. "Ordinal imitative dynamics," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 391-412, June.
  • Handle: RePEc:spr:jogath:v:51:y:2022:i:2:d:10.1007_s00182-021-00797-7
    DOI: 10.1007/s00182-021-00797-7
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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. , & , H., 2011. "Survival of dominated strategies under evolutionary dynamics," Theoretical Economics, Econometric Society, vol. 6(3), September.
    3. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    4. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
    5. repec:dau:papers:123456789/14432 is not listed on IDEAS
    6. 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.
    7. 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.
    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.
    9. Glenn Ellison & Drew Fudenberg, 1995. "Word-of-Mouth Communication and Social Learning," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 93-125.
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    Cited by:

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