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Cyclical behavior of evolutionary dynamics in coordination games with changing payoffs

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  • George Loginov

Abstract

The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how, for a population of myopic agents with homogeneous preferences, changes in the environment caused by current aggregate behavior may affect future payoffs and hence alter future behavior. The interaction between the agents is based on a symmetric two-strategy game with positive externalities and negative feedback from aggregate behavior to payoffs, so that at every point in time the population has an incentive to coordinate, whereas over time the more popular strategy becomes less appealing. Under the best response dynamics and the logit dynamics with small noise levels the joint trajectories of preferences and behavior converge to closed orbits around the unique steady state, whereas for large noise levels the steady state of the logit dynamics becomes a sink. Under the replicator dynamics the unique steady state of the system is repelling and the trajectories are unbounded unstable spirals.

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  • George Loginov, 2021. "Cyclical behavior of evolutionary dynamics in coordination games with changing payoffs," Papers 2106.08224, arXiv.org.
    • Handle: RePEc:arx:papers:2106.08224
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    1. Fudenberg, Drew & Levine, David, 1998. "Learning in games," European Economic Review, Elsevier, vol. 42(3-5), pages 631-639, May.
    2. Jonathan Newton, 2018. "Evolutionary Game Theory: A Renaissance," Games, MDPI, vol. 9(2), pages 1-67, May.
    3. William H. Sandholm, 2001. "Preference Evolution, Two-Speed Dynamics, and Rapid Social Change," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 4(3), pages 637-679, July.
    4. 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.
    5. Matsui Akihiko & Matsuyama Kiminori, 1995. "An Approach to Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 65(2), pages 415-434, April.
    6. Fuhito Kojima & Satoru Takahashi, 2007. "Anti-Coordination Games And Dynamic Stability," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(04), pages 667-688.
    7. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    8. Andrew R. Tilman & Joshua B. Plotkin & Erol Akçay, 2020. "Evolutionary games with environmental feedbacks," Nature Communications, Nature, vol. 11(1), pages 1-11, December.
    9. Gilboa, Itzhak & Matsui, Akihiko, 1991. "Social Stability and Equilibrium," Econometrica, Econometric Society, vol. 59(3), pages 859-867, May.
    10. Michel BenaÔm & J–rgen W. Weibull, 2003. "Deterministic Approximation of Stochastic Evolution in Games," Econometrica, Econometric Society, vol. 71(3), pages 873-903, May.
    11. Josef Hofbauer & Gerhard Sorger, 2002. "A Differential Game Approach To Evolutionary Equilibrium Selection," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 17-31.
    12. Eddie Dekel & Jeffrey C. Ely & Okan Yilankaya, 2007. "Evolution of Preferences -super-1," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(3), pages 685-704.
    13. Matsui, Akihiko, 1992. "Best response dynamics and socially stable strategies," Journal of Economic Theory, Elsevier, vol. 57(2), pages 343-362, August.
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