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Log-linear Dynamics and Local Potential

Author

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  • Daijiro Okada

    (Department of Economics, Rutgers, The State University of New Jersey)

  • Olivier Tercieux

    (Paris School of Economics and CNRS)

Abstract

We show that local potential maximizer ([15]) with constant weights is stochas- tically stable in the log-linear dynamics provided that the payo® function or the associated local potential function is supermodular. We illustrate and discuss, through a series of examples, the use of our main results as well as other concepts closely related to local potential maximizer: weighted potential maximizer, p- dominance. We also discuss the log-linear processes where each player's stochastic choice rule converges to the best response rule at di®erent rates. For 2£2 games, we examine a modi¯ed log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically sta- ble. This in particular implies that for 2 £ 2 games a strict (p1; p2)-dominant equilibrium with p1 + p2

Suggested Citation

  • Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers 0085, Institute for Advanced Study, School of Social Science.
    • Handle: RePEc:ads:wpaper:0085
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Arigapudi, Srinivas, 2020. "Transitions between equilibria in bilingual games under logit choice," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 24-34.
    2. Jun Honda, 2015. "Games with the Total Bandwagon Property," Department of Economics Working Papers wuwp197, Vienna University of Economics and Business, Department of Economics.
    3. Carlos Alós-Ferrer & Nick Netzer, 2015. "Robust stochastic stability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 31-57, January.
    4. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    5. Sung-Ha Hwang & Jonathan Newton, 2017. "Payoff-dependent dynamics and coordination games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(3), pages 589-604, October.
    6. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    7. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
    8. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    9. Hwang, Sung-Ha & Rey-Bellet, Luc, 2021. "Positive feedback in coordination games: Stochastic evolutionary dynamics and the logit choice rule," Games and Economic Behavior, Elsevier, vol. 126(C), pages 355-373.
    10. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.
    11. Christian Ewerhart, 2020. "Ordinal potentials in smooth games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(4), pages 1069-1100, November.
    12. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.

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    More about this item

    Keywords

    Log-linear dynamics; Relative log-linear dynamics; Stochastic stability; local potential maximizer; p-dominant equilibrium; equilibrium selection; stochastic order; comparison of Markov chains;
    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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