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Log-linear Dynamics and Local Potential

Author

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  • Daijiro Okada

    () (Rutgers)

  • Olivier Tercieux

    () (Ecole Normale Suprieure)

Abstract

We show that local potential maximizer (\cite{morris+05}) with constant weights is stochastically stable in the log-linear dynamics provided that the payoff 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 different rates. For 2 player 2 action games, we examine a modified log-linear dynamics (relative log-linear dynamics) under which local potential maximizer with strictly positive weights is stochastically stable. This in particular implies that for 2 player 2 action games a strict (p1,p2)-dominant equilibrium with p1+p2

Suggested Citation

  • Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers 200807, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200807
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. 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.
    2. Oyama, Daisuke & Tercieux, Olivier, 2009. "Iterated potential and robustness of equilibria," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1726-1769, July.
    3. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-0988-x is not listed on IDEAS
    4. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
    5. Christian Ewerhart, 2017. "Ordinal potentials in smooth games," ECON - Working Papers 265, Department of Economics - University of Zurich, revised Jul 2018.
    6. Candogan, Ozan & Ozdaglar, Asuman & Parrilo, Pablo A., 2013. "Dynamics in near-potential games," Games and Economic Behavior, Elsevier, vol. 82(C), pages 66-90.
    7. Daisuke Oyama & Satoru Takahashi, 2009. "Monotone and local potential maximizers in symmetric 3x3 supermodular games," Economics Bulletin, AccessEcon, vol. 29(3), pages 2123-2135.
    8. Staudigl, Mathias, 2012. "Stochastic stability in asymmetric binary choice coordination games," Games and Economic Behavior, Elsevier, vol. 75(1), pages 372-401.
    9. 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.
    10. Sawa, Ryoji, 2014. "Coalitional stochastic stability in games, networks and markets," Games and Economic Behavior, Elsevier, vol. 88(C), pages 90-111.

    More about this item

    Keywords

    Log-linear dynamics; Stochastic stability; Local potential maximizer; Equilibrium selection; Comparison of Markov Chains;

    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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