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Robust stochastic stability

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  • Carlos Alós–Ferrer
  • Nick Netzer

Abstract

A strategy profile of a game is called robustly stochastically stable if it is stochastically stable for a given behavioral model independently of the specification of revision opportunities and tie-breaking assumptions in the dynamics. We provide a simple radius-coradius result for robust stochastic stability and examine several applications. For the logit-response dynamics, the selection of potential maximizers is robust for the subclass of supermodular symmetric binary-action games. For the mistakes model, the weaker property of strategic complementarity suffices for robustness in this class of games. We also investigate the robustness of the selection of risk-dominant strategies in coordination games under best-reply and the selection of Walrasian strategies in aggregative games under imitation.

Suggested Citation

  • Carlos Alós–Ferrer & Nick Netzer, 2012. "Robust stochastic stability," ECON - Working Papers 063, Department of Economics - University of Zurich, revised Jan 2014.
  • Handle: RePEc:zur:econwp:063
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    1. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-1002-3 is not listed on IDEAS
    2. Fei Shi, 2015. "Long-run technology choice with endogenous local capacity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 59(2), pages 377-399, June.
    3. repec:spr:joecth:v:65:y:2018:i:4:d:10.1007_s00199-017-1047-y is not listed on IDEAS
    4. Carlos Alós-Ferrer & Georg Kirchsteiger, 2015. "Learning and market clearing: theory and experiments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 203-241, October.
    5. Kevin Hasker, 2014. "The Emergent Seed: A Representation Theorem for Models of Stochastic Evolution and two formulas for Waiting Time," Levine's Working Paper Archive 786969000000000954, David K. Levine.
    6. Cui, Zhiwei & Wang, Shouyang & Zhang, Jin & Zu, Lei, 2013. "Stochastic stability in one-way flow networks," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 410-421.
    7. Alós-Ferrer, Carlos & Buckenmaier, Johannes, 2017. "Trader matching and the selection of market institutions," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 118-127.
    8. repec:spr:joecth:v:64:y:2017:i:3:d:10.1007_s00199-016-0990-3 is not listed on IDEAS
    9. Carlos Alós-Ferrer & Nick Netzer, 2017. "On the convergence of logit-response to (strict) Nash equilibria," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(1), pages 1-8, April.
    10. Ennio Bilancini & Leonardo Boncinelli, 2018. "Social coordination with locally observable types," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 975-1009, June.

    More about this item

    Keywords

    Learning in games; stochastic stability; radius-coradius theorems; logit-response dynamics; mutations; imitation;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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