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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.

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Bibliographic Info

Paper provided by Department of Economics - University of Zurich in its series ECON - Working Papers with number 063.

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Date of creation: Feb 2012
Date of revision: Jan 2014
Handle: RePEc:zur:econwp:063

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

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  1. Arthur J Robson & Fernando Vega-Redondo, 1999. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Levine's Working Paper Archive 2112, David K. Levine.
  2. Myatt, David P. & Wallace, Chris, 2003. "A multinomial probit model of stochastic evolution," Journal of Economic Theory, Elsevier, vol. 113(2), pages 286-301, December.
  3. BERGIN, James & LIPMAN, Bart, 1994. "Evolution with State-Dependent Mutations," CORE Discussion Papers 1994055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers 0085, Institute for Advanced Study, School of Social Science.
  5. Maruta, Toshimasa & Okada, Akira, 2009. "Stochastically Stable Equilibria in Coordination Games with Multiple Populations," Discussion Papers 2009-01, Graduate School of Economics, Hitotsubashi University.
  6. repec:oxf:wpaper:090 is not listed on IDEAS
  7. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
  8. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  9. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
  10. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 551-585, November.
  11. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
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