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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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References

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  1. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Economics Working Papers 0085, Institute for Advanced Study, School of Social Science.
  2. 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).
  3. Robson, Arthur J. & Vega-Redondo, Fernando, 1996. "Efficient Equilibrium Selection in Evolutionary Games with Random Matching," Journal of Economic Theory, Elsevier, vol. 70(1), pages 65-92, July.
  4. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
  5. Carlos Alos-Ferrer & Nick Netzer, 2008. "The Logit-Response Dynamics," TWI Research Paper Series 28, Thurgauer Wirtschaftsinstitut, Universität Konstanz.
  6. David P. Myatt & Chris Wallace, 2002. "A Multinomial Probit Model of Stochastic Evolution," Economics Series Working Papers 90, University of Oxford, Department of Economics.
  7. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  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. repec:oxf:wpaper:090 is not listed on IDEAS
  10. Maruta, Toshimasa & Okada, Akira, 2009. "Stochastically Stable Equilibria in Coordination Games with Multiple Populations," Discussion Papers 2009-01, Graduate School of Economics, Hitotsubashi University.
  11. 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.
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