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Robust stochastic stability

  • Carlos Alós–Ferrer
  • Nick Netzer

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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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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  1. Alós-Ferrer, Carlos & Netzer, Nick, 2010. "The logit-response dynamics," Games and Economic Behavior, Elsevier, vol. 68(2), pages 413-427, March.
  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. 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.
  4. Maruta, Toshimasa, 2002. "Binary Games with State Dependent Stochastic Choice," Journal of Economic Theory, Elsevier, vol. 103(2), pages 351-376, April.
  5. Carlos Alós-Ferrer & Ana Ania, 2005. "The evolutionary stability of perfectly competitive behavior," Economic Theory, Springer, vol. 26(3), pages 497-516, October.
  6. Maruta, Toshimasa & Okada, Akira, 2009. "Stochastically Stable Equilibria in Coordination Games with Multiple Populations," Discussion Papers 2009-01, Graduate School of Economics, Hitotsubashi University.
  7. Daijiro Okada & Olivier Tercieux, 2008. "Log-linear Dynamics and Local Potential," Departmental Working Papers 200807, Rutgers University, Department of Economics.
  8. 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.
  9. repec:oxf:wpaper:090 is not listed on IDEAS
  10. Carlos Alós-Ferrer, 2000. "Finite Population Dynamics and Mixed Equilibria," Vienna Economics Papers 0008, University of Vienna, Department of Economics.
  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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