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On the Relationship Between Risk-Dominance and Stochastic Stability

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Toshimasa Maruta

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Abstract

In a 2 x2 symmetric game with two symmetric equilibria in pure strategies, one risk-dominates another if and only if the equilibrium strategy is a unique best response to any mixture that gives it at least a probability of one half. In a n x n symmetric game, we call a strategy globally risk-dominant if it is a unique best response to any mixture that gives it at least a probability of one half. We show that if a finite coordination game has a globally risk-dominant equilibrium then this is the one that is selected by the stochastic equilibrium selection processes proposed by Young and by Kandori, Mailath, and Rob.

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File URL: http://www.kellogg.northwestern.edu/research/math/papers/1122.pdf
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Paper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1122.

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Date of creation: Mar 1995
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Handle: RePEc:nwu:cmsems:1122

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  1. John C. Harsanyi & Reinhard Selten, 1988. "A General Theory of Equilibrium Selection in Games," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262582384.
  2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September. [Downloadable!] (restricted)
  3. Binmore, Ken & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Discussion Paper Serie B 275, University of Bonn, Germany.
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  4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-57, January. [Downloadable!] (restricted)
  5. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January. [Downloadable!] (restricted)
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  6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January. [Downloadable!] (restricted)
  7. repec:att:wimass:199410 is not listed on IDEAS
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. TERCIEUX, Olivier & VANNETELBOSCH, Vincent, 2004. "A characterization of stochastically stable networks," CORE Discussion Papers 2004056, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  2. Suren Basov, 2004. "Equilibrium selection in coordination games: Why do dominated strategies matter?," Economics Bulletin, Economics Bulletin, vol. 3(41), pages 1-3. [Downloadable!]
  3. David P. Myatt & Chris Wallace, 2002. "A Multinomial Probit Model of Stochastic Evolution," Economics Series Working Papers 090, University of Oxford, Department of Economics. [Downloadable!]
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