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On the Relationship Between Risk-Dominance and Stochastic Stability

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  • Toshimasa Maruta

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.

Suggested Citation

  • Toshimasa Maruta, 1995. "On the Relationship Between Risk-Dominance and Stochastic Stability," Discussion Papers 1122, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  • Handle: RePEc:nwu:cmsems:1122
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    References listed on IDEAS

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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 1047-1071, September.
    3. Carlsson, Hans & van Damme, Eric, 1993. "Global Games and Equilibrium Selection," Econometrica, Econometric Society, vol. 61(5), pages 989-1018, September.
    4. Morris, Stephen & Rob, Rafael & Shin, Hyun Song, 1995. "Dominance and Belief Potential," Econometrica, Econometric Society, vol. 63(1), pages 145-157, January.
    5. Kandori Michihiro & Rob Rafael, 1995. "Evolution of Equilibria in the Long Run: A General Theory and Applications," Journal of Economic Theory, Elsevier, vol. 65(2), pages 383-414, April.
    6. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, University Library of Munich, Germany.
    7. Blume Lawrence E., 1993. "The Statistical Mechanics of Strategic Interaction," Games and Economic Behavior, Elsevier, vol. 5(3), pages 387-424, July.
    8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    9. 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.
    10. Ken Binmore & Larry Samuelson, 1994. "Muddling Through: Noisy Equilibrium Selection," Game Theory and Information 9410002, EconWPA.
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    Cited by:

    1. Olivier Tercieux & Vincent Vannetelbosch, 2006. "A characterization of stochastically stable networks," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(3), pages 351-369, October.
    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. Morris, Stephen & Ui, Takashi, 2005. "Generalized potentials and robust sets of equilibria," Journal of Economic Theory, Elsevier, vol. 124(1), pages 45-78, September.
    4. Oyama, Daisuke, 2002. "p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics," Journal of Economic Theory, Elsevier, vol. 107(2), pages 288-310, December.
    5. J. Durieu & P. Solal & O. Tercieux, 2011. "Adaptive learning and p-best response sets," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(4), pages 735-747, November.
    6. Simon Weidenholzer, 2010. "Coordination Games and Local Interactions: A Survey of the Game Theoretic Literature," Games, MDPI, Open Access Journal, vol. 1(4), pages 1-35, November.
    7. Jacques Durieu & Philippe Solal, 2012. "Models of Adaptive Learning in Game Theory," Chapters,in: Handbook of Knowledge and Economics, chapter 11 Edward Elgar Publishing.
    8. Maruta, Toshimasa & Okada, Akira, 2012. "Stochastically stable equilibria in n-person binary coordination games," Mathematical Social Sciences, Elsevier, vol. 63(1), pages 31-42.
    9. Cui, Zhiwei, 2014. "More neighbors, more efficiency," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 103-115.
    10. Binmore, Ken & Samuelson, Larry, 2006. "The evolution of focal points," Games and Economic Behavior, Elsevier, vol. 55(1), pages 21-42, April.
    11. Kim, Chongmin & Wong, Kam-Chau, 2010. "Long-run equilibria with dominated strategies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 242-254, January.
    12. Suren Basov, 2004. "Equilibrium selection in coordination games: Why do dominated strategies matter?," Economics Bulletin, AccessEcon, vol. 3(41), pages 1-3.
    13. Agastya, Murali, 2004. "Stochastic stability in a double auction," Games and Economic Behavior, Elsevier, vol. 48(2), pages 203-222, August.
    14. Wallace, Chris & Young, H. Peyton, 2015. "Stochastic Evolutionary Game Dynamics," Handbook of Game Theory with Economic Applications, Elsevier.
    15. repec:ebl:ecbull:v:3:y:2004:i:41:p:1-3 is not listed on IDEAS
    16. Alos-Ferrer, Carlos & Weidenholzer, Simon, 2007. "Partial bandwagon effects and local interactions," Games and Economic Behavior, Elsevier, vol. 61(2), pages 179-197, November.
    17. Tercieux, Olivier, 2006. "p-Best response set," Journal of Economic Theory, Elsevier, vol. 131(1), pages 45-70, November.

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