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Stability of Equilibria in Games with Procedurally Rational Players

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  • Sethi, Rajiv

Abstract

One approach to the modeling of bounded rationality in strategic environments is based on the dynamics of evolution and learning in games. An entirely different approach has been developed recently by Osborne and Rubinstein (1998). This latter approach is static and equilibrium based, but relies on less stringent assumptions regarding the knowledge and understanding of players than does the standard theory of Nash equilibrium. This paper formalizes Osborne and Rubinstein's dynamic interpretation of their equilibrium concept and thereby facilitates a comparison of this approach with the explicitly dynamic approach of evolutionary game theory. It turns out that the two approaches give rise to radically different static and dynamic predictions. For instance, dynamically stable equilibria can involve the playing of strictly dominated actions, and equilibria in which strictly actions are played with probability 1 can be unstable. Sufficient conditions for the instability of equilibria are provided for symmetric and asymmetric games.
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  • Sethi, Rajiv, 2000. "Stability of Equilibria in Games with Procedurally Rational Players," Games and Economic Behavior, Elsevier, vol. 32(1), pages 85-104, July.
  • Handle: RePEc:eee:gamebe:v:32:y:2000:i:1:p:85-104
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    References listed on IDEAS

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    1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-1071, September.
    2. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-847, September.
    3. Simon, Herbert A, 1978. "Rationality as Process and as Product of Thought," American Economic Review, American Economic Association, vol. 68(2), pages 1-16, May.
    4. 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.
    5. Sethi, Rajiv, 1998. "Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics," Games and Economic Behavior, Elsevier, vol. 23(2), pages 284-304, May.
    6. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
    7. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
    8. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
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    Cited by:

    1. Huck Steffen & Sarin Rajiv, 2004. "Players With Limited Memory," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 4(1), pages 1-27, September.
    2. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2015. "Stable Sampling Equilibrium in Common Pool Resource Games," Games, MDPI, Open Access Journal, vol. 6(3), pages 1-19, August.
    3. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
    4. Shahi, Chander & Kant, Shashi, 2007. "An evolutionary game-theoretic approach to the strategies of community members under Joint Forest Management regime," Forest Policy and Economics, Elsevier, vol. 9(7), pages 763-775, April.
    5. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, Open Access Journal, vol. 2(3), pages 1-22, September.
    6. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers 0209, University of Vienna, Department of Economics.
    7. Oechssler, Jorg & Schipper, Burkhard, 2003. "Can you guess the game you are playing?," Games and Economic Behavior, Elsevier, vol. 43(1), pages 137-152, April.
    8. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 2015. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society, vol. 10(1), January.
    9. Juan Camilo Cárdenas & César Mantilla & Rajiv Sethi, 2013. "Commons without Tragedy: Sampling Dynamics and Cooperative Resource Extraction," DOCUMENTOS CEDE 011892, UNIVERSIDAD DE LOS ANDES-CEDE.

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    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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