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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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Bibliographic Info

Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 32 (2000)
Issue (Month): 1 (July)
Pages: 85-104

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Handle: RePEc:eee:gamebe:v:32:y:2000:i:1:p:85-104

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. 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.
  2. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  3. Osborne, M-J & Rubinstein, A, 1997. "Games with Procedurally Rational Players," Papers 4-97, Tel Aviv.
  4. Sethi, Rajiv, 1998. "Strategy-Specific Barriers to Learning and Nonmonotonic Selection Dynamics," Games and Economic Behavior, Elsevier, vol. 23(2), pages 284-304, May.
  5. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
  6. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  7. 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.
  8. E. Dekel & S. Scotchmer, 2010. "On the Evolution of Optimizing Behavior," Levine's Working Paper Archive 434, David K. Levine.
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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. Thorsten Chmura & Werner Güth, 2011. "The Minority of Three-Game: An Experimental and Theoretical Analysis," Games, MDPI, Open Access Journal, vol. 2(3), pages 333-354, September.
  3. 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.
  4. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers 0209, University of Vienna, Department of Economics.
  5. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
  6. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 0. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.
  7. Jörg Oechssler & Burkhard C. Schipper, 2000. "Can You Guess the Game You're Playing?," Bonn Econ Discussion Papers bgse11_2000, University of Bonn, Germany.
  8. 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.

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