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Stability of Equilibria in Games with Procedurally Rational Players

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  • Rajiv Sethi

    (Barnard College, Columbia University)

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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File URL: http://128.118.178.162/eps/game/papers/9811/9811003.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Game Theory and Information with number 9811003.

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Length: 23 pages
Date of creation: 16 Nov 1998
Date of revision: 04 Mar 1999
Handle: RePEc:wpa:wuwpga:9811003

Note: Type of Document - Tex; prepared on IBM PC; to print on HP/PostScript; pages: 23; figures: included
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Web page: http://128.118.178.162

Related research

Keywords: Dynamic Stability; S(1) Equilibrium; Procedural Rationality; Evolutionary Games;

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References

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  1. Ellison, Glenn, 1993. "Learning, Local Interaction, and Coordination," Econometrica, Econometric Society, vol. 61(5), pages 1047-71, September.
  2. Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
  3. Dekel, Eddie & Scotchmer, Suzanne, 1992. "On the evolution of optimizing behavior," Journal of Economic Theory, Elsevier, vol. 57(2), pages 392-406, August.
  4. 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.
  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. Samuelson, Larry & Zhang, Jianbo, 1992. "Evolutionary stability in asymmetric games," Journal of Economic Theory, Elsevier, vol. 57(2), pages 363-391, August.
  7. Osborne, Martin J & Rubinstein, Ariel, 1998. "Games with Procedurally Rational Players," American Economic Review, American Economic Association, vol. 88(4), pages 834-47, September.
  8. Young, H Peyton, 1993. "The Evolution of Conventions," Econometrica, Econometric Society, vol. 61(1), pages 57-84, January.
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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Sandholm, William H. & Tercieux, Olivier & Oyama, Daisuke, 0. "Sampling best response dynamics and deterministic equilibrium selection," Theoretical Economics, Econometric Society.
  5. 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.
  6. Jacek Miękisz & Michał Ramsza, 2013. "Sampling Dynamics of a Symmetric Ultimatum Game," Dynamic Games and Applications, Springer, vol. 3(3), pages 374-386, September.
  7. J. C. R. Alcantud & Carlos Alós-Ferrer, 2002. "Choice-Nash Equilibria," Vienna Economics Papers 0209, University of Vienna, Department of Economics.
  8. 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.

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