Stability of Equilibria in Games with Procedurally Rational Players

Barnard College, Working Paper No. 99-04

22 Pages Posted: 5 Jan 1999

See all articles by Rajiv Sethi

Rajiv Sethi

Barnard College, Columbia University; Santa Fe Institute

Date Written: November 16, 1998

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 dominant actions are played with probability 1 can be unstable. Sufficient conditions for the instability of equilibria are provided for symmetric and asymmetric games.

JEL Classification: C72

Suggested Citation

Sethi, Rajiv, Stability of Equilibria in Games with Procedurally Rational Players (November 16, 1998). Barnard College, Working Paper No. 99-04, Available at SSRN: https://ssrn.com/abstract=140128 or http://dx.doi.org/10.2139/ssrn.140128

Rajiv Sethi (Contact Author)

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HOME PAGE: http://www.columbia.edu/~rs328/

Santa Fe Institute

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