Epistemic Conditions for Rationalizability

31 Pages Posted: 6 May 2006

See all articles by Eduardo Zambrano

Eduardo Zambrano

California State Polytechnic University, San Luis Obispo - Economics

Date Written: August 2005

Abstract

In this paper I show that, just as with Nash Equilibrium, there are sparse conditions, not involving common knowledge of rationality, that lead to (correlated) rationalizability. The basic observation is that, if the actual world belongs to a set of states where the set Z of action profiles is played, each player knows her own payoffs, everyone is rational and it is mutual knowledge that the action profiles played are in Z, then the actions played at the actual world are rationalizable actions. Alternatively, if at the actual world the support of the conjecture of player i is Di, there is mutual knowledge of: (i) the game being played, (ii) that the players are rational, and (iii) that for every i the support of the conjecture of player i is contained in Di, then every strategy in the support of the conjectures is rationalizable. The results do not require common knowledge of anything, are valid for games with any number of players, and extend to refinements of rationalizability such as independent rationalizability and rationalizable conjectural equilibrium.

Keywords: Rationalizability, Iterated Strict Dominance, Interactive Epistemology

JEL Classification: C70

Suggested Citation

Zambrano, Eduardo, Epistemic Conditions for Rationalizability (August 2005). Available at SSRN: https://ssrn.com/abstract=899376 or http://dx.doi.org/10.2139/ssrn.899376

Eduardo Zambrano (Contact Author)

California State Polytechnic University, San Luis Obispo - Economics ( email )

Orfalea College of Business
San Luis Obispo, CA 93407
United States
805-756-5327 (Phone)
805-756-1473 (Fax)

HOME PAGE: http://calpoly.edu/~ezambran

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