Published in Topics in Theoretical Economics, Volume 4, Issue 1, November 10, 2004. Article 8. 25 pages. Copyright © 2004 by the author. This article is also available at http://www.bepress.com/bejte/topics/vol4/iss1/art8.
NOTE: At the time of publication, the author Eduardo Zambrano was not yet affiliated with Cal Poly.
When evaluating the rationality of a player in a game one has to examine counterfactuals such as "what would happen if the player were to do what he does not do?" In this paper I develop a model of a normal form game where counterfactuals of this sort are evaluated as in the philosophical literature (cf. Lewis, 1973; Stalnaker, 1968). According to this method one evaluates a statement like ``what would the player believe if he were to do what he does not do'' at the world that is closest to the actual world where the hypothetical deviation occurs. I show that in this model common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to follow from common knowledge of rationality. These assumptions suggest that rationalizability may not rely on weaker assumptions about belief consistency than Nash equilibrium.