Counterfactual Reasoning and Common Knowledge of Rationality in Normal Form Games
Topics in Theoretical Economics, Vol. 4, No. 1, 2004
Posted: 8 Jun 2006
When evaluating the rationality of a player in an epistemic model of a noncooperative game one has to examine counterfactuals such as ``what would happen if the player were to do what he actually does not do?'' In this paper I develop an epistemic 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 actually does not do'' at the world that is closest to the actual world in which the hypothetical deviation actually occurs. I show that, in this extended model, common knowledge of rationality need not lead to rationalizability. I also present assumptions that allow rationalizability to be a consequence of common knowledge of rationality in this extended model. These assumptions suggest that it may be misleading to believe that, from an epistemic point of view, rationalizability relies on weaker assumptions about belief consistency than Nash equilibrium.
Keywords: Common knowledge, counterfactual reasoning, interactive epistemology
JEL Classification: C70, D83
Suggested Citation: Suggested Citation