An epistemic analysis of the Harsanyi transformation

Harsanyi (1967–68) proposed a method for transforming uncertainty over the strategy sets of players into uncertainty over their payoffs. The transformation appears to rely on an assumption that the players are rational, or, indeed, that they are rational and that there is common belief of rationality. Such an assumption would be awkward from the perspective of the epistemic program, which is often interested in the implications of irrationality or a lack of common belief of rationality. This paper shows that without common belief of rationality, such implications are not necessarily maintained under a Harsanyi transformation. The paper then shows how, with the belief-system model of Aumann and Brandenburger (1995), such implications can be maintained in the absence of common belief of rationality. Received: December 2000/Revised: February 2002