On Defining Ex Ante Payoffs in Games with Diffuse Prior

Abstract

We formalize the notion of a diffuse prior and show that, in stationary games, strategies which admit well-defined expected payoffs under the diffuse prior are essentially stationary. We define the diffuse prior through a limit construction, using sequences of well-defined priors that become increasingly dispersed. Admissible strategies are those for which ex ante payoffs along these sequences converge to a limit that does not depend on the particular sequence. A secondary contribution of the paper is a generalization of the concept of distributional strategies (Milgrom and Weber, 1985) to multistage games.