On defining ex ante payoffs in games with diffuse prior

Journal Article (Journal Article)

While the diffuse prior has been widely used in applied economic theory for its technical convenience and as a way of modeling complete lack of knowledge, it is not formally defined, nor are ex ante payoffs in games under this prior. In this paper, we provide a formal treatment of the diffuse prior which can validate its application in games. We consider stationary games, in which players’ signals are translation invariant in the true state and players’ payoffs are translation invariant in actions together with the state. We show that strategies which admit well-defined expected payoffs under the diffuse prior are essentially stationary, being almost translation invariant in signals. Our analysis builds on two formal definitions. We define the diffuse prior through a limit construction, using sequences of well-defined priors that become increasingly dispersed. A class of strategy profiles is admissible if for any strategy profile, each player’s ex ante payoff along these sequences converges to a limit that does not depend on the particular sequence. A secondary contribution of the paper is an extension of the concept of distributional strategies (Milgrom and Weber in Math Oper Res 10:619–632, 1985) to a class of multistage games.

Full Text

Duke Authors

Cited Authors

  • Ambrus, A; Kolb, A

Published Date

  • September 1, 2021

Published In

Volume / Issue

  • 72 / 2

Start / End Page

  • 445 - 472

Electronic International Standard Serial Number (EISSN)

  • 1432-0479

International Standard Serial Number (ISSN)

  • 0938-2259

Digital Object Identifier (DOI)

  • 10.1007/s00199-020-01292-y

Citation Source

  • Scopus