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On defining ex ante payoffs in games with diffuse prior

Publication ,  Journal Article
Ambrus, A; Kolb, A
Published in: Economic Theory
September 1, 2021

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.

Duke Scholars

Published In

Economic Theory

DOI

EISSN

1432-0479

ISSN

0938-2259

Publication Date

September 1, 2021

Volume

72

Issue

2

Start / End Page

445 / 472

Related Subject Headings

  • Economic Theory
  • 3803 Economic theory
  • 3801 Applied economics
  • 3502 Banking, finance and investment
  • 1403 Econometrics
  • 1402 Applied Economics
  • 1401 Economic Theory
 

Citation

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Ambrus, A., & Kolb, A. (2021). On defining ex ante payoffs in games with diffuse prior. Economic Theory, 72(2), 445–472. https://doi.org/10.1007/s00199-020-01292-y
Ambrus, A., and A. Kolb. “On defining ex ante payoffs in games with diffuse prior.” Economic Theory 72, no. 2 (September 1, 2021): 445–72. https://doi.org/10.1007/s00199-020-01292-y.
Ambrus A, Kolb A. On defining ex ante payoffs in games with diffuse prior. Economic Theory. 2021 Sep 1;72(2):445–72.
Ambrus, A., and A. Kolb. “On defining ex ante payoffs in games with diffuse prior.” Economic Theory, vol. 72, no. 2, Sept. 2021, pp. 445–72. Scopus, doi:10.1007/s00199-020-01292-y.
Ambrus A, Kolb A. On defining ex ante payoffs in games with diffuse prior. Economic Theory. 2021 Sep 1;72(2):445–472.
Journal cover image

Published In

Economic Theory

DOI

EISSN

1432-0479

ISSN

0938-2259

Publication Date

September 1, 2021

Volume

72

Issue

2

Start / End Page

445 / 472

Related Subject Headings

  • Economic Theory
  • 3803 Economic theory
  • 3801 Applied economics
  • 3502 Banking, finance and investment
  • 1403 Econometrics
  • 1402 Applied Economics
  • 1401 Economic Theory