Belief-Free Equilibria in Games with Incomplete Information: Characterization and Existence

71 Pages Posted: 4 Nov 2009

See all articles by Johannes Horner

Johannes Horner

Yale University - Cowles Foundation

Stefano Lovo

HEC Paris - Finance Department

Tristan Tomala

Université Paris I Panthéon-Sorbonne

Date Written: November 3, 2009

Abstract

We characterize belief-free equilibria in infinitely repeated games with incomplete information with N \ge 2 players and arbitrary information structures. This characterization involves a new type of individual rational constraint linking the lowest equilibrium payoffs across players. The characterization is tight: we define a set of payoffs that contains all the belief-free equilibrium payoffs; conversely, any point in the interior of this set is a belief-free equilibrium payoff vector when players are sufficiently patient. Further, we provide necessary conditions and sufficient conditions on the information structure for this set to be non-empty, both for the case of known-own payoffs, and for arbitrary payoffs.

Keywords: Repeated games with incomplete information, Harsanyi doctrine, Belief-free equilibria

JEL Classification: C72, C73

Suggested Citation

Horner, Johannes and Lovo, Stefano and Tomala, Tristan, Belief-Free Equilibria in Games with Incomplete Information: Characterization and Existence (November 3, 2009). Cowles Foundation Discussion Paper No. 1739, Available at SSRN: https://ssrn.com/abstract=1499243 or http://dx.doi.org/10.2139/ssrn.1499243

Johannes Horner (Contact Author)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States

Stefano Lovo

HEC Paris - Finance Department ( email )

1 rue de la Liberation
Jouy-en-Josas Cedex, 78351
France

Tristan Tomala

Université Paris I Panthéon-Sorbonne ( email )

12, place du Panthéon
Paris, IL
France

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