Repeated Games Where the Payoffs and Monitoring Structure are Unknown

39 Pages Posted: 11 Nov 2010

See all articles by Drew Fudenberg

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Yuichi Yamamoto

University of Pennsylvania; Harvard University

Date Written: September 1, 2010


This paper studies repeated games with imperfect public monitoring where the players are uncertain both about the payoff functions and about the relationship between the distribution of signals and the actions played. We introduce the concept of perfect public ex post equilibrium (PPXE), and show that it can be characterized with an extension of the techniques used to study perfect public equilibria. We develop identifiability conditions that are sufficient for a folk theorem; these conditions imply that there are PPXE in which the payoffs are approximately the same as if the monitoring structure and payoff functions were known. Finally, we define perfect type-contingently public ex post equilibria (PTXE), which allows players to condition their actions on their initial private information, and we provide its linear programming characterization.

Keywords: Repeated Game, Public Monitoring, Incomplete Information, Perfect Public Equilibrium, Folk Theorem, Belief-Free Equilibrium, Ex Post Equilibrium

Suggested Citation

Fudenberg, Drew and Yamamoto, Yuichi, Repeated Games Where the Payoffs and Monitoring Structure are Unknown (September 1, 2010). Econometrica Vol. 78, No. 5, p. 1673, September 2010, Available at SSRN:

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
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Cambridge, MA 02139-4307
United States

Yuichi Yamamoto

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

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