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Learning from Private Information in Noisy Repeated Games

65 Pages Posted: 7 Nov 2010  

Drew Fudenberg

Massachusetts Institute of Technology (MIT)

Yuichi Yamamoto

University of Pennsylvania; Harvard University

Date Written: November 3, 2010

Abstract

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games with incomplete information where players observe imperfect public signals of the actions and the map from actions to signal distributions is itself unknown. The PTXE payoffs when players are patient are determined by the intersection of the maximal half spaces in various directions; we focus on the "cross-state" directions that consider payoffs in two or more states. We develop conditions under which the maximal half spaces in these directions impose no constraints on the equilibrium set, so that equilibrium play can be as if the players have learned the state. We use these conditions to provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.

Keywords: repeated game, public monitoring, incomplete information, perfect public equilibrium, folk theorem, belief-free equilibrium, ex-post equilibrium

JEL Classification: C72, C73

Suggested Citation

Fudenberg , Drew and Yamamoto, Yuichi, Learning from Private Information in Noisy Repeated Games (November 3, 2010). Available at SSRN: https://ssrn.com/abstract=1703580 or http://dx.doi.org/10.2139/ssrn.1703580

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

Yuichi Yamamoto

Harvard University ( email )

1875 Cambridge Street
Cambridge, MA 02138
United States

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

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