The Folk Theorem for Irreducible Stochastic Games with Imperfect Public Monitoring

32 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: March 5, 2010


In an irreducible stochastic game, no single player can prevent the stochastic process on states from being irreducible, so the other players can ensure that the current state has little effect on events in the distant future. This paper introduces stochastic games with imperfect public signals, and provides a sufficient condition for the folk theorem when the game is irreducible, thus generalizing the folk theorems of Dutta (1995) and Fudenberg, Levine, and Maskin (1994). To prove this theorem, the paper extends the concept of self-generation (Abreu, Pearce, and Stachetti (1990)) to "return generation," which explicitly tracks actions and incentives until the next time the state returns to its current value, and asks that players not wish to deviate given the way their continuation payoffs from the time of this return depend on the public signals that have been observed.

Keywords: Stochastic Game, Public Monitoring, Perfect Public Equilibrium, Folk Theorem

Suggested Citation

Fudenberg, Drew and Yamamoto, Yuichi, The Folk Theorem for Irreducible Stochastic Games with Imperfect Public Monitoring (March 5, 2010). Available at SSRN: or

Drew Fudenberg (Contact Author)

Massachusetts Institute of Technology (MIT) ( email )

77 Massachusetts Avenue
50 Memorial Drive
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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