Private Monitoring with Infinite Histories

Posted: 25 Jul 2008

See all articles by Christopher Phelan

Christopher Phelan

Federal Reserve Bank of Minneapolis

Andrzej Skrzypacz

Stanford University - Stanford Graduate School of Business

Date Written: November 1, 2006

Abstract

This paper develops new recursive methods for studying stationary sequential equilibria in games with private monitoring. We first consider games where play has occurred forever into the past and develop methods for analyzing a large class of stationary strategies, where the main restriction is that the strategy can be represented as a finite automaton. For a subset of this class, strategies which depend only on the players' signals in the last k periods, these methods allow the construction of all pure strategy equilibria. We then show that each sequential equilibrium in a game with infinite histories defines a correlated equilibrium for a game with a start date and derive simple necessary and sufficient conditions for determining if an arbitrary correlation device yields a correlated equilibrium. This allows, for games with a start date, the construction of all pure strategy sequential equilibria in this subclass.

Keywords: Private Monitoring, Repeated Games

JEL Classification: C73

Suggested Citation

Phelan, Christopher J. and Skrzypacz, Andrzej, Private Monitoring with Infinite Histories (November 1, 2006). Available at SSRN: https://ssrn.com/abstract=1172044

Christopher J. Phelan (Contact Author)

Federal Reserve Bank of Minneapolis ( email )

90 Hennepin Avenue
Minneapolis, MN 55480
United States
612-204-5615 (Phone)

HOME PAGE: http://phelan.mpls.frb.fed.us

Andrzej Skrzypacz

Stanford University - Stanford Graduate School of Business ( email )

655 Knight Way
Stanford, CA 94305-5015
United States
650-736-0987 (Phone)
650-725-9932 (Fax)

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