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Some Asymptotic Results in Discounted Repeated Games of One-Sided Incomplete Information

John M. Olin School of Business, Washington University in St. Louis, 1 Brookings Drive, St. Louis, MO 63130-4899
University of Edinburgh, Edinburgh, Scotland, UK
cripps{at}olin.wustl.edu
jps{at}st-and.ac.uk

The paper analyzes the Nash equilibria of two-person discounted repeated games with one-sided incomplete information and known own payoffs. If the informed player is arbitrarily patient, relative to the uninformed player, then the characterization for the informed player's payoffs is essentially the same as that in the undiscounted case. This implies that even small amounts of incomplete information can lead to a discontinuous change in the equilibrium payoff set. For the case of equal discount factors, however, and under an assumption that strictly individually rational payoffs exist, a result akin to the Folk Theorem holds when a complete information game is perturbed by a small amount of incomplete information.

Key Words: Reputation; Folk Theorem; repeated games; incomplete information
History: Received: August 1, 1998; revision received: June 1, 2000;revision received: July 1, 2001;revision received: December 1, 2002;