Reputation Effects and Equilibrium Degeneracy in Continuous-Time Games

51 Pages Posted: 27 Aug 2007

See all articles by Eduardo Faingold

Eduardo Faingold

Insper Institute of Education and Research

Yuliy Sannikov

University of California, Berkeley - Department of Economics; Princeton University - Department of Economics

Date Written: August 2007

Abstract

We study a class of continuous-time reputation games between a large player and a population of small players in which the actions of the large player are imperfectly observable. The large player is either a normal type, who behaves strategically, or a behavioral type, who is committed to playing a certain strategy. We provide a complete characterization of the set of sequential equilibrium payoffs of the large player using an ordinary differential equation. In addition, we identify a sufficient condition for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. An implication of our characterization is that when the small players are certain that they are facing the normal type, intertemporal incentives are trivial: the set of equilibrium payoffs of the large player coincides with the convex hull of the set of static Nash equilibrium payoffs.

Keywords: Repeated games, Reputation, Continuous time

JEL Classification: C73

Suggested Citation

Faingold, Eduardo and Sannikov, Yuliy, Reputation Effects and Equilibrium Degeneracy in Continuous-Time Games (August 2007). Cowles Foundation Discussion Paper No. 1624. Available at SSRN: https://ssrn.com/abstract=1010187

Eduardo Faingold (Contact Author)

Insper Institute of Education and Research ( email )

R Quata 300
Sao Paulo, 04542-030
Brazil

HOME PAGE: http://www.eduardofaingold.com

Yuliy Sannikov

University of California, Berkeley - Department of Economics ( email )

549 Evans Hall #3880
Berkeley, CA 94720-3880
United States

Princeton University - Department of Economics

Princeton, NJ 08544-1021
United States

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