Econometrica: May 2011, Volume 79, Issue 3

Reputation in Continuous‐Time Games

https://doi.org/10.3982/ECTA7377
p. 773-876

Eduardo Faingold, Yuliy Sannikov

We study reputation dynamics in continuous‐time games in which a large player (e.g., government) faces a population of small players (e.g., households) and the large player's actions are imperfectly observable. The major part of our analysis examines the case in which public signals about the large player's actions are distorted by a Brownian motion and the large player is either a , who plays strategically, or a , who is committed to playing a stationary strategy. We obtain a clean characterization of sequential equilibria using ordinary differential equations and identify general conditions for the sequential equilibrium to be unique and Markovian in the small players' posterior belief. We find that a rich equilibrium dynamics arises when the small players assign positive prior probability to the behavioral type. By contrast, when it is common knowledge that the large player is the normal type, every public equilibrium of the continuous‐time game is payoff‐equivalent to one in which a Nash equilibrium is played after every history. Finally, we examine variations of the model with Poisson signals and multiple behavioral types.

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Supplemental Material

Supplement to "Reputation in Continuous-Time Games"

Appendix for manuscript that shows in the reputation games (section 7), if a continuous-time public randomization device is available, then a Markov perfect equilibrium in publicly randomized strategies exists under Conditions 1 and 4.

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