Maintaining a Reputation When Strategies Are Imperfectly Observed.

This paper studies reputation effects in games with a single long-run player whose choice of stage-game strategy is imperfectly observed by his opponents. The authors obtain lower and upper bounds on the long-run player's payoff in any Nash equilibrium of the game. If the long-run player's stage-game strategy is statistically identified by the observed outcomes, then, for generic payoffs, the upper and lower bounds both converge, as the discount factor tends to one, to the long-run player's Stackelberg payoff, which is the most he could obtain by publicly committing himself to any strategy. Copyright 1992 by The Review of Economic Studies Limited.