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. We 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 1, to the long-run player's Stackelberg payoff, which is the most he could obtain by publicly committing himself to any strategy.