Reputation with Long Run Players and Imperfect Observation,” working paper

Previous work shows that reputation results may fail in repeated games between two long-run players with equal discount factors. We restrict attention to an infinitely repeated game where two players with equal discount factors play a stage game where actions are imperfectly observed and the first mover advantage is maximal. The set of types for player 1 is taken as any countable subset of the set of all finite automaton. In this context a one sided reputation result is provided. If player 1 is a Stackelberg type with positive probability and player 2’s actions are imperfectly observed, then player 1 receives the highest individually rational payoff in all Bayes Nash equilibria, as agents become patient