We consider an infinite dynamic game played by one large player and a large number of small players. State variables are allowed, and public histories include only the play of the large player, the aggregate play of the small players and the aggregate state variable. We use a reputational...

We analyze in a game between a patient player 1 and a non-myopic but less patient opponent, player 2. We assume that Player 1's type is private information and that players do not directly observe each other's action but rather see an imperfect signal of it. We show that in any Nash equilibrium...