This paper studies games in which the players are not locked into their relationship for a fixed number of periods. We consider two-player games where player 1 can decide to let the opponent continue in the game or replace it with a new player. We also allow the possibility of player 2 quitting the game. When only layoffs can occur, cooperation takes place in finite horizons due to the threat that termination of the relationship imposes on player 2. However, quits limit that cooperation to those cases where the outside option for player 2 is small (lower than some Nash equilibrium of the stage game).
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