Reputation and Repeated Bargaining with a Third Party∗

We study repeated bargaining between a privately informed long-run player and a sequence of short-run players. Should the players fail to reach an agreement, an unbiased yet imperfect third party is called upon to make a decision. In contrast to standard reputation models, the benefit from reputation is low. We construct a Markov perfect equilibrium and characterize its reputation building dynamics as a modified gambler’s ruin process. As the discount factor goes to 1, or as third party signals become more informative, the players adopt tougher bargaining postures and the third party is invoked for a wider range of beliefs. In each case, the probability of reputation building converges to a level strictly between 0 and 1. However, the two limiting cases differ in the number of third party signals invoked.