Gambling Reputation: Repeated Bargaining With Outside Options

Authors

  • Jihong Lee,

    1. Dept. of Economics, Seoul National University, Seoul 151-746, Korea; jihonglee@snu.ac.kr
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  • Qingmin Liu

    1. Dept. of Economics, Columbia University, 420 West 118th Street, New York, NY 10027, U.S.A.; qingmin.liu@columbia.edu
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    • The authors are grateful to a co-editor and the anonymous referees for their insightful suggestions. We also thank Heski Bar-Isaac, Yeon-Koo Che, Drew Fudenberg, Johannes Hörner, Navin Kartik, Mark Machina, George Mailath, Paul Niehaus, Nicola Persico, Hamid Sabourian, Larry Samuelson, Andrzej Skrzypacz, and Robert Wilson, as well as seminar participants at a number of institutions and conferences. Klaus Schmidt kindly sent us his doctoral dissertation, and Euncheol Shin and Jangsu Yoon provided excellent research assistance. Jihong Lee's research was supported by a National Research Foundation Grant funded by the Korean government (NRF-2011-330-B00063).


Abstract

We study the role of incomplete information and outside options in determining bargaining postures and surplus division in repeated bargaining between a long-run player and a sequence of short-run players. The outside option is not only a disagreement point, but reveals information privately held by the long-run player. In equilibrium, the uninformed short-run players' offers do not always respond to changes in reputation and the informed long-run player's payoffs are discontinuous. The long-run player invokes inefficient random outside options repeatedly to build reputation to a level where the subsequent short-run players succumb to his extraction of a larger payoff, but he also runs the risk of losing reputation and relinquishing bargaining power. We investigate equilibrium properties when the discount factor goes to 1 and when the informativeness of outside options diffuses. In both cases, bargaining outcomes become more inefficient and the limit reputation-building probabilities are interior.

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