A Model of Bargaining with Incomplete Information Edi Karni and Shmuel Zamir Johns Hopkins University and Hebrew University (preliminary draft of a work in progress; Comments are welcome.) October 11, 2006 Abstract We study the equilibrium outcomes of two-person bargaining problems in which each party has “outside option” known only to himself. We ex- amin two game forms, a sequential-move game and a simulteneous-move game. In this context we discuss the failure to reach agreements and the loss of efficiency thereof. Invoking the analogy between the sequential- move game and the familiar ultimatum game we also provide new inter- pretation of the experimental evidence regarding the players behavior in the ultimatum game. 1 Introduction In reality many bargaining end with disagreement leading, depending on the context, to strikes, wars, dissolution of partnerships, failure of buyer and seller to agree on a price etc. It is conceivable that sometimes the failure to reach an agreement is due to the bargaining strategies employed by the parties. In other words, it is conceivable that, in a given bargaining situation, the parties fail to reach an agreements even though there exist agreements beneficial to both parties. In this paper we explore this possibility. We model the bargaining as a game of incomplete information. We assume that the bargaining is over the division of a given resource, and that the parties present their demands, sequentially or simultaneously. If the demands are com- patible with the available resource, then the parties get their demand and split the surplus if such surplus is available. The incomplete information aspect of the model is intended to capture the idea that, when engaged in bargaining, the two parties involved have “outside options,” representing their best alternative available only in case they fail to reach an agreement. Moreover, while both parties are aware of this fact, the value of the outside option is private informa- tion. In this framework, we show that, not only it is possible that the parties may fail to agree, but it is possible that this failure entails a welfare loss in the Pareto sense, namely, they end up with their outside options that are inferior 1