Sequential bargaining mechanisms

A fundamental problem in economics is determining how agreements are reached in situations where the parties have some market power. Of particular interest are questions of efficiency and distribution: • How efficient is the agreement? • How can efficiency be improved? • How are the gains from agreement divided among the parties? Here, I explore these questions in the context of bilateral monopoly, in which a buyer and a seller are bargaining over the price of an object. Two features of my analysis, which are important in any bargaining setting, are information and impatience. The bargainers typically have private information about their preferences and will suffer some delay costs if agreement is postponed. Information asymmetries between bargainers will often lead to inefficiencies: The bargainers will be forced to delay agreement in order to communicate their preferences. Impatience will tend to encourage an early agreement and will make the parties' communication meaningful. Bargainers with high delay costs will accept inferior terms of trade in order to conclude agreement early, whereas patient bargainers will choose to wait for more appealing terms of trade. Some authors have examined the bargaining problem in a static context, focusing solely on the role of incomplete information and ignoring the sequential aspects of bargaining. Myerson and Satterthwaite (1983) analyze bargaining as a direct revelation game. In this game, the players agree to a pair of outcome functions: one that maps the players' statements of their types into an expected payment from buyer to seller, and one that maps the players' statements into a probability of trade. These outcome functions are chosen in such a way that truthful reporting is an equilibrium strategy for the players. An important feature of this game is that it is static: Outcome functions are selected, the players report their true types, and then dice are rolled to determine the payment and whether or not trade occurs. To ensure that the players have the proper incentives for truthful reporting, the game will end with positive probability in disagreement even when there are substantial gains from trade. Thus, in the event that the randomization device calls for disagreement, the players may find themselves in a situation in which it is common knowledge that there are gains from trade. Chatterjee and Samuelson (1983) analyze a strategic game in which both players make offers simultaneously, and trade occurs at a price between the two offers if …