Sequential Bargaining Mechanisms

A buyer and a seller are engaged in the trade of a single object. Each agent has private information about his preferences and is impatient in that delaying agreement is costly. In such a setting, a sequential bargaining mechanism is defined as a set of outcome functions that determine the time of agreement and payment between parties, given the parties reports of their private information. Necessary and sufficient conditions for a sequential bargaining mechanism to be individually rational and incentive compatible are derived. In addition to incentive compatibility and individual rationality, it is natural in situations where the bargainers are unable to commit to particular strategies to require that the bargaining mechanism be sequentially rational: negotiations must continue so long as the bargainers expect positive gains from continuing. The set of mechanisms (called perfect bargaining mechanisms) that satisfy incentive compatibility, individual rationality, and sequential rationality is analyzed. From the class of perfect bargaining mechanisms, those bargaining schemes that maximize the players ex ante utility are determined. It is shown that when the sellers delay costs are greater than the buyers, there exist perfect bargaining mechanisms that ex ante dominate the most efficient static mechanisms; whereas, when the buyers delay costs are higher, a static mechanism is optimal.