Information Aggregation in Bargaining

We study information aggregation in a bilateral bargaining model with two-sided incomplete information. In particular, we consider the case in which the size of the common-value pie is stochastic (i.i.d. over time) and players receive private signals on the size of the pie each period. Efficient agreement is a stochastic rule; delay is efficient if the expected size of the today's pie is small and the discount factor is high. Hence information aggregation is crucial for efficiency. We consider a random-proposer bargaining in which the proposer can make an offer of the deal upon agreement, potentially with a message about its own signal. In the case of divisible pie without transfers, an equilibrium that attains efficient agreement rule exists unless the discount factor is in the intermediate range and the accuracy of information is high (except for perfect information). We also show that cheap talk does not expand the attainability of efficient equilibrium. In the case of indivisible pie with transfers, an equilibrium that attains efficient agreement rule exists if the transfer can take continuous values, whereas the attainability is limited if the transfer is discrete.