Bilateral matching and bargaining with private information

We study equilibria of a dynamic matching and bargaining game (DMBG) with two-sided private information bilateral bargaining. The model is a private information replica of Mortensen and Wright (2002). There are two kinds of frictions: time discounting and explicit search costs. A simple necessary and sufficient condition on parameters for existence of a nontrivial equilibrium is obtained. This condition is the same regardless whether the information is private or not. In addition, it is shown that when the discount rate is sufficiently small, the equilibrium is unique and has the property that every meeting results in trade.