Robust Bilateral Trade and Mediated Bargaining

We consider bilateral trade problems subject to incomplete information on the reservation values of the agents. We address negotiations where the communication of proposals takes place through the filter of a third party, a mediator: traders submit proposals over continuous time to the mediator that receives bids and keeps them secret until they are compatible. A regular robust equilibrium (RRE) is an (undominated) ex post equilibrium where (with sufficient delay) all compatible traders reach agreement. We present a characterization of RRE for risk-neutral traders that discount the future at the same exponential rate. We show how to compute RRE strategy profiles, and we explicitly display the unique one where agreements split the net surplus in equal shares. Our results support the claim that bargaining through a mediator is an effective procedure to promote efficiency.