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 though 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 Robust regular equilibrium (RRE) is an (undominated) ex-post equilibria where (with sufficient delay) all compatible traders reach agreement. We present a characterizion of RRE for environments with 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 trough a mediator is an effective procedure to promote efficiency. ∗Čopič is at Cowles Foundation, Yale and UCLA ([email protected]) and Ponsat́ı is at Institut d’Anàlisi Econòmica -CSIC, Barcelona ([email protected]).