A Non-cooperative Bargaining Theory with Incomplete Information: Verifiable Types

We consider a non-cooperative sequential bargaining game with incomplete information where two players negotiate for mechanisms with ex post verifiable types at the interim stage. We prove the existence of a stationary sequential equilibrium of the bargaining game where the ex post Nash bargaining solution with no delay is asymptotically implemented with probability one. Further, the ex post Nash bargaining solution is a unique outcome of a stationary equilibrium under the property of Independence of Irrelevant Types (IIT), whereby the response of every type of a player is independent of allocations proposed to his other types, and under a self-selection property of their belief. Interim efficiency (insurance benefit) in the Bayesian bargaining problem is not necessarily supported in a non-cooperative approach.