Solving strategic bargaining with arbitrary one-sided uncertainty

Bilateral bargaining has received a lot of attention in the multi–agent literature and has been studied with different approaches. According to the strategic approach, bargaining is modeled as a non–cooperative game with uncertain information and infinite actions. Its resolution is a long–standing open problem and no algorithm addressing uncertainty over multiple parameters is known. In this paper, we provide an algorithm to solve bargaining with any kind of one–sided uncertainty. Our algorithm reduces a bargaining problem to a finite game, solves this last game, and then maps its strategies with the original continuous game. We prove that with multiple types the problem is hard and only small settings can be solved in exact way. In the other cases, we need to resort to concepts of approximate equilibrium and to abstractions for reducing the size of the game tree.