Nash Bargaining Via Flexible Budget Markets

We initiate a study of Nash bargaining games [Nas50] via combinatorial, polynomial time algorithms and we carry this program over to solving nonsymmetric bargaining games of Kalai [Kal77] as well. Since the solution to a Nash bargaining game is also the optimal solution to the corresponding convex program, this involves obtaining a combinatorial algorithm for the latter. This in turn can be viewed as the problem of finding an equilibrium for a market in a new model, called a flexible budget market. Our main result pertains to a natural Nash bargaining game derived from the linear case of the Arrow-Debreu market model. The structural insights gained from the combinatorial nature of our algorithms has led to novel insights into game-theoretic properties of the solution concepts of Nash and nonsymmetric bargaining games, see [CGV09]. ∗College of Computing, Georgia Institute of Technology, Atlanta, GA 30332–0280, E-mail: [email protected].