A New Approach to the Nash Bargaining Problem

Abstract

This paper explores a new approach to the Nash bargaining problem in which the axiom of symmetry is dropped and it is assumed that the final allocation depends on both the status quo and the threat point. The resulting final allocation, unlike that formalized by Nash, cannot be represented by a simple analytic expression; rather, it leads to a whole class of solutions. Properties of the final allocation are analyzed. It is shown that for every initial allocation there exists a Nash fiber, corresponding to the Nash allocation, that it is possible to determine the sign of the derivatives of the final allocation with respect to changes in the threat point, and that a Slutsky-like equation relates these derivatives to the derivatives with respect to the initial allocation. It is also shown that, under certaiia conditions, as play is repeated the final allocation asymptotically converges to the Nash allocation.