On the implementation of the L-Nash bargaining solution in two-person bargaining games

The ‘Nash program’ initiated by Nash (1953) is a research agenda aiming at representing every axiomatically determined cooperative solution to a game as a Nash outcome of a reasonable noncooperative bargaining game. The L–Nash solution first defined by Forgó (1983) is obtained as the limiting point of the Nash bargaining solution when the disagreement point goes to negative infinity in a fixed direction. In Forgó and Szidarovszky (2003), the L–Nash solution was related to the solution of multiciteria decision making and two different axiomatizations of the L–Nash solution were also given in this context. In this paper, finite bounds are established for the penalty of disagreement in certain special two–person bargaining problems, making it possible to apply all the implementation models designed for Nash bargaining problems with a finite disagreement point to obtain the L–Nash solution as well. For another set of problems where this method does not work, a version of Rubinstein's alternative offer game (1982) is shown to asymptotically implement the L–Nash solution. If penalty is internalized as a decision variable of one of the players, then a modification of Howard's game (1992) also implements the L–Nash solution.