COMMITMENTS TO THREAT STRATEGIES IN NASH BARGAINING

Nash's two-person bargaining model consists of two stages: threat stra tegies and utility demands are chosen in the first and second stages r espectively. Here players commit to play the threat strategies chosen in the first stage for the case where disagreement occurs in the secon d stage. Whether a player commits or not to play a threat strategy, ho wever, is voluntary in principle. This leads to some possible extensio ns of Nash's model so that players' commitment choices are taken into account. In this paper, we consider three extensions. In the two perso n case, these three extensions give essentially the same result as tha t given by Nash. This is not the case for more than two players; the r esult depends upon an extension. In one extension, Nash's result alway s holds for more than two players. In the other two extensions, howeve r, we give a three person example where not all players choose commitm ents in equilibrium.