Commitments to Threat Strategies in Nash Bargaining

Nash's two-person bargaining model consists of two stages: threat strategies and utility demands are chosen in the first and second stages respectively. Here players commit to play the threat strategies chosen in the first stage for the case where disagreement occurs in the second stage. Whether a player commits or not to play a threat strategy, however, is voluntary in principle. This leads to some possible extensions of Nash's model so that players' commitment choices are taken into account. In this paper, we consider three extensions. In the two person case, these three extensions give essentially the same result as that given by Nash. This is not the case for more than two players; the result depends upon an extension. In one extension, Nash's result always holds for more than two players. In the other two extensions, however, we give a three person example where not all players choose commitments in equilibrium.