The Harsanyi Solution to the Bargaining Problem

In the present chapter we introduce several generalizations to the formulation and solution of the bargaining problem. Until the early 1960s, the study of social power (including political power) had been carried out exclusively by social scholars. That changed in 1962, when Harsanyi managed to introduce the rigor of mathematical reasoning into the theory of social power. He achieved this by applying the analytical tools and models of game theory. In addition to certain significant contributions, Harsanyi provided a clear interpretation which eliminated much of the ambiguity that had plagued the theory of social power prior to the publication of Harsanyi’s works on the subject (Harsanyi 1962a, 1962b). Chapter 2 focused on Nash’s two-person bargaining problem which treats the bargaining parties’ conflict payoffs as given. This formulation suffers from two important drawbacks in the context of political policy formation. First, in many real world cases, the threats can actually be decided by the parties themselves. Nash himself recognized this and in a 1953 paper presented a model in which the determination of the threat payoff is the reflection of the parties’ strategic choices. In Section 3.2 we describe this more general model. Second, Nash’s original formulation of the bargaining problem dealt exclusively with the two-person bargaining problem. However, more often than not, the number of bargaining