Motivation and Design of the Study

Abstract

In his fundamental paper of 1950, Nash constructs a model of a bargaining situation with two persons and formulates a set of axioms which uniquely characterize a bargaining solution, the so-called Nash solution. In Nash’s model preferences of the persons over a set X of feasible alternatives are expressed by cardinal v. Neumann-Morgenstern utility functions. Among the alternatives in X there exists a certain alternative xo, the alternative of disagreement, often called status quo. In the general case of n ≥ 2 persons, the pair (X,x 0 ) is mapped by the utility functions of the persons onto a pair (S, d) in an n-dimensional utility space. (S,d) is called a bargaining situation with n persons, if S is a convex and compact subset of \( {{\mathbb{R}}^{n}} \), if d is an element in S,and if there exists an alternative x with an image s in S such that every person strictly prefers x to x0, i.e. s > d. For every bargaining situation a bargaining solution f selects a point f (S,d) in S.