Abstrakt
We are concerned with modeling situations in which rational individuals can conclude profitable agreements but they may disagree about which agreement to conclude. Since Nash's papers on bargaining and Raiffa's studies on arbitration in the beginning of 1950's, it has been customary to formulate this problem as a nonempty collection B of pairs (S, d) where each S from B is a nonempty subset of a finite-dimensional real linear space IRn and d is a point in S.
The elements of S are usually interpreted as the utility tuples that the players can obtain by cooperating, and d as the outcome when the players do not cooperate. We deal with point-valued solutions; that is, we wish to find a mapping from B into IRn which satisfies some plausible conditions like; for example, individual rationality, Pareto optimality, anonymity.
First we present major models (some old, some recent) and their solution concepts. Then we propose some directions for future research.
In particular, we discuss some of the solution functions that are called sequential solutions or stepwise solutions. These solutions are constructed with the help of two functions defined on B: a step function that gradually changes the point d while S is kept unchanged, and a solution function that assigns to (S,d) the limit of the sequence of points constructed by the step function.