Characterization of all individually monotonic bargaining solutions
The paper deals with Nash's two-person bargaining problem (a bargaining problem is a pair consisting of a convex compact set in \({\mathbb{R}}^ 2\) and a fixed element called disagreement point; a solution is a function assigning to each bargaining problem (S,d) its bargaining solution which is an element of S). The authors consider solutions satisfying the usual conditions of Individual Rationality, Pareto Optimality and Independence of Equivalent Utility Representations (here referred to as 1-3) as well as Kalai and Smorodinsky's condition of Individual Monotonicity (4) or its ''global'' version (4') [see \textit{E. Kalai} and \textit{M. Smorodinsky}, Econometrica 43, 513-518 (1975; Zbl 0308.90053)]. The main results of the paper establish a correspondence between solutions satisfying (1-4) (resp. 1-3,4') and coordinate-wise non- decreasing curves joining the interval \([(0,1);(1,0)]\subset {\mathbb{R}}^ 2\) with the point (1,1) (resp. joining (0,0) with (1,1)). Simple remarks also concern continuity and risk sensitivity of solutions satisfying (1- 4) or (1-3,4').
scientific article; zbMATH DE number 3936969
scientific article