Nonconvex \(n\)-person bargaining: efficient maxmin solutions
The present paper investigates an axiomatic characterization of non-convex \(n\)-person bargaining problems. The authors introduce the family of efficient maxmin solutions, which can be seen as generalizations of the Kalai-Smorodinsky solution to non-convex \(n\)-person bargaining. These solutions are shown to be derivable from the four axioms of non-convex \(n\)-person bargaining systems: Pareto optimality, restricted symmetry, restricted affine invariance, and comprehensive monotonicity (instead of the classical Nash's axiom of independence of irrelevance alternatives). Since for certain bargaining problems there exist several efficient maxmin solutions, the paper examines the question of (non-)uniqueness of the bargaining solution concept. This question is solved as follows: the authors consider the set of bargaining problems for which the payoff sets are unions of compact \(C^2\)-manifolds, and this set is endowed with the Whitney topology. In this settlement it is proved that for an open and dense set of bargaining problems, there is a unique efficient maxmin solution; this fact can be interpreted as follows: in the considered conditions of regularity, typically bargaining problems have a unique efficient maxmin solution. The consequences of the proposed axiomatic approach are interesting, at least from two points of view: (a) Bargaining problems can be embedded naturally within a decision-theoretic framework where maxmin rules are known to be met in Hurwicz's maxmin criterion and Rawls' criterion of distributive justice. (b) Bargaining solutions can be implemented in extensive form games, being obtained as outcomes in evolutionary game-theoretic models.
scientific article; zbMATH DE number 1887528