Nonconvex \(n\)-person bargaining: efficient maxmin solutions
type: Item
instance of: scholarly article
title: Nonconvex \(n\)-person bargaining: efficient maxmin solutions
zbMATH Open document ID: 1032.91059
author: Jens Leth Hougaard
author: Mich Tvede
published in: Economic Theory
publication date: 2003-03-25T00:00:00Z
review text: 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.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 91B26
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A22
Mathematics Subject Classification ID: 91B40
Mathematics Subject Classification ID: 91A06
zbMATH DE Number: 1887528
zbMATH Keywords: non-convex \(n\)-person bargaining
zbMATH Keywords: axiomatic approach
zbMATH Keywords: Kalai-Smorodinsky solution
zbMATH Keywords: unique efficient maxmin solution
zbMATH Keywords: decision-theoretic systems
zbMATH Keywords: evolutionary game-theoretic models
MaRDI profile type: Publication
full work available at URL: s00199-001-0246-7
OpenAlex ID: W1969826050
DOI: 10.1007/S00199-001-0246-7
description: scientific article; zbMATH DE number 1887528