Characterization of all individually monotonic bargaining solutions
type: Item
instance of: scholarly article
title: Characterization of all individually monotonic bargaining solutions
zbMATH Open document ID: 0584.90101
DOI: 10.1007/BF01769309
author: Hans Peters
author: Stef Tijs
published in: International Journal of Game Theory
publication date: 1985-01-01T00:00:00Z
review text: 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').
Mathematics Subject Classification ID: 91A12
Mathematics Subject Classification ID: 91A05
zbMATH DE Number: 3936969
zbMATH Keywords: two-person bargaining
zbMATH Keywords: Individual Monotonicity
zbMATH Keywords: continuity
zbMATH Keywords: risk sensitivity
reviewed by: Andrzej Wieczorek
MaRDI profile type: Publication
cites work: A Generalized Nash Solution for Two-Person Bargaining Games with Incomplete Information
cites work: Continuity of bargaining solutions
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cites work: Q3939631
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cites work: Axiomatic models of bargaining
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full work available at URL: https://doi.org/10.1007/bf01769309
OpenAlex ID: W2116636209
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description: scientific article; zbMATH DE number 3936969