An axiomatization of the egalitarian solutions
type: Item
instance of: scholarly article
title: An axiomatization of the egalitarian solutions
zbMATH Open document ID: 0569.90103
DOI: 10.1016/0165-4896(85)90019-8
author: Dov Samet
published in: Mathematical Social Sciences
publication date: 1985-01-01T00:00:00Z
review text: This paper considers the axiomatic solution of cooperative games without transferable utility with the egalitarian solution of E. Kalai and the author. Let S be a coalition and V(S), the utilities S can achieve. Let N be the grand coalition. Denote by \(G_ 0\) the class of games such that V(S) is closed, convex, and comprehensive for each S. Denote by \(G_ 1\) the class of games in \(G_ 0\) such that V(N) is smooth and not level. The main results are as follows. There is no solution function on \(G_ 0\) satisfying scale covariance, conditional additivity, independence of irrelevant alternatives, and unanimity. The importance of this is that both the NTU value and the Harsanyi solution satisfy these conditions on \(G_ 1\). However, there is a unique solution satisfying the above conditions (without scale invariance) and the following zero condition: if zero is on the boundary of V(S) for every S, then zero is a solution. This is the symmetric egalitarian solution on \(G_ 1\). If one asymmetrizes the unanimity condition, one has the nonsymmetric egalitarian solution.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 3910177
zbMATH Keywords: nontransferable utility
zbMATH Keywords: axiomatic solution of cooperative games
zbMATH Keywords: egalitarian solution
zbMATH Keywords: NTU value
zbMATH Keywords: Harsanyi solution
zbMATH Keywords: unanimity condition
MaRDI profile type: Publication
full work available at URL: 0165-4896(85)90019-8
OpenAlex ID: W2040855804
cites work: An Axiomatization of the Non-Transferable Utility Value
cites work: Q3252999
cites work: A Simplified Bargaining Model for the n-Person Cooperative Game
cites work: Monotonic Solutions to General Cooperative Games
cites work: Q5623557
description: scientific article; zbMATH DE number 3910177