The Chi-compromise value for non-transferable utility games
type: Item
instance of: scholarly article
title: The Chi-compromise value for non-transferable utility games
zbMATH Open document ID: 1064.91009
author: G. Bergantiños
author: Jordi Massó
published in: Mathematical Methods of Operations Research
publication date: 2003-07-14T00:00:00Z
full work available at URL: http://ddd.uab.cat/record/142922
review text: The paper extends two solution concepts formulated earlier for bargaining games, which are of the 'compromise' type in that it is a compromise between players' maximum and minimum aspirations. One of the solutions is the well known Kalai-Smorodonsky solution to pure bargaining games where solutions have to be unanimous, while the other was formulated earlier by the authors for bargaining games where partial agreements are possible and utility is transferable. The solutions are extended to general bargaining problems where the players may reach partial agreements and the utility is not necessarily transferable. The proposed solution is the efficient vector lying on the segment between the vectors of maximal and minimal aspirations, where the maximal aspiration for a player is his maximal (among all coalitions) marginal contribution and the minimum aspiration is the maximum remainder a player can get by going with a coalition of players and offering them their maximal aspirations. Some details follow. Let \(N=\{1,\dots,n\}\), where \(n\geq 2\), denote the finite set of players and \(V \) denote the characteristic function which assigns to each non-empty subset \( S\) of \(N\) a non empty subset of \(\mathbb R^{S}\). A cooperative game with non-transferable utility (NTU) is an ordered pair \((N,V)\). Let \(V_{N}\) denote the class of such games. Some standard properties of these are assumed. For each player \(i\), there is an individually rational payoff \(w_{i}\in\mathbb R\) such that \(V(i)=\{x\in\mathbb R\mid x\leq w_{i}\}\). Also, for each coalition \(S\), the set \(V(S)_{+}=\{x\in V(S)\mid x\geq w_{s}\}\) is bounded. A game is non-level if for each coalition \(S\) and for any \(x,y\in V(S)_{+}\) satisfying \(y\geq x\geq w_{S}\) and \(x\neq y\) there exists \(z\in V(S)\) such that \(z>x\). A game is totally essential if \(w_{S}\in V(S)\) for all \(S\subseteq N\). Denote by \(C_{N}\) the subclass of non-level and totally essential games with NTU. A solution on a sub…
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 1949083
zbMATH Keywords: NTU game
zbMATH Keywords: compromise value
MaRDI profile type: Publication
OpenAlex ID: W2111960417
DOI: 10.1007/S001860200193
description: scientific article; zbMATH DE number 1949083