Values and potential of games with cooperation structure
type: Item
instance of: scholarly article
title: Values and potential of games with cooperation structure
zbMATH Open document ID: 0954.91004
DOI: 10.1007/BF01243199
published in: International Journal of Game Theory
publication date: 2000-04-11T00:00:00Z
review text: For traditional cooperative games in which all coalitions are possible, there exist several natural ways of dividing the total payoff \(v(N)\), e.g., the Shapley value in which \(i\)-th player gets an average of what he brings to all possible coalitions: \(\Phi_i(N,v)=\sum_{S:i\in S\subseteq N} (s-1)!\cdot (n-s)!\cdot [v(S)-v(S-\{i\})]/n!\), where \(s\) is the number of players in \(S\), and \(n\) is the total number of players. In some real-life situations, not all coalitions are possible. The class of all possible coalitions is called a cooperative structure. The author generalizes the known values (including the Shapley value) to games with cooperative structure, shows how known algorithms for computing these values can be generalized to such games, and which properties of the values are preserved under this generalization. The proofs are based on convex geometry, a discrete analogue of convex sets.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 1429797
zbMATH Keywords: cooperative games
zbMATH Keywords: Shapley value
zbMATH Keywords: cooperative structure
author: Jésus Mario Bilbao
reviewed by: Olga Kosheleva
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01243199
OpenAlex ID: W4213177251
description: scientific article; zbMATH DE number 1429797