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Cooperative games under augmenting systems


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Author: Bilbao Arrese, Jesús Mario
Department: Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI)
Date: 2003
Published in: SIAM Journal on Discrete Mathematics, 17 (1), 122-133.
Document type: Article
Abstract: The goal of this paper is to develop a theoretical framework inorder to analyze cooperative games inwhic h only certaincoalition s are allowed to form. We will axiomatize the structure of such allowable coalitions using the theory of antimatroids, a notion developed for combinatorially abstract sets. There have been previous models developed to confront the problem of unallowable coalitions. Games restricted by a communication graph were introduced by Myerson and Owen. We introduce a new combinatorial structure called augmenting system, which is a generalization of the antimatroid structure and the system of connected subgraphs of a graph. The main result of the paper is a direct formula of Shapley and Banzhaf values for games under augmenting systems restrictions.
Cite: Bilbao Arrese, J.M. (2003). Cooperative games under augmenting systems. SIAM Journal on Discrete Mathematics, 17 (1), 122-133.
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DOI: 10.1137/S0895480102402745

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