Article
Cooperative games under augmenting systems
Author/s | Bilbao Arrese, Jesús Mario |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada II (ETSI) |
Publication Date | 2003 |
Deposit Date | 2017-04-17 |
Published in |
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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 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. |
Citation | Bilbao Arrese, J.M. (2003). Cooperative games under augmenting systems. SIAM Journal on Discrete Mathematics, 17 (1), 122-133. |
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