Cooperative games under augmenting systems
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...
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2003 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/57577 |
| Online Access: | http://hdl.handle.net/11441/57577 https://doi.org/10.1137/S0895480102402745 |
| Access Level: | Open access |
| Keyword: | Cooperative game Shapley value Banzhaf value Set systems |
| Summary: | 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. |
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