Ability to Separate Situations with a Priori Coalition Structures by Means of Symmetric Solutions

José Miguel Giménez

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Paper

Ability to Separate Situations with a Priori Coalition Structures by Means of Symmetric Solutions

Topics: Game Theory

In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems ICORES - Volume 1, 242-249, 2017 , Porto, Portugal

Author: José Miguel Giménez

Affiliation: Technical University of Catalonia, Spain

Keyword(s): Cooperative game, Coalition structure, Marginal contribution, Semivalue, Separability.

Related Ontology Subjects/Areas/Topics: Game Theory ; Methodologies and Technologies ; Operational Research

Abstract: We say that two situations described by cooperative games are inseparable by a family of solutions, when they obtain the same allocation by all solution concept of this family. The situation of separability by a family of linear solutions reduces to separability from the null game. This is the case of the family of solutions based on marginal contributions weighted by coefficients only dependent of the coalition size: the semivalues. It is known that for games with four or more players, the spaces of inseparable games from the null game contain games different to zero-game. We will prove that for five or more players, when a priori coalition blocks are introduced in the situation described by the game, the dimension of the vector spaces of inseparable games from the null game decreases in an important manner.

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Paper citation in several formats:

Giménez, J. (2017). Ability to Separate Situations with a Priori Coalition Structures by Means of Symmetric Solutions. In Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES; ISBN 978-989-758-218-9; ISSN 2184-4372, SciTePress, pages 242-249. DOI: 10.5220/0006116802420249

@conference{icores17,
author={José Miguel Giménez.},
title={Ability to Separate Situations with a Priori Coalition Structures by Means of Symmetric Solutions},
booktitle={Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES},
year={2017},
pages={242-249},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0006116802420249},
isbn={978-989-758-218-9},
issn={2184-4372},
}

TY - CONF

JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - ICORES
TI - Ability to Separate Situations with a Priori Coalition Structures by Means of Symmetric Solutions
SN - 978-989-758-218-9
IS - 2184-4372
AU - Giménez, J.
PY - 2017
SP - 242
EP - 249
DO - 10.5220/0006116802420249
PB - SciTePress