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

### José Miguel Giménez

#### 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 Harvard Style

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 - Volume 1: ICORES,* ISBN 978-989-758-218-9, pages 242-249. DOI: 10.5220/0006116802420249

#### in Bibtex Style

@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 - Volume 1: ICORES,},

year={2017},

pages={242-249},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0006116802420249},

isbn={978-989-758-218-9},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 6th International Conference on Operations Research and Enterprise Systems - Volume 1: ICORES,

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

SN - 978-989-758-218-9

AU - Giménez J.

PY - 2017

SP - 242

EP - 249

DO - 10.5220/0006116802420249