Commutation Games and Multilinear Extension

• Autores: José Miguel Giménez Pradales, Rafael Amer Ramon
• Localización: Abstracts of the Fifth Spanish Meeting on Game Theory and Applications / coord. por Jesús Mario Bilbao Arrese, Francisco Ramón Fernández García, 2002, ISBN 84-472-0733-1, pág. 91
• Idioma: inglés
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• Resumen

  • The semivalues, introduced by Dubey, Neyman and Weber in 1981, form an ample family of solutions for cooperative games with transferable utility and include, among others, the solutions of Shapley and Banzhaf.

    For one of these solutions, it can happen that different games obtain a same payoff vector. We say that two games are inseparable by semivalues if both games obtain the same payoff vector for any semivalue that is considered.

    The linearity of the semivalues allows to reduce the problem of the separation to the null game and to consider the games simpler than they are inseparable from the null game: the commutation games. It has been proven that all inseparable game from the null game is a linear combination of commutation games, which allows to know the dimension of this vector subspace for each space of cooperative games.