A new basis and the Shapley value

Koji Yokote, Yukihiko Funaki () and Yoshio Kamijo

Mathematical Social Sciences, 2016, vol. 80, issue C, 21-24

Abstract: The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value.

Date: 2016
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:80:y:2016:i:c:p:21-24

DOI: 10.1016/j.mathsocsci.2015.12.003

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