An Average Value Function for Cooperative Games

Vladimir Akimov and William Kerby
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Vladimir Akimov: Moscow state Institute for International Relationsá (University), prospekt Wernadskogo, Moscow, Russia
William Kerby: Mathematisches Seminar der Universitõt Hamburg, Hamburg, Germany

Homo Oeconomicus, 2000, vol. 17, 155-164

Abstract: The Shapely value measures the contribution of a player to the grand coalition. In many practical situations the grand coalition does not typically occur. A new value is introduced which by taking all possible coalitions into account measures the coalition supporting power of each player. It is shown that the Shapley value can be expressed as a sum of the coalition supporting value and the coalition suppressing value. The coalition supporting value of a player is his average Shapley value taken over all subgames and his coalition suppressing value is his average Shapley value taken over all dual subgames. An axiomatic characterisation of the value function is also presented. As an example the coalition supporting power (passing power) and the coalition supressing power (blocking power) in the voting system of the UN Security Council are computed.

Date: 2000
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Persistent link: https://EconPapers.repec.org/RePEc:hom:homoec:v:17:y:2000:p:155-164

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