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Title of Journal: Ann Oper Res

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Abbravation: Annals of Operations Research

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Springer US

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DOI

10.1002/2015SW001318

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1572-9338

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Autonomous coalitions

Authors: Stéphane Gonzalez Michel Grabisch
Publish Date: 2015/09/01
Volume: 235, Issue: 1, Pages: 301-317
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Abstract

We consider in this paper solutions for TUgames where it is not assumed that the grand coalition is necessarily the final state of cooperation Partitions of the grand coalition or balanced collections together with a system of balancing weights interpreted as a time allocation vector are considered as possible states of cooperation The former case corresponds to the ccore while the latter corresponds to the aspiration core or dcore where in both case the best configuration called a maximising collection is sought We study maximising collections and characterize them with autonomous coalitions that is coalitions for which any solution of the dcore yields a payment for that coalition equal to its worth In particular we show that the collection of autonomous coalitions is balanced and that one cannot have at the same time a single possible payment core element and a single possible configuration We also introduce the notion of inescapable coalitions that is those present in every maximising collection We characterize the class of games for which the sets of autonomous coalitions vital coalitions in the sense of Shellshear and Sudhölter and inescapable coalitions coincide and prove that the set of games having a unique maximising coalition is dense in the set of games

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