Coalition Formation and Stability

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Abstract

This paper aims to develop, for any cooperative game, a solution notion that enjoys stability and consists of a coalition structure and an associated payoff vector derived from the Shapley value. To this end, two concepts are combined: those of strong Nash equilibrium and Aumann–Drèze coalitional value. In particular, we are interested in conditions ensuring that the grand coalition is the best preference for all players. Monotonicity, convexity, cohesiveness and other conditions are used to provide several theoretical results that we apply to numerical examples including real-world economic situations.

Keywords

Game theory TU cooperative game Monotonicity Superadditivity Convexity Cohesiveness Shapley value Coalition structure Aumann–Drèze value Strong Nash equilibrium Stability 

Mathematics Subject Classification

91A12 

JEL Classification

C71 

Notes

Acknowledgements

The authors wish to thank Prof. Gregory Kersten, Editor-in-Chief, and two anonymous reviewers for their helpful comments. Research partially supported by Grant MTM2015-66818-P of the Economy and Competitiveness Spanish Ministry and the European Regional Development Fund.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Politècnica de Catalunya (UPC)TerrassaSpain

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