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The Consensus Value for Games in Partition Function Form

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  • Ju, Y.

    (Tilburg University, Center for Economic Research)

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Abstract

This paper studies a generalization of the consensus value (cf.Ju, Borm and Ruys (2004)) to the class of partition function form games.The concepts and axioms, related to the consensus value, are extended.This value is characterized as the unique function that satisfies efficiency, complete symmetry, the quasi null player property and additivity.By means of the transfer property, a second characterization is provided.Moreover, it is shown that this value satisfies the individual rationality under a certain condition, and well balances the trade-o® between coalition effects and externality effects.By modifying the stand-alone reduced game, a recursive formula for the value is established.A further generalization of the consensus value is discussed.Finally, two applications of the consensus value are given: one is for oligopoly games in partition function form and the other is about participation incentives in free-rider situations.

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Bibliographic Info

Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2004-60.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200460

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Keywords: oligopoly; game theory; games;

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References

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  1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer, vol. 28(4), pages 685-703, June.
  2. Bolger, E M, 1989. "A Set of Axioms for a Value for Partition Function Games," International Journal of Game Theory, Springer, vol. 18(1), pages 37-44.
  3. Kim Hang Pham Do & Henk Norde, 2007. "The Shapley Value For Partition Function Form Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(02), pages 353-360.
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Cited by:
  1. Yuan Ju & Peter Borm & Pieter Ruys, 2007. "The consensus value: a new solution concept for cooperative games," Social Choice and Welfare, Springer, vol. 28(4), pages 685-703, June.
  2. Ju, Y. & Borm, P.E.M., 2006. "A Non-cooperative Approach to the Compensation Rules for Primeval Games," Discussion Paper 2006-97, Tilburg University, Center for Economic Research.
  3. Ju, Yuan & Borm, Peter, 2008. "Externalities and compensation: Primeval games and solutions," Journal of Mathematical Economics, Elsevier, vol. 44(3-4), pages 367-382, February.
  4. Yuan Ju & David Wettstein, 2006. "Implementing Cooperative Solution Concepts: a Generalized Bidding Approach," Keele Economics Research Papers KERP 2006/06, Centre for Economic Research, Keele University.
  5. Joss Sanchez-Perez, 2014. "An application of the representations of symmetric groups to characterizing solutions of games in partition function form," Operations Research and Decisions, Wroclaw University of Technology, Institute of Organization and Management, vol. 2, pages 97-122.

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