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The consensus value : A new solution concept for cooperative games

Author

Listed:
  • Ju, Y.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

  • Ruys, P.H.M.

    (Tilburg University, School of Economics and Management)

Abstract

By generalizing the standard solution for 2-person games into n-person cases, this paper develops a new solution concept for cooperative games: the consensus value.We characterize the consensus value as the unique function that satisfies efficiency, symmetry, the quasi dummy property and additivity.By means of the transfer property, a second characterization is provided.By defining the stand-alone reduced game, a recursive formula for the value is established.We also show that this value is the average of the Shapley value and the equal surplus solution.Furthermore, we discuss a possible generalization.
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Suggested Citation

  • Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2007. "The consensus value : A new solution concept for cooperative games," Other publications TiSEM 6cd44a12-a909-47f8-8d85-e, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:6cd44a12-a909-47f8-8d85-e99198a40f3c
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    References listed on IDEAS

    as
    1. Yuan Ju, 2007. "The Consensus Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(03), pages 437-452.
    2. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    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. Borm, P.E.M. & Ju, Y. & Ruys, P.H.M., 2004. "Compensating Losses and Sharing Surpluses in Project-Allocation Situations (version 1)," Discussion Paper 2004-6, Tilburg University, Center for Economic Research.
    5. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October.
    6. Yuan Ju & David Wettstein, 2009. "Implementing cooperative solution concepts: a generalized bidding approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 39(2), pages 307-330, May.
    7. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    8. Quant, M. & Borm, P.E.M. & Maaten, R., 2005. "A Concede-and-Divide Rule for Bankruptcy Problems," Other publications TiSEM 23e9af88-9fb0-4f9d-bad5-2, Tilburg University, School of Economics and Management.
    9. René van den Brink & Yukihiko Funaki, 2004. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for Cooperative Games with Transferable Utility," Tinbergen Institute Discussion Papers 04-136/1, Tinbergen Institute.
    10. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    11. Peter Borm & René van den Brink & Marco Slikker, 2002. "An Iterative Procedure for Evaluating Digraph Competitions," Annals of Operations Research, Springer, vol. 109(1), pages 61-75, January.
    12. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
    13. Ju, Y. & Ruys, P.H.M. & Borm, P.E.M., 2004. "Compensating Losses and Sharing Surpluses in Project-Allocation Situations (version 2)," Other publications TiSEM 1dedb74a-cd24-4a65-b234-d, Tilburg University, School of Economics and Management.
    14. René van den Brink & Peter Borm, 2002. "Digraph Competitions and Cooperative Games," Theory and Decision, Springer, vol. 53(4), pages 327-342, December.
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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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