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The Consensus Value : A New Solution Concept for Cooperative Games

Author

Listed:
  • Ju, Y.

    (Tilburg University, Center For Economic Research)

  • Borm, P.E.M.

    (Tilburg University, Center For Economic Research)

  • Ruys, P.H.M.

    (Tilburg University, Center For Economic Research)

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.

Suggested Citation

  • Ju, Y. & Borm, P.E.M. & Ruys, P.H.M., 2004. "The Consensus Value : A New Solution Concept for Cooperative Games," Discussion Paper 2004-50, Tilburg University, Center for Economic Research.
  • Handle: RePEc:tiu:tiucen:ff51992e-6683-4596-a613-93ccaaee1062
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    References listed on IDEAS

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    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, January.
    3. Ju, Y. & Ruys, P.H.M. & Borm, P.E.M., 2004. "Compensating Losses and Sharing Surpluses in Project-Allocation Situations (version 2)," Discussion Paper 2004-37, Tilburg University, Center for Economic Research.
    4. 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.
    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. Ju, Y., 2004. "The Consensus Value for Games in Partition Function Form," Discussion Paper 2004-60, Tilburg University, Center for Economic Research.
    9. Quant, M. & Borm, P.E.M. & Maaten, R., 2005. "A Concede-and-Divide Rule for Bankruptcy Problems," Discussion Paper 2005-20, Tilburg University, Center for Economic Research.
    10. 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.
    11. 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.
    12. 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.
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    More about this item

    Keywords

    cooperative games; game theory;

    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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