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The consensus value: a new solution concept for cooperative games

  • Yuan Ju


  • Peter Borm
  • Pieter Ruys

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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Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 28 (2007)
Issue (Month): 4 (June)
Pages: 685-703

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Handle: RePEc:spr:sochwe:v:28:y:2007:i:4:p:685-703
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  1. 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.
  2. 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.
  3. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
  4. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, June.
  5. Borm, P.E.M. & van den Brink, J.R. & Slikker, M., 2000. "An Iterative Procedure for Evaluating Digraph Competitions," Research Memorandum 788, Tilburg University, School of Economics and Management.
  6. Ju, Y. & Ruys, P.H.M. & Borm, P.E.M., 2004. "Compensating Losses and Sharing Surpluses in Project-Allocation Situations (version 2)," Discussion Paper 2004-002, Tilburg University, Tilburg Law and Economic Center.
  7. Ju, Y. & Borm, P.E.M., 2008. "Externalities and compensation : Primeval games and solutions," Other publications TiSEM f6e1bcfc-f2a6-4fc7-ac90-7, Tilburg University, School of Economics and Management.
  8. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
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