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The consensus value : a new solution concept for cooperative games

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Author Info
Ju, Y.
Borm, P.E.M.
Ruys, P.H.M. (Tilburg University, Center for Economic Research)

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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 satis/es e1ciency, symmetry, the quasi dummy property and additivity. By means of the transfer property, a second characterization is provided. By de/ning 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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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 50.

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Date of creation: 2004
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Handle: RePEc:dgr:kubcen:200450

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Find related papers by 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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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Borm, P. & Brink, R. van den & Slikker, M., 2000. "An iterative procedure for evaluating digraph competitions," Research Memorandum 788, Tilburg University, Faculty of Economics and Business Administration. [Downloadable!]
  2. Yuan Ju & Peter Borm, 2005. "Externalities and Compensation:Primeval Games and Solutions," Keele Economics Research Papers KERP 2005/05, Centre for Economic Research, Keele University. [Downloadable!]
    Other versions:
  3. Borm, P.E.M. & Ju, Y. & Ruys, P.H.M., 2004. "Compensating losses and sharing surpluses in project-allocation situations," Discussion Paper 6, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  4. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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  6. 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. [Downloadable!]
    Other versions:
  7. Ju, Y., 2004. "The consensus value for games in partition function form," Discussion Paper 60, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  8. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, January.
  9. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  10. Quant, M. & Borm, Peter & Maaten, Rogier, 2005. "A concede-and-divide rule for bankruptcy problems," Discussion Paper 20, Tilburg University, Center for Economic Research. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Borm, P.E.M. & Ju, Y. & Ruys, P.H.M., 2004. "Compensating losses and sharing surpluses in project-allocation situations," Discussion Paper 6, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Brink, R. van den & Ruys, P.H.M., 2005. "Technological change, wages and firm size," Discussion Paper 22, Tilburg University, Tilburg Law and Economic Center. [Downloadable!]
  3. Ju, Y., 2004. "The consensus value for games in partition function form," Discussion Paper 60, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  4. Ju, Yuan & Borm, Peter, 2006. "A non-cooperative approach to the compensation rules for primeval games," Discussion Paper 97, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  5. Célestin Chameni Nembua & Nicolas Gabriel Andjiga, 2008. "Linear, efficient and symmetric values for TU-games," Economics Bulletin, Economics Bulletin, vol. 3(71), pages 1-10. [Downloadable!]
  6. 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. [Downloadable!]
    Other versions:
  7. René van den Brink & Yukihiko Funaki & Yuan Ju, 2007. "Consistency, Monotonicity and Implementation of Egalitarian Shapley Values," Tinbergen Institute Discussion Papers 07-062/1, Tinbergen Institute. [Downloadable!]
  8. Luis Hernandez-Lamoneda & Ruben Juarez & Francisco Sanchez-Sanchez, 2008. "Solutions without dummy axiom for TU cooperative games," Economics Bulletin, Economics Bulletin, vol. 3(1), pages 1-9. [Downloadable!]
  9. Quant, M. & Borm, Peter & Maaten, Rogier, 2005. "A concede-and-divide rule for bankruptcy problems," Discussion Paper 20, Tilburg University, Center for Economic Research. [Downloadable!]
  10. Ju, Yuan & Borm, Peter, 2005. "Externalities and compensation: primeval games and solutions," Discussion Paper 71, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  11. Dritan Osmani & Richard S.J. Tol, 2007. "A short note on joint welfare maximization assumptions," Working Papers FNU-150, Research unit Sustainability and Global Change, Hamburg University, revised Oct 2007. [Downloadable!]
    Other versions:
  12. Rene van den Brink & Pieter H.M. Ruys, 2005. "Positional Wages, Market Wages and Firm Size," Tinbergen Institute Discussion Papers 05-020/1, Tinbergen Institute. [Downloadable!]
  13. 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. [Downloadable!]
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