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An Ordinal Shapley Value for Economic Environments (Revised Version)

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Author Info
David Perez-Castrillo ()
David Wettstein ()

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Abstract

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The problem is formulated in the preferences-endowments space. The solution is defined recursively, incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and call it the Ordinal Shapley value (OSV). We characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone and anonymous. Finally, similarly to the weighted Shapely value for TU games, we construct a weighted OSV as well.

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Publisher Info
Paper provided by Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) in its series UFAE and IAE Working Papers with number 634.04.

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Length: 32
Date of creation: 14 Dec 2004
Date of revision:
Handle: RePEc:aub:autbar:634.04

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Related research
Keywords: Non-Transferable utility games; Shapley value; Ordinal Shapley value; consistency; fairness.;

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Find related papers by JEL classification:
C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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References listed on IDEAS
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. McLean, Richard P. & Postlewaite, Andrew, 1989. "Excess functions and nucleolus allocations of pure exchange economies," Games and Economic Behavior, Elsevier, vol. 1(2), pages 131-143, June. [Downloadable!] (restricted)
  2. Nicolo, Antonio & Perea, Andres, 2005. "Monotonicity and equal-opportunity equivalence in bargaining," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 221-243, March. [Downloadable!] (restricted)
  3. Hart, Sergiu, 1985. "An Axiomatization of Harsanyi's Nontransferable Utility Solution," Econometrica, Econometric Society, vol. 53(6), pages 1295-1313, November. [Downloadable!] (restricted)
    Other versions:
  4. Safra, Zvi & Samet, Dov, 2004. "An ordinal solution to bargaining problems with many players," Games and Economic Behavior, Elsevier, vol. 46(1), pages 129-142, 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)
    Other versions:
  6. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, vol. 92(4), pages 671-87, November. [Downloadable!] (restricted)
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  7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
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Cited by:
(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. David Pérez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," Economics Bulletin, Economics Bulletin, vol. 3(48), pages 1-8. [Downloadable!]
    Other versions:
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