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An Ordinal Shapley Value for Economic Environments (Revised Version)

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

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  1. Elisha A. Pazner & David Schmeidler, 1975. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," Discussion Papers 174, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. 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.
  3. Nicolo, Antonio & Perea, Andres, 2005. "Monotonicity and equal-opportunity equivalence in bargaining," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 221-243, March.
  4. 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.
  5. Sergiu Hart, 1983. "An Axiomatization of Harsanyi's Non-Transferable Utility Solution," Discussion Papers 573, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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Cited by:
  1. David Pérez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," UFAE and IAE Working Papers 647.05, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).

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