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An Ordinal Shapley Value for Economic Environments

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  • David Pérez-Castrillo
  • David Wettstein

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 (T U ) games. We show a solution exists, and call it an 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 Shapley value for T U games, we construct a weighted OSV as well.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 26.

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Date of creation: Jul 2003
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Handle: RePEc:bge:wpaper:26

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Keywords: Non-transferable utility games; shapley value; ordinal shapley value; consistency; fairness;

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  1. 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.
  2. Demange, Gabrielle, 1984. "Implementing Efficient Egalitarian Equivalent Allocations," Econometrica, Econometric Society, Econometric Society, vol. 52(5), pages 1167-77, September.
  3. Perez-Castrillo, D. & Wettstein, D., 1999. "Bidding for the Surplus: a Non-Cooperative Approach to the Shapley Value. ation," Papers, Tel Aviv 24-99, Tel Aviv.
  4. Barry O'Neill & Dov Samet & Zvi Wiener & Eyal Winter, 2001. "Bargaining with an Agenda," Game Theory and Information, EconWPA 0110004, EconWPA.
  5. Crawford, Vincent P, 1979. "A Procedure for Generating Pareto-Efficient Egalitarian-Equivalent Allocations," Econometrica, Econometric Society, Econometric Society, vol. 47(1), pages 49-60, January.
  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. Sergiu Hart, 1983. "An Axiomatization of Harsanyi's Non-Transferable Utility Solution," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 573, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  8. Pazner, Elisha A & Schmeidler, David, 1978. "Egalitarian Equivalent Allocations: A New Concept of Economic Equity," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 92(4), pages 671-87, November.
  9. Hart, Sergiu & Mas-Colell, Andreu, 1996. "Bargaining and Value," Econometrica, Econometric Society, Econometric Society, vol. 64(2), pages 357-80, March.
  10. Aumann, Robert J, 1985. "An Axiomatization of the Non-transferable Utility Value," Econometrica, Econometric Society, Econometric Society, vol. 53(3), pages 599-612, May.
  11. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, Econometric Society, vol. 57(3), pages 589-614, May.
  12. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers, Northwestern University, Center for Mathematical Studies in Economics and Management Science 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  13. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
  14. Nicolo, Antonio & Perea, Andres, 2005. "Monotonicity and equal-opportunity equivalence in bargaining," Mathematical Social Sciences, Elsevier, Elsevier, vol. 49(2), pages 221-243, March.
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Cited by:
  1. Vidal-Puga, Juan, 2013. "A non-cooperative approach to the ordinal Shapley rule," MPRA Paper 43790, University Library of Munich, Germany.
  2. Yildirim, Huseyin, 2007. "Proposal power and majority rule in multilateral bargaining with costly recognition," Journal of Economic Theory, Elsevier, vol. 136(1), pages 167-196, September.
  3. Geoffroy de Clippel & David Pérez-Castrillo & David Wettstein, 2010. "Egalitarian Equivalence under Asymmetric Information," UFAE and IAE Working Papers, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC) 813.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. David Pérez-Castrillo & David Wettstein, 2005. "Implementation of the Ordinal Shapley Value for a three-agent economy," Economics Bulletin, AccessEcon, vol. 3(48), pages 1-8.

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