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Sharing the surplus in games with externalities within and across issues

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  • Effrosyni Diamantoudi
  • Inés Macho-Stadler
  • David Pérez-Castrillo
  • Licun Xue

Abstract

We consider environments in which agents can cooperate on multiple issues and externalities are present both within and across issues. We propose a way to extend (Shapley) values that have been put forward to deal with externalities within issues to games where there are externalities within and across issues. We characterize our proposal through axioms that extend the Shapley axioms to our more general environment.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 569.

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Date of creation: Aug 2011
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Handle: RePEc:bge:wpaper:569

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Keywords: externalities; cooperative game theory; Shapley value; linked issues;

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  1. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
  2. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2007. "Sharing the surplus: An extension of the Shapley value for environments with externalities," Journal of Economic Theory, Elsevier, vol. 135(1), pages 339-356, July.
  3. Francis Bloch & Geoffroy de Clippel, 2009. "Cores of Combined Games," Working Papers 2009-1, Brown University, Department of Economics.
  4. Macho-Stadler, Ines & Perez-Castrillo, David & Wettstein, David, 2006. "Efficient bidding with externalities," Games and Economic Behavior, Elsevier, vol. 57(2), pages 304-320, November.
  5. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  6. Pham Do, K.H. & Norde, H.W., 2002. "The Shapley Value for Partition Function Form Games," Discussion Paper 2002-4, Tilburg University, Center for Economic Research.
  7. M. J. Albizuri & J. Arin & J. Rubio, 2005. "An Axiom System For A Value For Games In Partition Function Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 63-72.
  8. Dutta, Bhaskar & Ehlers, Lars & Kar, Anirban, 2010. "Externalities, potential, value and consistency," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2380-2411, November.
  9. McQuillin, Ben, 2008. "The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure," MPRA Paper 12049, University Library of Munich, Germany.
  10. Beja, A & Gilboa, Itzhak, 1990. "Values for Two-Stage Games: Another View of the Shapley Axioms," International Journal of Game Theory, Springer, vol. 19(1), pages 17-31.
  11. Bulow, Jeremy I & Geanakoplos, John D & Klemperer, Paul D, 1985. "Multimarket Oligopoly: Strategic Substitutes and Complements," Journal of Political Economy, University of Chicago Press, vol. 93(3), pages 488-511, June.
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