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On three Shapley-like solutions for cooperative games with random payoffs

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  • Judith Timmer

    ()

  • Peter Borm
  • Stef Tijs

Abstract

Three solution concepts for cooperative games with random payoffs are introduced. These are the marginal value, the dividend value and the selector value. Inspiration for their definitions comes from several equivalent formulations of the Shapley value for cooperative TU games. An example shows that the equivalence is not preserved since these solutions can all be different for cooperative games with random payoffs. Properties are studied and a characterization on a subclass of games is provided. Copyright Springer-Verlag 2004

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File URL: http://hdl.handle.net/10.1007/s001820400181
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Bibliographic Info

Article provided by Springer in its journal International Journal of Games Theory.

Volume (Year): 32 (2004)
Issue (Month): 4 (08)
Pages: 595-613

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Handle: RePEc:spr:jogath:v:32:y:2004:i:4:p:595-613

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Related research

Keywords: Cooperative games; Random variables; Shapley value; C71;

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References

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  1. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38.
  2. Judith Timmer & Peter Borm & Stef Tijs, 2005. "Convexity In Stochastic Cooperative Situations," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 25-42.
  3. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
  4. Suijs, J.P.M., 1996. "A Nucleolus for Stochastic Cooperative Games," Discussion Paper 1996-90, Tilburg University, Center for Economic Research.
  5. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. K. Ortmann, 1998. "Conservation of energy in value theory," Computational Statistics, Springer, vol. 47(3), pages 423-449, October.
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Cited by:
  1. D. Bauso & J. Timmer, 2009. "Robust dynamic cooperative games," International Journal of Game Theory, Springer, vol. 38(1), pages 23-36, March.
  2. Timmer, J.B., 2001. "Cooperative Behaviour, Uncertainty and Operations Research," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86973, Tilburg University.
  3. Voorneveld, Mark & Grahn, Sofia, 2001. "A Minimal Test for Convex Games and the Shapley Value," Working Paper Series 2001:2, Uppsala University, Department of Economics.
  4. Judith Timmer, 2006. "The Compromise Value for Cooperative Games with Random Payoffs," Computational Statistics, Springer, vol. 64(1), pages 95-106, August.
  5. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
  6. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(1), pages 1-41, July.
  7. Timmer, J.B., 2000. "The Compromise Value for Cooperative Games with Random Payoffs," Discussion Paper 2000-98, Tilburg University, Center for Economic Research.

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