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

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  • Timmer, J.B.

    (Tilburg University)

  • Borm, P.E.M.

    (Tilburg University)

  • Tijs, S.H.

    (Tilburg University)

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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Bibliographic Info

Paper provided by Tilburg University in its series Open Access publications from Tilburg University with number urn:nbn:nl:ui:12-142543.

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Date of creation: 2003
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Publication status: Published in International Journal of Game Theory (2003) v.32, p.595-613
Handle: RePEc:ner:tilbur:urn:nbn:nl:ui:12-142543

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Web page: http://www.tilburguniversity.edu/

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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. Roger B. Myerson, 1978. "Conference Structures and Fair Allocation Rules," Discussion Papers 363, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  3. Timmer, J.B. & Borm, P.E.M. & Tijs, S.H., 2000. "Convexity in Stochastic Cooperative Situations," Discussion Paper 2000-04, Tilburg University, Center for Economic Research.
  4. K. Ortmann, 1998. "Conservation of energy in value theory," Computational Statistics, Springer, vol. 47(3), pages 423-449, October.
  5. Suijs, J.P.M., 1996. "A Nucleolus for Stochastic Cooperative Games," Discussion Paper 1996-90, Tilburg University, Center for Economic Research.
  6. 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. Voorneveld, M. & Grahn, S., 2001. "A Minimal Test for Convex Games and the Shapley Value," Papers 2001:02, Uppsala - Working Paper Series.
  2. Judith Timmer, 2006. "The Compromise Value for Cooperative Games with Random Payoffs," Computational Statistics, Springer, vol. 64(1), pages 95-106, August.
  3. Dinko Dimitrov & Stef Tijs & Rodica Branzei, 2003. "Shapley-like values for interval bankruptcy games," Economics Bulletin, AccessEcon, vol. 3(9), pages 1-8.
  4. Timmer, J.B., 2000. "The Compromise Value for Cooperative Games with Random Payoffs," Discussion Paper 2000-98, Tilburg University, Center for Economic Research.
  5. Timmer, J.B., 2001. "Cooperative Behaviour, Uncertainty and Operations Research," Open Access publications from Tilburg University urn:nbn:nl:ui:12-86973, Tilburg University.
  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. D. Bauso & J. Timmer, 2009. "Robust dynamic cooperative games," International Journal of Game Theory, Springer, vol. 38(1), pages 23-36, March.

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