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Convexity In Stochastic Cooperative Situations

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  • JUDITH TIMMER

    ()
    (Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • PETER BORM

    (Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • STEF TIJS

    (Center and Department of Econometrics and Operations Research, Tilburg University, P. O. Box 90153, 5000 LE Tilburg, The Netherlands)

Abstract

This paper introduces a new model concerning cooperative situations in which the payoffs are modeled by random variables. We analyze these situations by means of cooperative games with random payoffs. Special attention is paid to three types of convexity, namely coalitional-merge, individual-merge and marginal convexity. The relations between these types are studied and in particular, as opposed to their deterministic counterparts for TU games, we show that these three types of convexity are not equivalent. However, all types imply that the core of the game is nonempty. Sufficient conditions on the preferences are derived such that the Shapley value, defined as the average of the marginal vectors, is an element of the core of a convex game.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 07 (2005)
Issue (Month): 01 ()
Pages: 25-42

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Handle: RePEc:wsi:igtrxx:v:07:y:2005:i:01:p:25-42

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Keywords: Cooperative games; random variables; preferences; convexity; Subject Classification: 91A12;

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References

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  1. Suijs, Jeroen & Borm, Peter, 1999. "Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents," Games and Economic Behavior, Elsevier, vol. 27(2), pages 331-345, May.
  2. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
  3. Suijs, Jeroen & De Waegenaere, Anja & Borm, Peter, 1998. "Stochastic cooperative games in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 22(3), pages 209-228, July.
  4. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
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Citations

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Cited by:
  1. Judith Timmer & Peter Borm & Stef Tijs, 2004. "On three Shapley-like solutions for cooperative games with random payoffs," International Journal of Game Theory, Springer, vol. 32(4), pages 595-613, 08.
  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. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Discussion Paper 2000-108, Tilburg University, Center for Economic Research.
  4. Tijs, S.H. & Timmer, J.B. & Brânzei, R., 2001. "Compensations in Information Collecting Situations," Discussion Paper 2001-2, Tilburg University, Center for Economic Research.
  5. D. Bauso & J. Timmer, 2009. "Robust dynamic cooperative games," International Journal of Game Theory, Springer, vol. 38(1), pages 23-36, March.
  6. Timmer, J.B., 2000. "The Compromise Value for Cooperative Games with Random Payoffs," Discussion Paper 2000-98, Tilburg University, Center for Economic Research.
  7. Yanovskaya, E. & Brânzei, R. & Tijs, S.H., 2008. "Monotonicity Problems of Interval Solutions and the Dutta-Ray Solution for Convex Interval Games," Discussion Paper 2008-102, Tilburg University, Center for Economic Research.
  8. Alparslan Gök, S.Z. & Branzei, O. & Branzei, R. & Tijs, S., 2011. "Set-valued solution concepts using interval-type payoffs for interval games," Journal of Mathematical Economics, Elsevier, vol. 47(4-5), pages 621-626.
  9. Francesco Passarelli, 2007. "Asymmetric Bargaining," ISLA Working Papers 26, ISLA, Centre for research on Latin American Studies and Transition Economies, Universita' Bocconi, Milano, Italy, revised Jan 2007.

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