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Set-valued solution concepts using interval-type payoffs for interval games

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  • Alparslan Gök, S.Z.
  • Branzei, O.
  • Branzei, R.
  • Tijs, S.
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    Abstract

    Uncertainty is a daily presence in the real world. It affects our decision making and may have influence on cooperation. Often uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e., payoffs lie in some intervals. A suitable game theoretic model to support decision making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core and the interval stable sets for cooperative interval games, are introduced and studied. The main results contained in the paper are a necessary and sufficient condition for the non-emptiness of the interval core of a cooperative interval game and the relations between the interval core, the interval dominance core and the interval stable sets of such a game.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000802
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 4-5 ()
    Pages: 621-626

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:4:p:621-626

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Cooperative games; Interval games; The core; The dominance core; Stable sets;

    References

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    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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    1. Brânzei, R. & Tijs, S.H. & Alparslan-Gok, S.Z., 2008. "Some Characterizations of Convex Interval Games," Discussion Paper 2008-55, Tilburg University, Center for Economic Research.
    2. Rodica Branzei & Stef Tijs & S. Zeynep Alparslan Gok, 2008. "Some Characterizations of Convex Interval Games," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 2(3), pages 219-226, December.
    3. Brânzei, R. & Dimitrov, D.A. & Tijs, S.H., 2003. "Shapley-like values for interval bankruptcy games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-121815, Tilburg University.
    4. Luisa Carpente & Balbina Casas-Méndez & Ignacio García-Jurado & Anne Nouweland, 2010. "The truncated core for games with upper bounds," International Journal of Game Theory, Springer, vol. 39(4), pages 645-656, October.
    5. S. Alparslan-Gök & Silvia Miquel & Stef Tijs, 2009. "Cooperation under interval uncertainty," Computational Statistics, Springer, vol. 69(1), pages 99-109, March.
    6. repec:ebl:ecbull:v:3:y:2003:i:9:p:1-8 is not listed on IDEAS
    7. 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.
    8. 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.
    9. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
    10. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    11. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
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