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Cooperative Games in Stochastic Characteristic Function Form

Author

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  • Daniel Granot

    (Simon Fraser University)

Abstract

Additional results are presented in this paper which further extend and modify the theory of cooperative games in characteristic function form so as to encompass situations where the values of the coalitions are random variables with given distribution functions. We reintroduce the prior nucleolus and provide a new characterization of it in terms of an optimal solution to a finite sequence of consistent and bounded NLP problems. From this new characterization it follows immediately that the prior nucleolus is unique for strictly monotone increasing distribution functions. We also extend the notions of objections and counterobjections to these games and construct and study the prior kernel and prior bargaining set \scr{P}\scr{R} 1 (i) . A new notion of solution for the second part of the play of these games is suggested.

Suggested Citation

  • Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
  • Handle: RePEc:inm:ormnsc:v:23:y:1977:i:6:p:621-630
    DOI: 10.1287/mnsc.23.6.621
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    Cited by:

    1. Habis, Helga & Herings, P. Jean-Jacques, 2011. "Transferable utility games with uncertainty," Journal of Economic Theory, Elsevier, vol. 146(5), pages 2126-2139, September.
    2. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    3. O. Palancı & S. Alparslan Gök & G. Weber, 2014. "Cooperative games under bubbly uncertainty," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(2), pages 129-137, October.
    4. J. Puerto & F. Fernández & Y. Hinojosa, 2008. "Partially ordered cooperative games: extended core and Shapley value," Annals of Operations Research, Springer, vol. 158(1), pages 143-159, February.
    5. 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.
    6. R. Branzei & S. Gök & O. Branzei, 2011. "Cooperative games under interval uncertainty: on the convexity of the interval undominated cores," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 523-532, December.
    7. Kim, Jeong-Yoo & Lee, Seewoo, 2019. "Apportionment of liability by the stochastic Shapley value," International Review of Law and Economics, Elsevier, vol. 60(C).
    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. Suijs, J.P.M. & Borm, P.E.M., 1996. "Cooperative Games with Stochastic Payoffs : Determanistic Equivalents," Research Memorandum 713, Tilburg University, School of Economics and Management.
    10. Panfei Sun & Dongshuang Hou & Hao Sun, 2022. "Optimization implementation of solution concepts for cooperative games with stochastic payoffs," Theory and Decision, Springer, vol. 93(4), pages 691-724, November.
    11. 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.
    12. 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.
    13. Laszlo A. Koczy, 2019. "The risk-based core for cooperative games with uncertainty," CERS-IE WORKING PAPERS 1906, Institute of Economics, Centre for Economic and Regional Studies.
    14. Németh, Tibor & Pintér, Miklós, 2017. "The non-emptiness of the weak sequential core of a transferable utility game with uncertainty," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 1-6.
    15. Hsien-Chung Wu, 2018. "Interval-Valued Cores and Interval-Valued Dominance Cores of Cooperative Games Endowed with Interval-Valued Payoffs," Mathematics, MDPI, vol. 6(11), pages 1-26, November.
    16. Benati, Stefano & López-Blázquez, Fernando & Puerto, Justo, 2019. "A stochastic approach to approximate values in cooperative games," European Journal of Operational Research, Elsevier, vol. 279(1), pages 93-106.
    17. Monroy, L. & Hinojosa, M.A. & Mármol, A.M. & Fernández, F.R., 2013. "Set-valued cooperative games with fuzzy payoffs. The fuzzy assignment game," European Journal of Operational Research, Elsevier, vol. 225(1), pages 85-90.

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