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Partially ordered cooperative games: extended core and Shapley value

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  • J. Puerto
  • F. Fernández
  • Y. Hinojosa

Abstract

In this paper we analyze cooperative games whose characteristic function takes values in a partially ordered linear space. Thus, the classical solution concepts in cooperative game theory have to be revisited and redefined: the core concept, Shapley–Bondareva theorem and the Shapley value are extended for this class of games. The classes of standard, vector-valued and stochastic cooperative games among others are particular cases of this general theory. Copyright Springer Science+Business Media, LLC 2008

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:158:y:2008:i:1:p:143-159:10.1007/s10479-007-0242-9
    DOI: 10.1007/s10479-007-0242-9
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    1. Suijs, J.P.M. & De Waegenaere, A.M.B. & Borm, P.E.M., 1996. "Stochastic Cooperative Games in Insurance and Reinsurance," Other publications TiSEM f2cd7428-cd39-4462-af76-2, Tilburg University, School of Economics and Management.
    2. Predtetchinski, Arkadi & Jean-Jacques Herings, P., 2004. "A necessary and sufficient condition for non-emptiness of the core of a non-transferable utility game," Journal of Economic Theory, Elsevier, vol. 116(1), pages 84-92, May.
    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. 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.
    5. F. R. Fernández & M. A. Hinojosa & J. Puerto, 2002. "Core Solutions in Vector-Valued Games," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 331-360, February.
    6. Timmer, J.B., 2001. "Cooperative behaviour, uncertainty and operations research," Other publications TiSEM 4a00d965-b7c4-4f43-8f76-5, Tilburg University, School of Economics and Management.
    7. Kannai, Yakar, 1992. "The core and balancedness," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 12, pages 355-395, Elsevier.
    8. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    9. Daniel Granot, 1977. "Cooperative Games in Stochastic Characteristic Function Form," Management Science, INFORMS, vol. 23(6), pages 621-630, February.
    10. F. R. Fernández & J. Puerto & M. J. Zafra, 2002. "Cores Of Stochastic Cooperative Games With Stochastic Orders," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 265-280.
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    Cited by:

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    2. Monroy, Luisa & Fernández, Francisco R., 2011. "The Shapley-Shubik index for multi-criteria simple games," European Journal of Operational Research, Elsevier, vol. 209(2), pages 122-128, March.
    3. R. Branzei & O. Branzei & S. Alparslan Gök & S. Tijs, 2010. "Cooperative interval games: a survey," 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. 18(3), pages 397-411, September.
    4. 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.
    5. Lucia Pusillo, 2013. "Banzhaf LikeValue for Games with Interval Uncertainty," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 7(1), pages 005-014, March.
    6. Dan C. Popescu & Philip Kilby, 2020. "Approximation of the Shapley value for the Euclidean travelling salesman game," Annals of Operations Research, Springer, vol. 289(2), pages 341-362, June.
    7. 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.
    8. 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.
    9. 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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