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On the coincidence of the Prenucleolus and the Shapley Value

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  • Kar, Anirban
  • Mitra, Manipushpak
  • Mutuswami, Suresh

Abstract

We identify a sufficient class of coalitional form games with transferable utility for which prenucleolus coincides with the Shapley value. We then apply our result to simple games and to generalized queueing games

Suggested Citation

  • Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2005. "On the coincidence of the Prenucleolus and the Shapley Value," Economics Discussion Papers 8892, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:8892
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    Cited by:

    1. Conan Mukherjee, 2013. "Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 131-163, February.
    2. José M. Jiménez Gómez & María del Carmen Marco Gil & Pedro Gadea Blanco, 2010. "Some game-theoretic grounds for meeting people half-way," Working Papers. Serie AD 2010-04, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    3. Luis Guardiola & Ana Meca & Justo Puerto, 2020. "Quid Pro Quo allocations in Production-Inventory games," Papers 2002.00953, arXiv.org.
    4. Youngsub Chun & Manipushpak Mitra & Suresh Mutuswami, 2019. "Recent developments in the queueing problem," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 1-23, April.
    5. Jose A. García-Martínez & Ana Meca & G. Alexander Vergara, 2022. "Cooperative Purchasing with General Discount: A Game Theoretical Approach," Mathematics, MDPI, vol. 10(22), pages 1-20, November.
    6. Bendel, Dan & Haviv, Moshe, 2018. "Cooperation and sharing costs in a tandem queueing network," European Journal of Operational Research, Elsevier, vol. 271(3), pages 926-933.
    7. Julio González-Díaz & Estela Sánchez-Rodríguez, 2014. "Understanding the coincidence of allocation rules: symmetry and orthogonality in TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(4), pages 821-843, November.
    8. Trudeau, Christian & Vidal-Puga, Juan, 2020. "Clique games: A family of games with coincidence between the nucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 8-14.
    9. Youngsub Chun & Nari Park & Duygu Yengin, 2015. "Coincidence of Cooperative Game Theoretic Solutions in the Appointment Problem," School of Economics and Public Policy Working Papers 2015-09, University of Adelaide, School of Economics and Public Policy.
    10. Youngsub Chun, 2016. "Queueing Problems with Two Parallel Servers," Studies in Choice and Welfare, in: Fair Queueing, chapter 0, pages 141-157, Springer.
    11. García-Martínez, Jose A. & Mayor-Serra, Antonio J. & Meca, Ana, 2020. "Efficient Effort Equilibrium in Cooperation with Pairwise Cost Reduction," MPRA Paper 105604, University Library of Munich, Germany.
    12. Pedro Gadea-Blanco & José-Manuel Giménez-Gómez & M. Carmen Marco-Gil, 2016. "Compromising in bifocal distribution games: the average value," Theory and Decision, Springer, vol. 81(3), pages 449-465, September.
    13. Chang, Chih & Tseng, Ying-Chih, 2011. "On the coincidence property," Games and Economic Behavior, Elsevier, vol. 71(2), pages 304-314, March.
    14. Yokote, Koji & Funaki, Yukihiko & Kamijo, Yoshio, 2017. "Coincidence of the Shapley value with other solutions satisfying covariance," Mathematical Social Sciences, Elsevier, vol. 89(C), pages 1-9.
    15. Luis A. Guardiola & Ana Meca & Justo Puerto, 2021. "Enforcing fair cooperation in production-inventory settings with heterogeneous agents," Annals of Operations Research, Springer, vol. 305(1), pages 59-80, October.
    16. Emilio Calvo, 2021. "Redistribution of tax resources: a cooperative game theory approach," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 12(4), pages 633-686, December.
    17. Koji Yokote & Yukihiko Funaki, 2015. "Several bases of a game space and an application to the Shapley value," Working Papers 1419, Waseda University, Faculty of Political Science and Economics.

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