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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 extend the literature on the coincidence of the prenucleolus and the Shapley value, by identifying a class of coalitional form games called PS games. We analyse the role of PS games in the context of queueing problems, and show that in the class of generalized queueing games only those queueing games with 'linear externalities' are PS games.

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  • Kar, Anirban & Mitra, Manipushpak & Mutuswami, Suresh, 2009. "On the coincidence of the prenucleolus and the Shapley value," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 16-25, January.
    • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:16-25
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    Cited by:

    1. 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).
    2. Dehez, Pierre & Mêgnigbêto, Eustache, 2024. "Measuring the extent of synergies among innovation actors and their contributions: the Helix as a cooperative game," LIDAM Discussion Papers CORE 2024006, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    5. 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.
    6. Youngsub Chun, 2016. "Queueing Problems with Two Parallel Servers," Studies in Choice and Welfare, in: Fair Queueing, chapter 0, pages 141-157, Springer.
    7. 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.
    8. Chang, Chih & Tseng, Ying-Chih, 2011. "On the coincidence property," Games and Economic Behavior, Elsevier, vol. 71(2), pages 304-314, March.
    9. Banerjee, Sreoshi, 2024. "On identifying efficient, fair and stable allocations in "generalized" sequencing games," MPRA Paper 120188, University Library of Munich, Germany.
    10. 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.
    11. 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.
    12. 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.
    13. Luis Guardiola & Ana Meca & Justo Puerto, 2020. "Quid Pro Quo allocations in Production-Inventory games," Papers 2002.00953, arXiv.org.
    14. 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.
    15. 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.
    16. 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.
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