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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.

Suggested Citation

  • 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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    1. A. van den Nouweland & P. Borm & W. van Golstein Brouwers & R. Groot Bruinderink & S. Tijs, 1996. "A Game Theoretic Approach to Problems in Telecommunication," Management Science, INFORMS, vol. 42(2), pages 294-303, February.
    2. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, pages 90-103.
    3. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, January.
    4. Winter, Eyal, 2002. "The shapley value," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 53, pages 2025-2054 Elsevier.
    5. Chun, Youngsub, 2006. "A pessimistic approach to the queueing problem," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 171-181, March.
    6. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    7. repec:cup:apsrev:v:48:y:1954:i:03:p:787-792_00 is not listed on IDEAS
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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. 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.
    4. Youngsub Chun & Nari Park & Duygu Yengin, 2016. "Coincidence of cooperative game theoretic solutions in the appointment problem," International Journal of Game Theory, Springer;Game Theory Society, pages 699-708.
    5. Youngsub Chun & Eun Jeong Heo, 2008. "Queueing problems with two parallel servers," International Journal of Economic Theory, The International Society for Economic Theory, vol. 4(2), pages 299-315.
    6. 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.
    7. Chang, Chih & Tseng, Ying-Chih, 2011. "On the coincidence property," Games and Economic Behavior, Elsevier, vol. 71(2), pages 304-314, March.
    8. repec:eee:matsoc:v:89:y:2017:i:c:p:1-9 is not listed on IDEAS

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