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Partitioning Sequencing Situations and Games

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  • Gerichhausen, M.
  • Hamers, H.J.M.

    (Tilburg University, Center for Economic Research)

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    Abstract

    The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research. This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors.

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    Bibliographic Info

    Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2007-40.

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    Date of creation: 2007
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    Handle: RePEc:dgr:kubcen:200740

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    Web page: http://center.uvt.nl

    Related research

    Keywords: Sequencing situations; sequencing games;

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    1. Le Breton, M. & Owen, G. & Weber, S., 1991. "Strongly Balanced Cooperative Games," Papers 92-3, York (Canada) - Department of Economics.
    2. Calleja, P. & Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2004. "Job Scheduling, Cooperation and Control," Discussion Paper 2004-65, Tilburg University, Center for Economic Research.
    3. Hamers, Herbert & Klijn, Flip & Suijs, Jeroen, 1999. "On the balancedness of multiple machine sequencing games," European Journal of Operational Research, Elsevier, vol. 119(3), pages 678-691, December.
    4. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
    5. Hamers, H.J.M. & Klijn, F. & Velzen, S. van, 2002. "On the Convexity of Precedence Sequencing Games," Discussion Paper 2002-112, Tilburg University, Center for Economic Research.
    6. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
    7. Hamers, H. & Borm, P. & Tijs, S., 1993. "A Games Corresponding to Sequencing Situations with Ready Times," Papers 9316, Tilburg - Center for Economic Research.
    8. Borm, Peter & Fiestras-Janeiro, Gloria & Hamers, Herbert & Sanchez, Estela & Voorneveld, Mark, 2002. "On the convexity of games corresponding to sequencing situations with due dates," European Journal of Operational Research, Elsevier, vol. 136(3), pages 616-634, February.
    9. Reijnierse, Hans & Maschler, Michael & Potters, Jos & Tijs, Stef, 1996. "Simple Flow Games," Games and Economic Behavior, Elsevier, vol. 16(2), pages 238-260, October.
    10. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154192, Tilburg University.
    11. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
    12. Feltkamp, V. & Tijs, S.H. & Muto, S., 1994. "Minimum cost spanning extension problems: The proportional rule and the decentralized rule," Discussion Paper 1994-96, Tilburg University, Center for Economic Research.
    13. Suijs, J.P.M. & Hamers, H.J.M. & Tijs, S.H., 1997. "On the consistency of reward allocation rules in sequencing situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74764, Tilburg University.
    14. Thomson, A., 1989. "The Consistency Principle," RCER Working Papers 192, University of Rochester - Center for Economic Research (RCER).
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