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Sequencing games with repeated players

Author

Listed:
  • Estevez Fernandez, M.A.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

  • Calleja, P.
  • Hamers, H.J.M.

    (Tilburg University, School of Economics and Management)

Abstract

Two classes of one machine sequencing situations are considered in which each job corresponds to exactly one player but a player may have more than one job to be processed, so called RP(repeated player) sequencing situations. In max-RP sequencing situations it is assumed that each player’s cost function is linear with respect to the maximum completion time of his jobs, whereas in min-RP sequencing situations the cost functions are linear with respect to the minimum completion times. For both classes, following explicit procedures to go from the initial processing order to an optimal order for the coalition of all players, equal gain splitting rules are defined. It is shown that these rules lead to core elements of the associated RP sequencing games. Moreover, it is seen that min-RP sequencing games are convex. Copyright Springer Science+Business Media, LLC 2008
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Suggested Citation

  • Estevez Fernandez, M.A. & Borm, P.E.M. & Calleja, P. & Hamers, H.J.M., 2008. "Sequencing games with repeated players," Other publications TiSEM e80f7089-c7f4-4683-9f13-4, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:e80f7089-c7f4-4683-9f13-44991be6a279
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    References listed on IDEAS

    as
    1. 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.
    2. Sprumont, Yves, 1990. "Population monotonic allocation schemes for cooperative games with transferable utility," Games and Economic Behavior, Elsevier, vol. 2(4), pages 378-394, December.
    3. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Other publications TiSEM cd695be5-0f54-4548-a952-2, Tilburg University, School of Economics and Management.
    4. Wayne E. Smith, 1956. "Various optimizers for single‐stage production," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 59-66, March.
    5. Lloyd S. Shapley, 1967. "On balanced sets and cores," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 14(4), pages 453-460.
    6. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
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    Citations

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    Cited by:

    1. Marieke Quant & Marc Meertens & Hans Reijnierse, 2008. "Processing games with shared interest," Annals of Operations Research, Springer, vol. 158(1), pages 219-228, February.
    2. Schouten, Jop, 2022. "Cooperation, allocation and strategy in interactive decision-making," Other publications TiSEM d5d41448-8033-4f6b-8ec0-c, Tilburg University, School of Economics and Management.
    3. Estevez Fernandez, M.A. & Mosquera, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2006. "Proportionate Flow Shop Games," Other publications TiSEM d54cb827-3347-4150-9792-b, Tilburg University, School of Economics and Management.
    4. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Other publications TiSEM 3e1db5c9-0f77-4f91-a075-c, Tilburg University, School of Economics and Management.
    5. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Other publications TiSEM 17013f33-1d65-4294-802c-b, Tilburg University, School of Economics and Management.
    6. Davila-Pena, Laura & Borm, Peter & Garcia-Jurado, Ignacio & Schouten, Jop, 2023. "An Allocation Rule for Graph Machine Scheduling Problems," Discussion Paper 2023-009, Tilburg University, Center for Economic Research.
    7. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, G., 2020. "Sequencing Situations and Games with Non-Linear Cost Functions," Discussion Paper 2020-006, Tilburg University, Center for Economic Research.
    8. Estévez-Fernández, Arantza & Hamers, Herbert, 2020. "Chinese postman games with multi-located players," European Journal of Operational Research, Elsevier, vol. 285(2), pages 458-469.
    9. Schouten, Jop & Saavedra-Nieves, Alejandro & Fiestras-Janeiro, M. Gloria, 2021. "Sequencing situations and games with non-linear cost functions under optimal order consistency," European Journal of Operational Research, Elsevier, vol. 294(2), pages 734-745.
    10. Arantza (M.A.) Estevez-Fernandez & Herbert Hamers, 2018. "Chinese postman games with repeated players," Tinbergen Institute Discussion Papers 18-081/II, Tinbergen Institute.
    11. Herbert Hamers & Flip Klijn & Marco Slikker, 2013. "Price of Anarchy in Sequencing Situations and the Impossibility to Coordinate," Working Papers 709, Barcelona School of Economics.

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    More about this item

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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