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Step out–Step in sequencing games

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  • Musegaas, M.
  • Borm, P.E.M.
  • Quant, M.

Abstract

In this paper a new class of relaxed sequencing games is introduced: the class of Step out–Step in sequencing games. In this relaxation any player within a coalition is allowed to step out from his position in the processing order and to step in at any position later in the processing order. First, we show that if the value of a coalition in a relaxed sequencing game is bounded from above by the gains made by all possible neighbor switches, then the game has a non-empty core. After that, we show that this is the case for Step out –Step in sequencing games. Moreover, this paper provides a polynomial time algorithm to determine the values of the coalitions in Step out–Step in sequencing games.

Suggested Citation

  • Musegaas, M. & Borm, P.E.M. & Quant, M., 2015. "Step out–Step in sequencing games," European Journal of Operational Research, Elsevier, vol. 246(3), pages 894-906.
    • Handle: RePEc:eee:ejores:v:246:y:2015:i:3:p:894-906
    DOI: 10.1016/j.ejor.2015.05.045
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    7. Grundel, Soesja & Çiftçi, Barış & Borm, Peter & Hamers, Herbert, 2013. "Family sequencing and cooperation," European Journal of Operational Research, Elsevier, vol. 226(3), pages 414-424.
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    10. Edwin Lohmann & Peter Borm & Marco Slikker, 2014. "Sequencing situations with Just-in-Time arrival, and related games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 285-305, December.
    11. 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.
    12. Bas van Velzen & Herbert Hamers, 2003. "On the balancedness of relaxed sequencing games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(2), pages 287-297, May.
    13. Flip Klijn & Estela Sánchez, 2006. "Sequencing games without initial order," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 53-62, February.
    14. 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. Saavedra-Nieves, Alejandro & Schouten, Jop & Borm, Peter, 2020. "On interactive sequencing situations with exponential cost functions," European Journal of Operational Research, Elsevier, vol. 280(1), pages 78-89.
    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. 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.
    4. Yang, Guangjing & Sun, Hao & Hou, Dongshuang & Xu, Genjiu, 2019. "Games in sequencing situations with externalities," European Journal of Operational Research, Elsevier, vol. 278(2), pages 699-708.
    5. Atay, Ata & Calleja, Pedro & Soteras, Sergio, 2021. "Open shop scheduling games," European Journal of Operational Research, Elsevier, vol. 295(1), pages 12-21.
    6. M. Musegaas & P. E. M. Borm & M. Quant, 2018. "On the convexity of step out–step in sequencing games," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 68-109, April.
    7. Slikker, Marco, 2023. "The stable gain splitting rule for sequencing situations," European Journal of Operational Research, Elsevier, vol. 310(2), pages 902-913.
    8. 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.
    9. Ata Atay & Christian Trudeau, 2022. "Queueing games with an endogenous number of machines," Working Papers 2202, University of Windsor, Department of Economics.

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    More about this item

    Keywords

    (Cooperative) game theory; Sequencing games; Core;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory

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