IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v62y2008i1p116-139.html
   My bibliography  Save this article

Core stability in chain-component additive games

Author

Listed:
  • van Velzen, Bas
  • Hamers, Herbert
  • Solymosi, Tamas

Abstract

Chain-component additive games are graph-restricted superadditive games, where an exogenously given line-graph determines the cooperative possibilities of the players.These games can model various multi-agent decision situations, such as strictly hierarchical organisations or sequencing / scheduling related problems, where an order of the agents is fixed by some external factor, and with respect to this order only consecutive coalitions can generate added value. In this paper we characterise core stability of chain-component additive games in terms of polynomial many linear inequalities and equalities that arise from the combinatorial structure of the game.Furthermore we show that core stability is equivalent to essential extendibility.We also obtain that largeness of the core as well as extendibility and exactness of the game are equivalent properties which are all sufficient for core stability.Moreover, we also characterise these properties in terms of linear inequalities.
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract was borrowed from another version of this item.)
(This abstract w
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • van Velzen, Bas & Hamers, Herbert & Solymosi, Tamas, 2008. "Core stability in chain-component additive games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 116-139, January.
    • Handle: RePEc:eee:gamebe:v:62:y:2008:i:1:p:116-139
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(07)00045-0
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1994. "Sequencing and cooperation," Other publications TiSEM be67f9e9-7a4a-47f1-9fb9-7, Tilburg University, School of Economics and Management.
    2. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(4), pages 419-427.
    3. Hamers, H.J.M. & Borm, P.E.M. & Tijs, S.H., 1993. "On games corresponding to sequencing situations with ready times," Other publications TiSEM 8e2af556-5430-4f98-9334-c, Tilburg University, School of Economics and Management.
    4. Imma Curiel & Jos Potters & Rajendra Prasad & Stef Tijs & Bart Veltman, 1994. "Sequencing and Cooperation," Operations Research, INFORMS, vol. 42(3), pages 566-568, June.
    5. J. R. G. van Gellekom & J. A. M. Potters & J. H. Reijnierse, 1999. "Prosperity properties of TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 211-227.
    6. Tamás Solymosi & Harry Aarts & Theo Driessen, 1998. "On Computing the Nucleolus of a Balanced Connected Game," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 983-1009, November.
    7. 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.
    8. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    9. Flip Klijn & Dries Vermeulen & Herbert Hamers & Tamás Solymosi & Stef Tijs & Joan Pere Villar, 2003. "Neighbor games and the leximax solution," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(2), pages 191-208, November.
    10. Herbert Hamers & Flip Klijn & Bas Velzen, 2005. "On the Convexity of Precedence Sequencing Games," Annals of Operations Research, Springer, vol. 137(1), pages 161-175, July.
    11. Biswas, A. K. & Parthasarathy, T. & Potters, J. A. M. & Voorneveld, M., 1999. "Large Cores and Exactness," Games and Economic Behavior, Elsevier, vol. 28(1), pages 1-12, July.
    12. Amit K. Biswas & G. Ravindran & T. Parthasarathy, 2000. "Stability and largeness of core for symmetric games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 11-22.
    13. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
    14. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ata Atay & Marina Núñez, 2019. "Multi-sided assignment games on m-partite graphs," Annals of Operations Research, Springer, vol. 279(1), pages 271-290, August.
    2. Estévez-Fernández, Arantza, 2012. "New characterizations for largeness of the core," Games and Economic Behavior, Elsevier, vol. 76(1), pages 160-180.
    3. Péter Csóka & P. Herings & László Kóczy, 2011. "Balancedness conditions for exact games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(1), pages 41-52, August.
    4. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Other publications TiSEM 68df1061-50bc-43bf-b79c-a, Tilburg University, School of Economics and Management.
    5. Sylvain Béal & Eric Rémila & Philippe Solal, 2013. "Accessibility and stability of the coalition structure core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 187-202, October.
    6. van Velzen, S., 2005. "Simple Combinatorial Optimisation Cost Games," Discussion Paper 2005-118, Tilburg University, Center for Economic Research.
    7. van Velzen, S., 2005. "Cooperation in Networks and Scheduling," Other publications TiSEM 81d927bb-fc40-4306-8f7f-a, Tilburg University, School of Economics and Management.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gerichhausen, M. & Hamers, H.J.M., 2007. "Partitioning Sequencing Situations and Games," Discussion Paper 2007-40, Tilburg University, Center for Economic Research.
    2. Gerichhausen, Marloes & Hamers, Herbert, 2009. "Partitioning sequencing situations and games," European Journal of Operational Research, Elsevier, vol. 196(1), pages 207-216, July.
    3. van Velzen, S. & Hamers, H.J.M., 2002. "On the Balancedness of Relaxed Sequencing Games," Discussion Paper 2002-49, Tilburg University, Center for Economic Research.
    4. van Velzen, Bas, 2006. "Sequencing games with controllable processing times," European Journal of Operational Research, Elsevier, vol. 172(1), pages 64-85, July.
    5. van Velzen, S., 2003. "Sequencing Games with Controllable Processing Time," Discussion Paper 2003-105, Tilburg University, Center for Economic Research.
    6. Gerichhausen, M. & Hamers, H.J.M., 2007. "Partitioning Sequencing Situations and Games," Other publications TiSEM 2bddbf5c-c56d-4b10-ba47-5, Tilburg University, School of Economics and Management.
    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.
    8. Ciftci, B.B. & Borm, P.E.M. & Hamers, H.J.M. & Slikker, M., 2008. "Batch Sequencing and Cooperation," Other publications TiSEM ed1f8fce-da76-41a6-9a9e-9, Tilburg University, School of Economics and Management.
    9. Estevez Fernandez, M.A. & Mosquera, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2006. "Proportionate Flow Shop Games," Discussion Paper 2006-63, Tilburg University, Center for Economic Research.
    10. Pedro Calleja & Peter Borm & Herbert Hamers & Flip Klijn & Marco Slikker, 2002. "On a New Class of Parallel Sequencing Situations and Related Games," Annals of Operations Research, Springer, vol. 109(1), pages 265-277, January.
    11. Min Ji & Sai Liu & Xiaolin Zhang & Keke Cao & T. C. E. Cheng, 2017. "Sequencing Games with Slack Due Windows and Group Technology Considerations," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(2), pages 121-133, February.
    12. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    13. Herbert Hamers & Flip Klijn & Bas van Velzen, 2002. "On Games corresponding to Sequencing Situations with Precedence Relations," UFAE and IAE Working Papers 553.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    14. 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.
    15. Imma Curiel, 2010. "Multi-stage sequencing situations," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 151-162, March.
    16. Calleja, P. & Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2004. "Job Scheduling, Cooperation and Control," Other publications TiSEM 05906ac6-b582-4ee7-875e-9, Tilburg University, School of Economics and Management.
    17. Imma Curiel & Herbert Hamers & Stef Tijs & Jos Potters, 1997. "Restricted component additive games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 45(2), pages 213-220, June.
    18. Fragnelli, V. & Llorca, N. & Sánchez-Soriano, J. & Tijs, S.H., 2006. "Convex Games with Countable Number of Players and Sequencing Situations," Discussion Paper 2006-119, Tilburg University, Center for Economic Research.
    19. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    20. Hirai, Toshiyuki & Watanabe, Naoki, 2018. "von Neumann–Morgenstern stable sets of a patent licensing game: The existence proof," Mathematical Social Sciences, Elsevier, vol. 94(C), pages 1-12.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:62:y:2008:i:1:p:116-139. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.