IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/08569957-5741-4082-ae18-c96731113da4.html
   My bibliography  Save this paper

On the Core of Multiple Longest Traveling Salesman Games

Author

Listed:
  • Estevez Fernandez, M.A.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

  • Hamers, H.J.M.

    (Tilburg University, School of Economics and Management)

Abstract

In this paper we introduce multiple longest traveling salesman (MLTS) games. An MLTS game arises from a network in which a salesman has to visit each node (player) precisely once, except its home location, in an order that maximizes the total reward.First it is shown that the value of a coalition of an MLTS game is determined by taking the maximum of suitable combinations of one and two person coalitions.Secondly it is shown that MLTS games with ¯ve or less players have a nonempty core.However, a six player MLTS game may have an empty core.For the special instance where the reward between a pair of nodes is equal to 0 or 1, we provide relations between the structure of the core and the underlying network.
(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 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 vers
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Estevez Fernandez, M.A. & Borm, P.E.M. & Hamers, H.J.M., 2003. "On the Core of Multiple Longest Traveling Salesman Games," Other publications TiSEM 08569957-5741-4082-ae18-c, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:08569957-5741-4082-ae18-c96731113da4
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/599564/127.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Potters, J.A.M. & Curiel, I. & Tijs, S.H., 1992. "Traveling salesman games," Other publications TiSEM 0dd4cf3d-25fa-4179-80f6-6, Tilburg University, School of Economics and Management.
    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. Grabisch, Michel & Li, Tong, 2011. "On the set of imputations induced by the k-additive core," European Journal of Operational Research, Elsevier, vol. 214(3), pages 697-702, November.
    2. Arantza Estévez-Fernández & Peter Borm & Marc Meertens & Hans Reijnierse, 2009. "On the core of routing games with revenues," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 291-304, June.

    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. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
    2. Kovalenkov, A. & Holtz Wooders, M., 1997. "Epsilon Cores of Games and Economies With Limited Side Payments," UFAE and IAE Working Papers 392.97, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    3. van den Brink, René, 2012. "Efficiency and collusion neutrality in cooperative games and networks," Games and Economic Behavior, Elsevier, vol. 76(1), pages 344-348.
    4. Haimanko, Ori & Le Breton, Michel & Weber, Shlomo, 2004. "Voluntary formation of communities for the provision of public projects," Journal of Economic Theory, Elsevier, vol. 115(1), pages 1-34, March.
    5. Herings, P.J.J. & van der Laan, G. & Talman, A.J.J., 2005. "The component fairness solution for cycle-free graph games," Research Memorandum 057, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. 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.
    7. Arantza Estévez-Fernández & Peter Borm & Marc Meertens & Hans Reijnierse, 2009. "On the core of routing games with revenues," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 291-304, June.
    8. Debasis Mishra & A. Talman, 2010. "A characterization of the average tree solution for tree games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 105-111, March.
    9. Trine Platz & Herbert Hamers, 2015. "On games arising from multi-depot Chinese postman problems," Annals of Operations Research, Springer, vol. 235(1), pages 675-692, December.
    10. Boros, E. & Gurvich, V. & Vasin, A., 1997. "Stable families of coalitions and normal hypergraphs1," Mathematical Social Sciences, Elsevier, vol. 34(2), pages 107-123, October.
    11. Herings, P. Jean Jacques & van der Laan, Gerard & Talman, Dolf, 2008. "The average tree solution for cycle-free graph games," Games and Economic Behavior, Elsevier, vol. 62(1), pages 77-92, January.
    12. Estévez-Fernández, Arantza & Reijnierse, Hans, 2014. "On the core of cost-revenue games: Minimum cost spanning tree games with revenues," European Journal of Operational Research, Elsevier, vol. 237(2), pages 606-616.
    13. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Tvede, Mich & Østerdal, Lars Peter, 2017. "Sharing the proceeds from a hierarchical venture," Games and Economic Behavior, Elsevier, vol. 102(C), pages 98-110.
    14. Osicka, Ondrej & Guajardo, Mario & Jörnsten, Kurt, 2019. "Cooperation of customers in traveling salesman problems with profits," Discussion Papers 2019/17, Norwegian School of Economics, Department of Business and Management Science.
    15. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, September.
    16. Iehle, Vincent, 2007. "The core-partition of a hedonic game," Mathematical Social Sciences, Elsevier, vol. 54(2), pages 176-185, September.
    17. 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.
    18. Kimms, A. & Kozeletskyi, I., 2016. "Core-based cost allocation in the cooperative traveling salesman problem," European Journal of Operational Research, Elsevier, vol. 248(3), pages 910-916.
    19. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
    20. Daniel Granot & Jeroen Kuipers & Sunil Chopra, 2002. "Cost Allocation for a Tree Network with Heterogeneous Customers," Mathematics of Operations Research, INFORMS, vol. 27(4), pages 647-661, November.

    More about this item

    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:tiu:tiutis:08569957-5741-4082-ae18-c96731113da4. 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: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    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.