IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v108y2018icp162-169.html
   My bibliography  Save this article

A note on the Shapley value for airport cost pooling game

Author

Listed:
  • Hou, Dongshuang
  • Sun, Hao
  • Sun, Panfei
  • Driessen, Theo

Abstract

The main goal of this paper is two-fold. First, we introduce the so-called airport cost pooling game, which is a generalization of the well-known class of airport game (Littlechild and Thompson, 1977). We determine the Shapley value of this class of game through a decomposition method for this game into unanimity cost games, exploiting the linearity of the Shapley value. Second, we characterize the Shapley value for airport cost pooling game by applying the so-called collective balanced contributions property, meaning that for any two airplanes from two different airlines, the withdrawal of one airline leads to the same loss to the airplane in the other.

Suggested Citation

  • Hou, Dongshuang & Sun, Hao & Sun, Panfei & Driessen, Theo, 2018. "A note on the Shapley value for airport cost pooling game," Games and Economic Behavior, Elsevier, vol. 108(C), pages 162-169.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:162-169
    DOI: 10.1016/j.geb.2017.04.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825617300714
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.geb.2017.04.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Dongshuang Hou & Theo Driessen, 2013. "CONVEXITY OF THE "AIRPORT PROFIT GAME" ANDk-CONVEXITY OF THE "BANKRUPTCY GAME"," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-13.
    2. Yoshio Kamijo, 2013. "The collective value: a new solution for games with coalition structures," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 572-589, October.
    3. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    4. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    5. Tijs, S.H. & Driessen, T.S.H., 1986. "Game theory and cost allocation problems," Other publications TiSEM 376c24c5-c95d-4d29-96b6-4, Tilburg University, School of Economics and Management.
    6. Rodica Brânzei & Elena Iñarra & Stef Tijs & José Zarzuelo, 2006. "A Simple Algorithm for the Nucleolus of Airport Profit Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 259-272, August.
    7. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    8. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    9. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    10. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 389-407.
    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. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    2. Dongshuang Hou & Aymeric Lardon & Hao Sun, 2020. "On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations," Working Papers 2019, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    3. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2023. "Sharing the cost of hazardous transportation networks and the Priority Shapley value," Working Papers hal-04222245, HAL.
    4. Léa Munich, 2023. "Schedule Situations and their Cooperative Games," Working Papers of BETA 2023-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    5. Dongshuang Hou & Aymeric Lardon & Hao Sun, 2020. "On the Internal and External Stability of Coalitions and Application to Group Purchasing Organizations," Working Papers halshs-02860639, HAL.
    6. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    7. Luo, Chunlin & Zhou, Xiaoyang & Lev, Benjamin, 2022. "Core, shapley value, nucleolus and nash bargaining solution: A Survey of recent developments and applications in operations management," Omega, Elsevier, vol. 110(C).
    8. Grahame F. Thompson, 2020. "Deal or no deal? Some reflections on the ‘Baker-Thompson rule,’ ‘matching,’ and ‘market design’," Journal of Cultural Economy, Taylor & Francis Journals, vol. 13(5), pages 652-662, September.

    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. Vásquez-Brage, M. & van den Nouweland, C.G.A.M. & García-Jurado, I., 1995. "Owen's coalitional value and aircraft landing fees," Discussion Paper 1995-104, Tilburg University, Center for Economic Research.
    2. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    3. Paula González & Carmen Herrero, 2004. "Optimal sharing of surgical costs in the presence of queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 59(3), pages 435-446, July.
    4. Casas-Mendez, Balbina & Garcia-Jurado, Ignacio & van den Nouweland, Anne & Vazquez-Brage, Margarita, 2003. "An extension of the [tau]-value to games with coalition structures," European Journal of Operational Research, Elsevier, vol. 148(3), pages 494-513, August.
    5. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cooperative Interval Games Arising from Airport Situations with Interval Data," Other publications TiSEM 5ded50b5-2a11-4d25-8511-b, Tilburg University, School of Economics and Management.
    6. Alparslan-Gok, S.Z. & Brânzei, R. & Tijs, S.H., 2008. "Cooperative Interval Games Arising from Airport Situations with Interval Data," Discussion Paper 2008-57, Tilburg University, Center for Economic Research.
    7. Vásquez-Brage, M. & van den Nouweland, C.G.A.M. & García-Jurado, I., 1995. "Owen's coalitional value and aircraft landing fees," Other publications TiSEM 3f2bc27b-b5c8-4517-8ffd-8, Tilburg University, School of Economics and Management.
    8. Léa Munich, 2023. "Schedule Situations and their Cooperative Games," Working Papers of BETA 2023-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    9. Vazquez-Brage, M. & van den Nouweland, A. & Garcia-Jurado, I., 1997. "Owen's coalitional value and aircraft landing fees," Mathematical Social Sciences, Elsevier, vol. 34(3), pages 273-286, October.
    10. Grahn-Voorneveld, Sofia, 2012. "Sharing costs in Swedish road ownership associations," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(4), pages 645-651.
    11. Juan Aparicio & Joaquín Sánchez-Soriano, 2008. "Depreciation games," Annals of Operations Research, Springer, vol. 158(1), pages 205-218, February.
    12. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    13. Grahn-Voorneveld, Sofia, 2011. "Sharing costs in Swedish road ownership associations," Working papers in Transport Economics 2011:6, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
    14. Norde, Henk & Fragnelli, Vito & Garcia-Jurado, Ignacio & Patrone, Fioravante & Tijs, Stef, 2002. "Balancedness of infrastructure cost games," European Journal of Operational Research, Elsevier, vol. 136(3), pages 635-654, February.
    15. Hougaard, Jens Leth & Tvede, Mich & Østerdal, Lars Peter, 2013. "Cost Sharing in Chains and Other Fixed Trees," Discussion Papers on Economics 12/2013, University of Southern Denmark, Department of Economics.
    16. Bergantiños, Gustavo & Martínez, Ricardo, 2014. "Cost allocation in asymmetric trees," European Journal of Operational Research, Elsevier, vol. 237(3), pages 975-987.
    17. Fragnelli, Vito & Marina, Maria Erminia, 2010. "An axiomatic characterization of the Baker-Thompson rule," Economics Letters, Elsevier, vol. 107(2), pages 85-87, May.
    18. Xun-Feng Hu, 2020. "The weighted Shapley-egalitarian value for cooperative games with a coalition structure," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 193-212, April.
    19. M. Albizuri & J. Echarri & J. Zarzuelo, 2015. "A non-cooperative mechanism for the Shapley value of airport problems," Annals of Operations Research, Springer, vol. 235(1), pages 1-11, December.
    20. Christian Basteck & Frank Huettner, 2023. "Coalitional Manipulations and Immunity of the Shapley Value," Papers 2310.20415, arXiv.org.

    More about this item

    Keywords

    Shapley value; Airport cost pooling game; Characterization; Collective balanced contributions property;
    All these keywords.

    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:108:y:2018:i:c:p:162-169. 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.