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A note on the Shapley value for airport cost pooling game

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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
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    References listed on IDEAS

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    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.
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    3. 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.
    4. Calvo, Emilio & Gutiérrez, Esther, 2010. "Solidarity in games with a coalition structure," Mathematical Social Sciences, Elsevier, vol. 60(3), pages 196-203, November.
    5. 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.
    6. 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.
    7. 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.
    8. S. H. Tijs & T. S. H. Driessen, 1986. "Game Theory and Cost Allocation Problems," Management Science, INFORMS, vol. 32(8), pages 1015-1028, August.
    9. 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.
    10. 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.
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    Cited by:

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    2. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2023. "Sharing the cost of hazardous transportation networks and the Priority Shapley value," Working Papers 2023-03, CRESE.
    3. Léa Munich, 2023. "Schedule Situations and their Cooperative Games," Working Papers of BETA 2023-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.

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    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

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