IDEAS home Printed from https://ideas.repec.org/p/crb/wpaper/2023-03.html
   My bibliography  Save this paper

Sharing the cost of hazardous transportation networks and the Priority Shapley value

Author

Listed:
  • Sylvain Béal

    (Université de Franche-Comté, CRESE, F-25000 Besançon, France)

  • Adriana Navarro-Ramos

    (Université de Saint-Etienne, GATE Lyon Saint-Etienne UMR 5824, F-42023 Saint-Etienne, France)

  • Eric Rémila

    (Université de Saint-Etienne, GATE Lyon Saint-Etienne UMR 5824, F-42023 Saint-Etienne, France)

  • Philippe Solal

    (Université de Saint-Etienne, GATE Lyon Saint-Etienne UMR 5824, F-42023 Saint-Etienne, France)

Abstract

We consider the cost sharing issue resulting from the maintenance of a hazardous waste transportation network represented by a sink tree. The participating agents are located on the nodes of the network and must transport their waste to the sink through costly network portions. We introduce the Liability rule, which is inspired by the principles applied by the courts to settle cost-allocation disputes in the context of hazardous waste. We provide an axiomatic characterization of this rule. Furthermore, we show that the Liability rule coincides with the Priority Shapley value, a new allocation rule on an appropriate class of multi-choice games arising from hazardous waste transportation problems. Finally, we also axiomatize the Priority Shapley value on the full domain of multi-choice games.

Suggested Citation

  • 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.
    • Handle: RePEc:crb:wpaper:2023-03
    as

    Download full text from publisher

    File URL: https://crese.univ-fcomte.fr/uploads/wp/WP-2023-03.pdf
    File Function: First version, 2023
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Michel Grabisch & Lijue Xie, 2007. "A new approach to the core and Weber set of multichoice games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 491-512, December.
    2. Alcalde-Unzu, Jorge & Gómez-Rúa, María & Molis, Elena, 2015. "Sharing the costs of cleaning a river: the Upstream Responsibility rule," Games and Economic Behavior, Elsevier, vol. 90(C), pages 134-150.
    3. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    4. Kar, Anirban, 2002. "Axiomatization of the Shapley Value on Minimum Cost Spanning Tree Games," Games and Economic Behavior, Elsevier, vol. 38(2), pages 265-277, February.
    5. Youngsub Chun & Cheng‐Cheng Hu & Chun‐Hsien Yeh, 2012. "Characterizations of the sequential equal contributions rule for the airport problem," International Journal of Economic Theory, The International Society for Economic Theory, vol. 8(1), pages 77-85, March.
    6. Gök Sırma Zeynep Alparslan & Rodica Branzei & Stef Tijs, 2009. "Airport interval games and their Shapley value," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(2), pages 9-18.
    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. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 351-360.
    9. 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.
    10. Cruijssen, Frans & Borm, Peter & Fleuren, Hein & Hamers, Herbert, 2010. "Supplier-initiated outsourcing: A methodology to exploit synergy in transportation," European Journal of Operational Research, Elsevier, vol. 207(2), pages 763-774, December.
    11. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    12. José Zarzuelo & Marco Slikker & Flip Klijn, 1999. "Characterizations of a multi-choice value," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 521-532.
    13. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.
    14. S. Z. Alparslan Gök, 2012. "On the Interval Baker-Thompson Rule," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-5, May.
    15. Fragnelli, Vito & Marina, Maria Erminia, 2010. "An axiomatic characterization of the Baker-Thompson rule," Economics Letters, Elsevier, vol. 107(2), pages 85-87, May.
    16. Flisberg, Patrik & Frisk, Mikael & Rönnqvist, Mikael & Guajardo, Mario, 2015. "Potential savings and cost allocations for forest fuel transportation in Sweden: A country-wide study," Energy, Elsevier, vol. 85(C), pages 353-365.
    17. 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.
    18. 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.
    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. Lowing, David, 2024. "Cost allocation in energy distribution networks," Journal of Mathematical Economics, Elsevier, vol. 110(C).

    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. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    2. S. Béal & A. Lardon & E. Rémila & P. Solal, 2012. "The average tree solution for multi-choice forest games," Annals of Operations Research, Springer, vol. 196(1), pages 27-51, July.
    3. 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.
    4. David Lowing & Makoto Yokoo, 2023. "Sharing values for multi-choice games: an axiomatic approach," Working Papers hal-04018735, HAL.
    5. Thomson, William, 2024. "Cost allocation and airport problems," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 17-31.
    6. Kevin Techer, 2023. "Hazardous waste transportation: a cost allocation analysis," Working Papers hal-04099139, HAL.
    7. David Lowing, 2023. "Cost allocation in energy distribution networks," Working Papers hal-03680156, HAL.
    8. Stefano Moretti & Fioravante Patrone, 2008. "Transversality of the Shapley value," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 1-41, July.
    9. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    10. Wu, Hao & van den Brink, René & Estévez-Fernández, Arantza, 2024. "Highway toll allocation," Transportation Research Part B: Methodological, Elsevier, vol. 180(C).
    11. 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.
    12. Lowing, David, 2024. "Cost allocation in energy distribution networks," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    13. Encarnacion Algaba & Rene van den Brink, 2021. "Networks, Communication and Hierarchy: Applications to Cooperative Games," Tinbergen Institute Discussion Papers 21-019/IV, Tinbergen Institute.
    14. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    15. 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.
    16. Hao Wu & Rene van den Brink & Arantza Estevez-Fernandez, 2022. "Highway toll allocation," Tinbergen Institute Discussion Papers 22-036/II, Tinbergen Institute.
    17. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    18. Giulia Cesari & Roberto Lucchetti & Stefano Moretti, 2017. "Generalized additive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 919-939, November.
    19. Derks, Jean & Peters, Hans, 1997. "Consistent restricted Shapley values," Mathematical Social Sciences, Elsevier, vol. 33(1), pages 75-91, February.
    20. René Brink & P. Herings & Gerard Laan & A. Talman, 2015. "The Average Tree permission value for games with a permission tree," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 58(1), pages 99-123, January.

    More about this item

    Keywords

    Hazardous waste; transportation network; Liability rule; Priority Shapley value; multi- choice games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • Q53 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Environmental Economics - - - Air Pollution; Water Pollution; Noise; Hazardous Waste; Solid Waste; Recycling
    • R42 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Government and Private Investment Analysis; Road Maintenance; Transportation Planning

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:crb:wpaper:2023-03. 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: Lauent Kondratuk (email available below). General contact details of provider: https://edirc.repec.org/data/crufcfr.html .

    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.