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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
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    References listed on IDEAS

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    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. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. S. Z. Alparslan Gök, 2012. "On the Interval Baker-Thompson Rule," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-5, May.
    9. Fragnelli, Vito & Marina, Maria Erminia, 2010. "An axiomatic characterization of the Baker-Thompson rule," Economics Letters, Elsevier, vol. 107(2), pages 85-87, May.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
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    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

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