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A cooperative game approach to cost allocation in a rapid-transit network

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  • Rosenthal, Edward C.

Abstract

We consider the problem of allocating costs of a regional transit system to its users, who employ shortest path routes between all pairs of nodes in the system network. We provide an axiomatic set of conditions that a solution should satisfy and use cooperative game theory to model the cost allocation problem. We provide an allocation, called the equal cost share solution, which is efficient to compute and is the unique solution that satisfies the conditions. In addition, we show not only that the cost allocation game has a nonempty core, but further, that the game is concave, meaning that the Shapley value allocation, which coincides with the equal cost share solution, always lies in the core of the game. We provide an application of the equal cost share solution to the Washington, D.C. Metro transit network and compare it to the existing fare pricing structure. As compared to equal cost share pricing, the Metro overcharges for short downtown trips and undercharges for very long commutes. The equal cost share solution is easy to update in real time as the cost data and user distribution change, or when the transit network expands.

Suggested Citation

  • Rosenthal, Edward C., 2017. "A cooperative game approach to cost allocation in a rapid-transit network," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 64-77.
    • Handle: RePEc:eee:transb:v:97:y:2017:i:c:p:64-77
    DOI: 10.1016/j.trb.2016.11.014
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    4. Bahel, Eric & Gómez-Rúa, María & Vidal-Puga, Juan, 2024. "Stable and weakly additive cost sharing in shortest path problems," Journal of Mathematical Economics, Elsevier, vol. 110(C).
    5. Gusev, Vasily V., 2020. "The vertex cover game: Application to transport networks," Omega, Elsevier, vol. 97(C).
    6. Adil Baykasoğlu & Burcu Kubur Özbel, 2021. "Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty," Operational Research, Springer, vol. 21(3), pages 2149-2179, September.
    7. Léa Munich, 2023. "Schedule Situations and their Cooperative Games," Working Papers of BETA 2023-08, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    8. Xiaohui Wu & Ren He & Meiling He, 2021. "Chaos Analysis of Urban Low-Carbon Traffic Based on Game Theory," IJERPH, MDPI, vol. 18(5), pages 1-12, February.
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    10. Hao Wu & Rene van den Brink & Arantza Estevez-Fernandez, 2022. "Highway toll allocation," Tinbergen Institute Discussion Papers 22-036/II, Tinbergen Institute.
    11. Dan C. Popescu & Philip Kilby, 2020. "Approximation of the Shapley value for the Euclidean travelling salesman game," Annals of Operations Research, Springer, vol. 289(2), pages 341-362, June.
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    13. Munich, Léa, 2024. "Schedule situations and their cooperative game theoretic representations," European Journal of Operational Research, Elsevier, vol. 316(2), pages 767-778.
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