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On shortest path games

Author

Listed:
  • Vito Fragnelli
  • Ignacio García-Jurado
  • Luciano Méndez-Naya

Abstract

A class of cooperative TU-games arising from shortest path problems is introduced and analyzed. Some conditions under which a shortest path game is balanced are obtained. Also an axiomatic characterization of the Shapley value for this class of games is provided. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • Vito Fragnelli & Ignacio García-Jurado & Luciano Méndez-Naya, 2000. "On shortest path games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 251-264, November.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:2:p:251-264
    DOI: 10.1007/s001860000061
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    Citations

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    Cited by:

    1. Algaba, Encarnación & Fragnelli, Vito & Llorca, Natividad & Sánchez-Soriano, Joaquin, 2019. "Horizontal cooperation in a multimodal public transport system: The profit allocation problem," European Journal of Operational Research, Elsevier, vol. 275(2), pages 659-665.
    2. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2021. "Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations," Annals of Operations Research, Springer, vol. 302(1), pages 23-47, July.
    3. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    4. Rosenthal, Edward C., 2013. "Shortest path games," European Journal of Operational Research, Elsevier, vol. 224(1), pages 132-140.
    5. Miklós Pintér & Anna Radványi, 2013. "The Shapley value for shortest path games: a non-graph-based approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(4), pages 769-781, December.
    6. 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).
    7. Andreas Darmann & Christian Klamler & Ulrich Pferschy, 2015. "Sharing the Cost of a Path," Studies in Microeconomics, , vol. 3(1), pages 1-12, June.
    8. F. Fernández & J. Puerto, 2012. "The minimum cost shortest-path tree game," Annals of Operations Research, Springer, vol. 199(1), pages 23-32, October.
    9. Perea, F. & Puerto, J. & Fernández, F.R., 2009. "Modeling cooperation on a class of distribution problems," European Journal of Operational Research, Elsevier, vol. 198(3), pages 726-733, November.
    10. Sylvain Béal & André Casajus & Eric Rémila & Philippe Solal, 2019. "Cohesive efficiency in TU-games: Two extensions of the Shapley value," Working Papers 2019-03, CRESE.
    11. 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.
    12. Molinero, Xavier & Riquelme, Fabián & Serna, Maria, 2015. "Forms of representation for simple games: Sizes, conversions and equivalences," Mathematical Social Sciences, Elsevier, vol. 76(C), pages 87-102.
    13. Pantelidis, Theodoros P. & Chow, Joseph Y.J. & Rasulkhani, Saeid, 2020. "A many-to-many assignment game and stable outcome algorithm to evaluate collaborative mobility-as-a-service platforms," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 79-100.
    14. Grahn, Sofia, 2001. "Core and Bargaining Set of Shortest Path Games," Working Paper Series 2001:3, Uppsala University, Department of Economics.

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