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A Game Theoretic Approach to the Determination of Hyperpaths in Transportation Networks

In: Transportation and Traffic Theory 2009: Golden Jubilee

Author

Listed:
  • Jan-Dirk Schmöcker

    (Tokyo Institute of Technology)

  • Michael G.H. Bell

    (Imperial College London)

  • Fumitaka Kurauchi

    (Gifu University)

  • Hiroshi Shimamoto

    (Hiroshima University)

Abstract

In transit assignment, the common lines problem leads to the notion of a hyperpath, which is a set of paths that when used according to the “take whichever attractive line arrives next” strategy minimises the expected travel time. Similarly, the game theoretic approach to risk-averse traffic assignment leads to the generation of a set of paths which minimises expected travel time when a pessimistic assumption is made about on-trip events. The equivalence between the hyperpath of transit assignment and the set of paths generated by a multi-agent, zero sum game is shown in this paper. In particular, game theory is used to show that the path split probabilities proposed by Spiess and Florian (1989) are optimal for the risk-averse traveller who needs to make an on-the-spot decision between alternative routes. An alternative two-agent (single demon), zero-sum game is considered. The results of the multiple- and two-agent games are compared on a small example network, showing that the single demon game can lead to denser hyperpaths.

Suggested Citation

  • Jan-Dirk Schmöcker & Michael G.H. Bell & Fumitaka Kurauchi & Hiroshi Shimamoto, 2009. "A Game Theoretic Approach to the Determination of Hyperpaths in Transportation Networks," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 1-18, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4419-0820-9_1
    DOI: 10.1007/978-1-4419-0820-9_1
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    Citations

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    Cited by:

    1. Bell, Michael G.H. & Fonzone, Achille & Polyzoni, Chrisanthi, 2014. "Depot location in degradable transport networks," Transportation Research Part B: Methodological, Elsevier, vol. 66(C), pages 148-161.
    2. Huang, Di & Liu, Zhiyuan & Liu, Pan & Chen, Jun, 2016. "Optimal transit fare and service frequency of a nonlinear origin-destination based fare structure," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 96(C), pages 1-19.
    3. Saeed Maadi & Jan-Dirk Schmöcker, 2020. "Route choice effects of changes from a zonal to a distance-based fare structure in a regional public transport network," Public Transport, Springer, vol. 12(3), pages 535-555, October.
    4. Bell, Michael G.H. & Trozzi, Valentina & Hosseinloo, Solmaz Haji & Gentile, Guido & Fonzone, Achille, 2012. "Time-dependent Hyperstar algorithm for robust vehicle navigation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(5), pages 790-800.
    5. Fu, Xiao & Wu, Youqi & Huang, Di & Wu, Jianjun, 2022. "An activity-based model for transit network design and activity location planning in a three-party game framework," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 168(C).
    6. Pablo E. Achurra-Gonzalez & Panagiotis Angeloudis & Nils Goldbeck & Daniel J. Graham & Konstantinos Zavitsas & Marc E. J. Stettler, 2019. "Evaluation of port disruption impacts in the global liner shipping network," Journal of Shipping and Trade, Springer, vol. 4(1), pages 1-21, December.
    7. Li, Qianfei & (Will) Chen, Peng & (Marco) Nie, Yu, 2015. "Finding optimal hyperpaths in large transit networks with realistic headway distributions," European Journal of Operational Research, Elsevier, vol. 240(1), pages 98-108.

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