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Fictitious play for finding system optimal routings in dynamic traffic networks

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  • Garcia, Alfredo
  • Reaume, Daniel
  • Smith, Robert L.

Abstract

We introduce a novel procedure to compute system optimal routings in a dynamic traffic network. Fictitious play is utilized within a game of identical interests wherein vehicles are treated as players with the common payoff of average trip time experienced in the network. This decentralized approach via repeated play of the fictitious game is proven to converge to a local system optimal routing. Results from a large-scale computational test on a real network are presented.

Suggested Citation

  • Garcia, Alfredo & Reaume, Daniel & Smith, Robert L., 2000. "Fictitious play for finding system optimal routings in dynamic traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(2), pages 147-156, February.
    • Handle: RePEc:eee:transb:v:34:y:2000:i:2:p:147-156
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    References listed on IDEAS

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    Cited by:

    1. Swenson, Brian & Murray, Ryan & Kar, Soummya, 2020. "Regular potential games," Games and Economic Behavior, Elsevier, vol. 124(C), pages 432-453.
    2. Enrique Campos-Nañez & Alfredo Garcia & Chenyang Li, 2008. "A Game-Theoretic Approach to Efficient Power Management in Sensor Networks," Operations Research, INFORMS, vol. 56(3), pages 552-561, June.
    3. Dusica Joksimovic & Erik T. Verhoef & Michiel Bliemer, 2005. "Different Policy Objectives of the Road Pricing Problem – a Game Theory Approach," ERSA conference papers ersa05p430, European Regional Science Association.
    4. Lu, Chung-Cheng & Liu, Jiangtao & Qu, Yunchao & Peeta, Srinivas & Rouphail, Nagui M. & Zhou, Xuesong, 2016. "Eco-system optimal time-dependent flow assignment in a congested network," Transportation Research Part B: Methodological, Elsevier, vol. 94(C), pages 217-239.
    5. Theodore J. Lambert & Marina A. Epelman & Robert L. Smith, 2005. "A Fictitious Play Approach to Large-Scale Optimization," Operations Research, INFORMS, vol. 53(3), pages 477-489, June.
    6. Ulrich Berger, 2004. "Some Notes on Learning in Games with Strategic Complementarities," Game Theory and Information 0409001, University Library of Munich, Germany.
    7. Ulrich Berger, 2004. "Two More Classes of Games with the Fictitious Play Property," Game Theory and Information 0408003, University Library of Munich, Germany.
    8. Bell, Michael G. H. & Cassir, Chris, 2002. "Risk-averse user equilibrium traffic assignment: an application of game theory," Transportation Research Part B: Methodological, Elsevier, vol. 36(8), pages 671-681, September.
    9. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    10. Alfredo Garcia & Stephen D. Patek & Kaushik Sinha, 2007. "A Decentralized Approach to Discrete Optimization via Simulation: Application to Network Flow," Operations Research, INFORMS, vol. 55(4), pages 717-732, August.
    11. Berger, Ulrich, 2005. "Fictitious play in 2 x n games," Journal of Economic Theory, Elsevier, vol. 120(2), pages 139-154, February.
    12. Berger, Ulrich, 2007. "Two more classes of games with the continuous-time fictitious play property," Games and Economic Behavior, Elsevier, vol. 60(2), pages 247-261, August.
    13. Irina S. Dolinskaya & Marina A. Epelman & Esra Şişikoğlu Sir & Robert L. Smith, 2016. "Parameter-Free Sampled Fictitious Play for Solving Deterministic Dynamic Programming Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 631-655, May.

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