IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2409.11908.html
   My bibliography  Save this paper

Cognitive Hierarchy in Day-to-day Network Flow Dynamics

Author

Listed:
  • Minyu Shen
  • Feng Xiao
  • Weihua Gu
  • Hongbo Ye

Abstract

When making route decisions, travelers may engage in a certain degree of reasoning about what the others will do in the upcoming day, rendering yesterday's shortest routes less attractive. This phenomenon was manifested in a recent virtual experiment that mimicked travelers' repeated daily trip-making process. Unfortunately, prevailing day-to-day traffic dynamical models failed to faithfully reproduce the collected flow evolution data therein. To this end, we propose a day-to-day traffic behavior modeling framework based on the Cognitive Hierarchy theory, in which travelers with different levels of strategic-reasoning capabilities form their own beliefs about lower-step travelers' capabilities when choosing their routes. Two widely-studied day-to-day models, the Network Tatonnement Process dynamic and the Logit dynamic, are extended into the framework and studied as examples. Calibration of the virtual experiment is performed using the extended Network Tatonnement Process dynamic, which fits the experimental data reasonably well. We show that the two extended dynamics have multiple equilibria, one of which is the classical user equilibrium. While analyzing global stability is intractable due to the presence of multiple equilibria, local stabilities near equilibria are developed analytically and verified by numerical experiments. General insights on how key parameters affect the stability of user equilibria are unveiled.

Suggested Citation

  • Minyu Shen & Feng Xiao & Weihua Gu & Hongbo Ye, 2024. "Cognitive Hierarchy in Day-to-day Network Flow Dynamics," Papers 2409.11908, arXiv.org.
  • Handle: RePEc:arx:papers:2409.11908
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2409.11908
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Wei & Szeto, Wai Yuen, 2020. "Learning and managing stochastic network traffic dynamics with an aggregate traffic representation," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 19-46.
    2. Terry L. Friesz & David Bernstein & Nihal J. Mehta & Roger L. Tobin & Saiid Ganjalizadeh, 1994. "Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems," Operations Research, INFORMS, vol. 42(6), pages 1120-1136, December.
    3. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    4. Martin L. Hazelton & David P. Watling, 2004. "Computation of Equilibrium Distributions of Markov Traffic-Assignment Models," Transportation Science, INFORMS, vol. 38(3), pages 331-342, August.
    5. Vincent P. Crawford & Miguel A. Costa-Gomes, 2006. "Cognition and Behavior in Two-Person Guessing Games: An Experimental Study," American Economic Review, American Economic Association, vol. 96(5), pages 1737-1768, December.
    6. Kumar, Amit & Peeta, Srinivas, 2015. "A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand," Transportation Research Part B: Methodological, Elsevier, vol. 80(C), pages 235-256.
    7. Feng Xiao & Minyu Shen & Zhengtian Xu & Ruijie Li & Hai Yang & Yafeng Yin, 2019. "Day-to-Day Flow Dynamics for Stochastic User Equilibrium and a General Lyapunov Function," Transportation Science, INFORMS, vol. 53(3), pages 683-694, May.
    8. Watling, David, 1996. "Asymmetric problems and stochastic process models of traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 30(5), pages 339-357, October.
    9. Smith, M. J., 1983. "The existence and calculation of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 291-303, August.
    10. Chong, Juin-Kuan & Ho, Teck-Hua & Camerer, Colin, 2016. "A generalized cognitive hierarchy model of games," Games and Economic Behavior, Elsevier, vol. 99(C), pages 257-274.
    11. Jin, Wen-Long, 2007. "A dynamical system model of the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 32-48, January.
    12. Wen-yi Zhang & Wei Guan & Ji-hui Ma & Jun-fang Tian, 2015. "A Nonlinear Pairwise Swapping Dynamics to Model the Selfish Rerouting Evolutionary Game," Networks and Spatial Economics, Springer, vol. 15(4), pages 1075-1092, December.
    13. Michael J. Smith, 1984. "The Stability of a Dynamic Model of Traffic Assignment---An Application of a Method of Lyapunov," Transportation Science, INFORMS, vol. 18(3), pages 245-252, August.
    14. He, Xiaozheng & Guo, Xiaolei & Liu, Henry X., 2010. "A link-based day-to-day traffic assignment model," Transportation Research Part B: Methodological, Elsevier, vol. 44(4), pages 597-608, May.
    15. Colin F. Camerer & Teck-Hua Ho & Juin-Kuan Chong, 2004. "A Cognitive Hierarchy Model of Games," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 861-898.
    16. Anna Nagurney & Ding Zhang, 1997. "Projected Dynamical Systems in the Formulation, Stability Analysis, and Computation of Fixed-Demand Traffic Network Equilibria," Transportation Science, INFORMS, vol. 31(2), pages 147-158, May.
    17. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    18. Tsakas, Elias & Voorneveld, Mark, 2009. "The target projection dynamic," Games and Economic Behavior, Elsevier, vol. 67(2), pages 708-719, November.
    19. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    20. Ekkehard Köhler & Martin Strehler, 2019. "Traffic Signal Optimization: Combining Static and Dynamic Models," Service Science, INFORMS, vol. 53(1), pages 21-41, February.
    21. G. E. Cantarella & E. Cascetta, 1995. "Dynamic Processes and Equilibrium in Transportation Networks: Towards a Unifying Theory," Transportation Science, INFORMS, vol. 29(4), pages 305-329, November.
    22. Avi Goldfarb & Mo Xiao, 2011. "Who Thinks about the Competition? Managerial Ability and Strategic Entry in US Local Telephone Markets," American Economic Review, American Economic Association, vol. 101(7), pages 3130-3161, December.
    23. Li, Ruijie & Liu, Xiaobo & Nie, Yu (Marco), 2018. "Managing partially automated network traffic flow: Efficiency vs. stability," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 300-324.
    24. Smith, M. J., 1979. "The existence, uniqueness and stability of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 295-304, December.
    25. Yang, Hai & Zhang, Xiaoning & Meng, Qiang, 2007. "Stackelberg games and multiple equilibrium behaviors on networks," Transportation Research Part B: Methodological, Elsevier, vol. 41(8), pages 841-861, October.
    26. Yang, Fan & Zhang, Ding, 2009. "Day-to-day stationary link flow pattern," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 119-126, January.
    27. Teck-Hua Ho & Xuanming Su, 2013. "A Dynamic Level-k Model in Sequential Games," Management Science, INFORMS, vol. 59(2), pages 452-469, March.
    28. Han, Linghui & Wang, David Z.W. & Lo, Hong K. & Zhu, Chengjuan & Cai, Xingju, 2017. "Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 1-16.
    29. Horowitz, Joel L., 1984. "The stability of stochastic equilibrium in a two-link transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 18(1), pages 13-28, February.
    30. Smith, M. J., 1979. "Traffic control and route-choice; a simple example," Transportation Research Part B: Methodological, Elsevier, vol. 13(4), pages 289-294, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Xu, Xiangdong & Qu, Kai & Chen, Anthony & Yang, Chao, 2021. "A new day-to-day dynamic network vulnerability analysis approach with Weibit-based route adjustment process," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 153(C).
    2. Sun, Mingmei, 2023. "A day-to-day dynamic model for mixed traffic flow of autonomous vehicles and inertial human-driven vehicles," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 173(C).
    3. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    4. Ren-Yong Guo & Hai-Jun Huang & Hai Yang, 2019. "Tradable Credit Scheme for Control of Evolutionary Traffic Flows to System Optimum: Model and its Convergence," Networks and Spatial Economics, Springer, vol. 19(3), pages 833-868, September.
    5. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    6. Li, Pengbo & Tian, Lijun & Xiao, Feng & Zhu, Hongwei, 2022. "Can day-to-day dynamic model be solved analytically? New insights on portraying equilibrium and accommodating autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 374-395.
    7. Han, Linghui & Wang, David Z.W. & Lo, Hong K. & Zhu, Chengjuan & Cai, Xingju, 2017. "Discrete-time day-to-day dynamic congestion pricing scheme considering multiple equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 1-16.
    8. Feng Xiao & Minyu Shen & Zhengtian Xu & Ruijie Li & Hai Yang & Yafeng Yin, 2019. "Day-to-Day Flow Dynamics for Stochastic User Equilibrium and a General Lyapunov Function," Transportation Science, INFORMS, vol. 53(3), pages 683-694, May.
    9. Peeta, Srinivas, 2016. "A marginal utility day-to-day traffic evolution model based on one-step strategic thinkingAuthor-Name: He, Xiaozheng," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 237-255.
    10. Jiayang Li & Zhaoran Wang & Yu Marco Nie, 2023. "Wardrop Equilibrium Can Be Boundedly Rational: A New Behavioral Theory of Route Choice," Papers 2304.02500, arXiv.org, revised Feb 2024.
    11. Rambha, Tarun & Boyles, Stephen D., 2016. "Dynamic pricing in discrete time stochastic day-to-day route choice models," Transportation Research Part B: Methodological, Elsevier, vol. 92(PA), pages 104-118.
    12. Li, Ruijie & Liu, Xiaobo & Nie, Yu (Marco), 2018. "Managing partially automated network traffic flow: Efficiency vs. stability," Transportation Research Part B: Methodological, Elsevier, vol. 114(C), pages 300-324.
    13. Wei Nai & Zan Yang & Dan Li & Lu Liu & Yuting Fu & Yuao Guo, 2024. "Urban Day-to-Day Travel and Its Development in an Information Environment: A Review," Sustainability, MDPI, vol. 16(6), pages 1-29, March.
    14. Lie Han, 2022. "Proportional-Switch Adjustment Process with Elastic Demand and Congestion Toll in the Absence of Demand Functions," Networks and Spatial Economics, Springer, vol. 22(4), pages 709-735, December.
    15. Hongbo Ye & Hai Yang, 2017. "Rational Behavior Adjustment Process with Boundedly Rational User Equilibrium," Transportation Science, INFORMS, vol. 51(3), pages 968-980, August.
    16. G. E. Cantarella & D. P. Watling, 2016. "Modelling road traffic assignment as a day-to-day dynamic, deterministic process: a unified approach to discrete- and continuous-time models," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 69-98, March.
    17. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Tan, Zhijia, 2015. "Link-based day-to-day network traffic dynamics and equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 248-260.
    18. Farokhi, Farhad & Johansson, Karl H., 2015. "A piecewise-constant congestion taxing policy for repeated routing games," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 123-143.
    19. Xiaomei Zhao & Chunhua Wan & Jun Bi, 2019. "Day-to-Day Assignment Models and Traffic Dynamics Under Information Provision," Networks and Spatial Economics, Springer, vol. 19(2), pages 473-502, June.
    20. Wang, Guanfeng & Jia, Hongfei & Feng, Tao & Tian, Jingjing & Wu, Ruiyi & Gao, Heyao & Liu, Chao, 2024. "Modelling the dual dynamic traffic flow evolution with information perception differences between human-driven vehicles and connected autonomous vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2409.11908. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.