IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v45y2011i10p1572-1589.html
   My bibliography  Save this article

On a mean field game approach modeling congestion and aversion in pedestrian crowds

Author

Listed:
  • Lachapelle, Aimé
  • Wolfram, Marie-Therese

Abstract

In this paper we present a new class of pedestrian crowd models based on the mean field games theory introduced by Lasry and Lions in 2006. This macroscopic approach is based on a microscopic model, that considers smart pedestrians who rationally interact and anticipate the future. This leads to a forward-backward structure in time. We focus on two-population interactions and validate the modeling with simple examples. Two complementary classes of problems are addressed, namely the case of crowd aversion and the one of congestion. In both cases we describe the model and present numerical solvers (based on the optimization formulation and the partial differential equations respectively). Finally we present numerical tests involving anticipation phenomena and complex group behaviors such as lane formation.

Suggested Citation

  • Lachapelle, Aimé & Wolfram, Marie-Therese, 2011. "On a mean field game approach modeling congestion and aversion in pedestrian crowds," Transportation Research Part B: Methodological, Elsevier, vol. 45(10), pages 1572-1589.
    • Handle: RePEc:eee:transb:v:45:y:2011:i:10:p:1572-1589
    DOI: 10.1016/j.trb.2011.07.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261511001111
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2011.07.011?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guesnerie, Roger, 1992. "An Exploration of the Eductive Justifications of the Rational-Expectations Hypothesis," American Economic Review, American Economic Association, vol. 82(5), pages 1254-1278, December.
    2. Tanimoto, Jun & Hagishima, Aya & Tanaka, Yasukaka, 2010. "Study of bottleneck effect at an emergency evacuation exit using cellular automata model, mean field approximation analysis, and game theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5611-5618.
    3. Zheng, Xiaoping & Cheng, Yuan, 2011. "Conflict game in evacuation process: A study combining Cellular Automata model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(6), pages 1042-1050.
    4. repec:dau:papers:123456789/3001 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Cheng, Yuan & Zheng, Xiaoping, 2018. "Emergence of cooperation during an emergency evacuation," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 485-494.
    2. Aurell, Alexander & Djehiche, Boualem, 2019. "Modeling tagged pedestrian motion: A mean-field type game approach," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 168-183.
    3. Xu, Qiancheng & Chraibi, Mohcine & Tordeux, Antoine & Zhang, Jun, 2019. "Generalized collision-free velocity model for pedestrian dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Abdelghany, Ahmed & Abdelghany, Khaled & Mahmassani, Hani, 2016. "A hybrid simulation-assignment modeling framework for crowd dynamics in large-scale pedestrian facilities," Transportation Research Part A: Policy and Practice, Elsevier, vol. 86(C), pages 159-176.
    5. von Sivers, Isabella & Köster, Gerta, 2015. "Dynamic stride length adaptation according to utility and personal space," Transportation Research Part B: Methodological, Elsevier, vol. 74(C), pages 104-117.
    6. Cristiani, E. & Menci, M. & Malagnino, A. & Amaro, G.G., 2023. "An all-densities pedestrian simulator based on a dynamic evaluation of the interpersonal distances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    7. Zhou, Zi-Xuan & Nakanishi, Wataru & Asakura, Yasuo, 2021. "Data-driven framework for the adaptive exit selection problem in pedestrian flow: Visual information based heuristics approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    8. Ji, Xiangfeng & Zhang, Jian & Hu, Yongkai & Ran, Bin, 2016. "Pedestrian movement analysis in transfer station corridor: Velocity-based and acceleration-based," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 416-434.

    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. Li, Jun & Fu, Siyao & He, Haibo & Jia, Hongfei & Li, Yanzhong & Guo, Yi, 2015. "Simulating large-scale pedestrian movement using CA and event driven model: Methodology and case study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 304-321.
    2. Zheng, Ying & Jia, Bin & Li, Xin-Gang & Zhu, Nuo, 2011. "Evacuation dynamics with fire spreading based on cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(18), pages 3147-3156.
    3. Zou, Baobao & Lu, Chunxia & Mao, Shirong & Li, Yi, 2020. "Effect of pedestrian judgement on evacuation efficiency considering hesitation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    4. Tian, Huan-huan & Wei, Yan-fang & Dong, Li-yun & Xue, Yu & Zheng, Rong-sen, 2018. "Resolution of conflicts in cellular automaton evacuation model with the game-theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 991-1006.
    5. Guo, Wei & Wang, Xiaolu & Liu, Mengting & Cheng, Yuan & Zheng, Xiaoping, 2015. "Modification of the dynamic floor field model by the heterogeneous bosons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 417(C), pages 358-366.
    6. Song, Xiao & Ma, Liang & Ma, Yaofei & Yang, Chen & Ji, Hang, 2016. "Selfishness- and Selflessness-based models of pedestrian room evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 455-466.
    7. Ji, Xiangfeng & Zhang, Jian & Hu, Yongkai & Ran, Bin, 2016. "Pedestrian movement analysis in transfer station corridor: Velocity-based and acceleration-based," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 416-434.
    8. Miyagawa, Daiki & Ichinose, Genki, 2020. "Cellular automaton model with turning behavior in crowd evacuation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    9. Dekel, E. & Wolinsky, A., 2000. "Rationalizable Outcomes of Large Independent Private-Value First-Price Discrete Auctions," Papers 00-13, Tel Aviv.
    10. Roger Guesnerie & Pedro Jara-Moroni, 2007. "Expectational coordination in a class of economic models: Strategic substitutabilities versus strategic complementarities," PSE Working Papers halshs-00587837, HAL.
    11. Desgranges, Gabriel & Gauthier, Stéphane, 2016. "Rationalizability and efficiency in an asymmetric Cournot oligopoly," International Journal of Industrial Organization, Elsevier, vol. 44(C), pages 163-176.
    12. Huo, Feizhou & Li, Chao & Li, Yufei & Lv, Wei & Ma, Yaping, 2022. "An extended model for describing pedestrian evacuation considering the impact of obstacles on the visual view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    13. Lawrence Christiano & Husnu Dalgic & Xiaoming Li, 2022. "Modelling the Great Recession as a Bank Panic: Challenges," Economica, London School of Economics and Political Science, vol. 89(S1), pages 200-238, June.
    14. Gabriel Desgranges & Stéphane Gauthier, 2013. "Asymmetric information and rationalizability," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(3), pages 789-804, November.
    15. Giovanni Facchini & Thierry Verdier, 2009. "Symposium on organization, heterogeneity and trade," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(3), pages 433-436, March.
    16. Roger Guesnerie, 2001. "The Government and Market Expectations," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 157(1), pages 116-126, March.
    17. Desgranges, Gabriel & Negroni, Giorgio, 2003. "Expectations Coordination On A Sunspot Equilibrium: An Eductive Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 7(1), pages 7-41, February.
    18. Jara-Moroni, Pedro, 2018. "Rationalizability and mixed strategies in large games," Economics Letters, Elsevier, vol. 162(C), pages 153-156.
    19. Sögner, Leopold, 2015. "Learning, convergence and economic constraints," Mathematical Social Sciences, Elsevier, vol. 75(C), pages 27-43.
    20. Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, vol. 75(2), pages 668-684.

    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:eee:transb:v:45:y:2011:i:10:p:1572-1589. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    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.