IDEAS home Printed from https://ideas.repec.org/a/kap/netspa/v22y2022i2d10.1007_s11067-019-09475-4.html
   My bibliography  Save this article

Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model

Author

Listed:
  • Fabio Bagagiolo

    (Università di Trento)

  • Silvia Faggian

    (Università Ca’ Foscari Venezia)

  • Rosario Maggistro

    (Università Ca’ Foscari Venezia)

  • Raffaele Pesenti

    (Università Ca’ Foscari Venezia)

Abstract

Art heritage cities are popular tourist destinations but for many of them overcrowding is becoming an issue. In this paper, we address the problem of modeling and analytically studying the flow of tourists along the narrow alleys of the historic center of a heritage city. We initially present a mean field game model, where both continuous and switching decisional variables are introduced to respectively describe the position of a tourist and the point of interest that he/she may visit. We prove the existence of a mean field equilibrium. A mean field equilibrium is Nash-type equilibrium in the case of infinitely many players. Then, we study an optimization problem for an external controller who aims to induce a suitable mean field equilibrium.

Suggested Citation

  • Fabio Bagagiolo & Silvia Faggian & Rosario Maggistro & Raffaele Pesenti, 2022. "Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists’ Flow Model," Networks and Spatial Economics, Springer, vol. 22(2), pages 243-266, June.
    • Handle: RePEc:kap:netspa:v:22:y:2022:i:2:d:10.1007_s11067-019-09475-4
    DOI: 10.1007/s11067-019-09475-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11067-019-09475-4
    File Function: Abstract
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11067-019-09475-4?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. Smith, M. J., 1979. "The marginal cost taxation of a transportation network," Transportation Research Part B: Methodological, Elsevier, vol. 13(3), pages 237-242, September.
    2. repec:dau:papers:123456789/3001 is not listed on IDEAS
    3. Robert B. Dial, 1999. "Network-Optimized Road Pricing: Part I: A Parable and a Model," Operations Research, INFORMS, vol. 47(1), pages 54-64, February.
    4. Abhijit V. Banerjee, 1992. "A Simple Model of Herd Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 797-817.
    5. Fabio Bagagiolo & Dario Bauso & Rosario Maggistro & Marta Zoppello, 2017. "Game Theoretic Decentralized Feedback Controls in Markov Jump Processes," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 704-726, May.
    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. Joseph Andria & Rosario Maggistro & Raffaele Pesenti, 2023. "Sustainable Management of Tourist Flow Networks: A Mean Field Model," Journal of Optimization Theory and Applications, Springer, vol. 196(2), pages 730-761, February.

    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. Yang, Hai & Huang, Hai-Jun, 2004. "The multi-class, multi-criteria traffic network equilibrium and systems optimum problem," Transportation Research Part B: Methodological, Elsevier, vol. 38(1), pages 1-15, January.
    2. Ruomeng Cui & Dennis J. Zhang & Achal Bassamboo, 2019. "Learning from Inventory Availability Information: Evidence from Field Experiments on Amazon," Management Science, INFORMS, vol. 65(3), pages 1216-1235, March.
    3. Jonas Hedlund & Carlos Oyarzun, 2018. "Imitation in heterogeneous populations," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 65(4), pages 937-973, June.
    4. Cao, Melanie & Shi, Shouyong, 2006. "Signaling in the Internet craze of initial public offerings," Journal of Corporate Finance, Elsevier, vol. 12(4), pages 818-833, September.
    5. Kraemer, Carlo & Noth, Markus & Weber, Martin, 2006. "Information aggregation with costly information and random ordering: Experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 59(3), pages 423-432, March.
    6. Fishman, Arthur & Fishman, Ram & Gneezy, Uri, 2019. "A tale of two food stands: Observational learning in the field," Journal of Economic Behavior & Organization, Elsevier, vol. 159(C), pages 101-108.
    7. Cavatorta, Elisa & Guarino, Antonio & Huck, Steffen, 2024. "Social learning with partial and aggregate information: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 146(C), pages 292-307.
    8. Edgardo Arturo Ayala Gaytán, 2009. "Social network externalities and price dispersion in online markets," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 1-28, November.
    9. Buechel, Berno & Hellmann, Tim & Klößner, Stefan, 2015. "Opinion dynamics and wisdom under conformity," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 240-257.
    10. Boğaçhan Çelen & Kyle Hyndman, 2012. "An experiment of social learning with endogenous timing," Review of Economic Design, Springer;Society for Economic Design, vol. 16(2), pages 251-268, September.
    11. Hiroshi Kitamura, 2007. "Capacity Expansion in Markets with Intertemporal Consumption Externalities," Discussion Papers in Economics and Business 07-11, Osaka University, Graduate School of Economics.
    12. Bohl, Martin T. & Branger, Nicole & Trede, Mark, 2017. "The case for herding is stronger than you think," Journal of Banking & Finance, Elsevier, vol. 85(C), pages 30-40.
    13. Hussinger, Katrin & Pellens, Maikel, 2019. "Guilt by association: How scientific misconduct harms prior collaborators," Research Policy, Elsevier, vol. 48(2), pages 516-530.
    14. Di Bella, Gabriel & Grigoli, Francesco, 2019. "Optimism, pessimism, and short-term fluctuations," Journal of Macroeconomics, Elsevier, vol. 60(C), pages 79-96.
    15. Umar, Muhammad & Su, Chi-Wei & Rizvi, Syed Kumail Abbas & Lobonţ, Oana-Ramona, 2021. "Driven by fundamentals or exploded by emotions: Detecting bubbles in oil prices," Energy, Elsevier, vol. 231(C).
    16. Wang, Peiwen & Chen, Minghua & Wu, Ji & Yan, Yuanyun, 2023. "Do peer effects matter in bank risk? Some cross-country evidence," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 88(C).
    17. Battaglini, Marco, 2005. "Sequential voting with abstention," Games and Economic Behavior, Elsevier, vol. 51(2), pages 445-463, May.
    18. Malik, Saif Ullah & Elahi, Muhammad Ather, 2014. "Analysis of Herd Behavior Using Quantile Regression: Evidence from Karachi Stock Exchange (KSE)," MPRA Paper 55322, University Library of Munich, Germany.
    19. Bartosz Wilczek, 2020. "Misinformation and herd behavior in media markets: A cross-national investigation of how tabloids’ attention to misinformation drives broadsheets’ attention to misinformation in political and business," PLOS ONE, Public Library of Science, vol. 15(11), pages 1-22, November.
    20. Hans Schenk, 1996. "Bandwagon mergers, international competitiveness, and government policy," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 23(3), pages 255-278, October.

    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:kap:netspa:v:22:y:2022:i:2:d:10.1007_s11067-019-09475-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.