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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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. repec:dau:papers:123456789/3001 is not listed on IDEAS
    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.
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    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.

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