Optimal Control of the Mean Field Equilibrium for a Pedestrian Tourists' Flow Model
Fabio BagagioloDepartment of Mathematics, Università di Trento, Trento, ItalySilvia FaggianDepartment of Economy, Università Ca’ Foscari Venezia, Venice, ItalyRosario MaggistroDepartment of Management, Università Ca’ Foscari Venezia, Venice, ItalyPesenti RaffaeleDepartment of Management, Università Ca’ Foscari Venezia, Venice, Italy
2018en
ABI
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 ow of tourists along the narrow alleys of the historic center of a heritage city. We initially presenta mean field game model, where both continuous and switching decisional variables are introduced to respectively describe the position of a tourist andthe 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.
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