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

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.

Automated summary

This paper addresses the issue of modeling and studying tourist flow in the narrow alleys of historic heritage cities. It introduces a mean field game model and an optimization problem to study the existence of mean field equilibrium.