Optimal control of the mean field equilibrium for a pedestrian tourists' flow model

TL;DR

This paper models and analyzes tourist flow in heritage city centers using mean field game theory, proving equilibrium existence and exploring control strategies to manage overcrowding effectively.

Contribution

It introduces a novel mean field game model with switching decisions for tourist movement and interest points, and proves the existence of equilibrium in this context.

Findings

Existence of a mean field equilibrium proven.

Model incorporates both continuous movement and switching interests.

Control strategies can influence tourist flow to reduce overcrowding.

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.