Sustainable Management of Tourist Flow Networks: A Mean Field Model

2023

In this article, we propose a mean field game approach for modeling the flows of excursionists within a network of tourist attractions. We prove the existence of an equilibrium within the network using a balance ordinary differential equation together with optimality conditions in terms of the value function. We also propose a bi-level formulation of the problem where we aim at achieving a sustainable-oriented control strategy in the upper level and at maximizing excursionists’ satisfaction in the lower level. Our proposed model may provide an effective management tool for local authorities who deal with the challenging problem of finding an optimal control policy to the often conflicting o…

Sustainability and tourist flow networks: a mean field bi-level optimization approach

The widespread acknowledgement of tourism as a strategic pillar for economic growth and development has boosted competitiveness among tourist destinations. This concept has been greatly emphasized during the current COVID-19 pandemic crisis. Nevertheless, the massive presence of tourists imposes the challenge of adopting sustainable tourism practices to balance economic prosperity opportunities with potential threats to the environment and local communities. There are many definitions for sustainability, but the most effective one is ``the capacity to endure'' [Emel et al, 1997]: from an economic perspective this leads to find an equilibrium between short and long-term objectives so that to…

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

2017

This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state-space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and to global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is ill…