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 maximize short-term revenues along with long-term growth strategies. Within the tourism industry a straight definition is provided by the WTO for which sustainable tourism is ``tourism that takes full account of its current and future economic, social and environmental impacts, addressing the needs of visitors, the industry, the environment and host communities''[UNWTO, 2005]. In this study we apply the tools of the mean field game theory [Lasry et al, 2007] to support a local authorities to deal with the challenging problem of finding the total visitors' experiential satisfaction while attaining the maximum sustainability benefits. To this end, inspired by the study in [Bagagiolo et al, 2021], we introduce a theoretical model that describes the visitors flows in a network which depicts an area of tourist attractions. We also propose and formalize a bi-level optimal control model which addresses the often conflicting objectives of defining a sustainable-oriented policy by the local authorities while visitor aim at maximizing their satisfaction [Andria et al, 2020]. Specifically, the model upper level addresses the problem of selecting an optimal sustainable oriented control strategy, while its lower level describes the visitor flows in the assumption that the visitor satisfaction can be expressed in terms of the minimization of an appropriate cost function.