Optimal Maritime Transport through Mean Field Games and inference of its parameters
Man Field Games for Maritime Traffic
Charles-Albert Lehalle 
Abstract
A New paper with Giulia Livieri: Competition among seaports through Mean Field Games and real-world data
This paper presents a Mean Field Game (MFG) model for maritime traffic flow, treating the navigation of ships between seaports as a large-scale stochastic control problem. The MFG framework enables the modeling of agents at a microscopic level as rational decision-makers who seek to optimize their utility, thereby translating complex microscopic behaviors into macroscopic models. We build upon this MFG framework to develop a mesoscopic-scale MFG model that defines the payoff and cost functions for a coordinator at each seaport considered in our study. The coordinator determines the routes taken by ships transporting goods between ports by evaluating several key factors: transportation costs, expected profit margins from loading specific goods at the seaports and unloading them at various destinations, and a congestion term that reflects the costs associated with accessing the destination port. We derive an explicit solution for the stationary version of the model under certain approximations and establish conditions necessary to ensure the uniqueness of the corresponding Mean Field Equilibrium (MFE). Furthermore, we introduce a statistical methodology to infer the parameters of the game from real-world data, specifically focusing on costs and the components of expected commercial margins. To validate our model in a real-world context, we analyze the ShipFix dataset of daily ‘’Dry Coal’’ shipments worldwide from 2015 to 2025. Our discussion highlights the influence of empirical traffic flow on various components of costs. We believe that this research represents a significant advancement in the application of MFGs for effective maritime traffic management and offers valuable insights for practitioners in the field.
