Capacitated Human Migration Networks and Subsidization

Large-scale migration flows are posing immense challenges for governments around the globe, with drivers ranging from climate change and disasters to wars, violence, and poverty. In this paper, we introduce multiclass human migration models under user-optimizing and system-optimizing behavior in which the locations associated with migration are subject to capacities. We construct alternative variational inequality formulations of the governing equilibrium/optimality conditions that utilize Lagrange multipliers and then derive formulae for subsidies that, when applied, guarantee that migrants will locate themselves, acting independently and selfishly, in a manner that is also optimal from a societal perspective. An algorithm is proposed, implemented, and utilized to compute solutions to numerical examples. Our framework can be applied by governmental authorities to manage migration flows and population distributions for enhanced societal welfare.