Optimal allocation of resources via optimal transport

In this work, we propose a Stackelberg-like model for a resource allocation problem over an urban region. The model incorporates transportation costs, distribution costs, and utility functions. A social planner aims to minimize the total cost while maximizing the welfare of the population that receives the resource. The resulting formulation is a bilevel optimization problem—also known as a Stackelberg game in game theory. The existence of the best-response function is established by means of results from optimal transport theory.