Strategic dynamic vehicle routing with spatio-temporal dependent demands

We study a zero-sum game formulation of a dynamic vehicle routing problem: a system planner seeks to design dynamic routing policies for a team of vehicles to minimize the average waiting time of demands that are strategically placed in a region by an adversarial agent with unitary capacity operating from a depot. We characterize an equilibrium in the limiting case where vehicles travel arbitrarily slower than the agent (heavy load). We show that such an equilibrium consists of a routing policy based on performing successive TSP tours through outstanding demands and a unique power-law spatial density centered at the depot location.