Abstract-We study a dynamic vehicle routing problem where demands are strategically placed in the region by an adversarial agent with unitary capacity operating from a depot. In particular, we focus on the following problem: a system planner seeks to design dynamic vehicle routing policies for a vehicle that minimize the average waiting time of a typical demand, defined as the time difference between the moment the demand is placed in the region until its location is visited by the vehicle; while the agent aims at the opposite, strategically choosing the spatial distribution to place demands. We model the problem as a complete information zero-sum game and characterize an equilibrium in the limiting case where the vehicle travels arbitrarily slower than the agent. We show that such an equilibrium is constituted by a routing policy based on performing successive traveling salesperson tours through outstanding demands and a unique power-law spatial density centered at the depot location
