When Competition Helps: Achieving Optimal Traffic Flow with Multiple Autonomous Planners

The inefficiency of selfish routing in congested networks is a classical problem in algorithmic game theory, often captured by the Price of Anarchy (i.e., the ratio between the social cost of decentralized decisions and that of a centrally optimized solution.) With the advent of autonomous vehicles, capable of receiving and executing centrally assigned routes, it is natural to ask whether their deployment can eliminate this inefficiency. At first glance, a central authority could simply compute an optimal traffic assignment and instruct each vehicle to follow its assigned path. However, this vision overlooks critical challenges: routes must be individually rational (no vehicle has an incentive to deviate), and in practice, multiple planning agents (e.g., different companies) may coexist and compete. Surprisingly, we show that such competition is not merely an obstacle but a necessary ingredient for achieving optimal outcomes. In this work, we design a routing mechanism that embraces competition and converges to an optimal assignment, starting from the classical Pigou network as a foundational case.