Adaptive pricing and learning in the multi-market routing problem

In modern urban transportation networks, multiple self-interested travel providers (public transit, micromobility providers, ride-sharing platforms and toll roads) compete for heterogenous transportation users that wish to balance time and cost. Traditional congestion models assume fixed, exogenous costs, while dynamic‑pricing frameworks typically focus on a single operator, overlooking the rich strategic interplay among decentralised transportation providers. This paper introduces the Multi‑Market Routing Problem (MMRP), a game‑theoretic model in which each provider utilises adaptive pricing to maximise profit and heterogeneous transportation users which aim to minimise their travel time and cost.<br/><br/>We present the MMRP as an extension of traditional congestion games, and extend it to consider online instances for adaptive pricing under dynamic and stochastic congestion. We demonstrate the computational complexity for game-theoretic and exact solutions to the MMRP, reflecting the computational complexity of coordinating routing in dynamic and uncertain settings. To address this, we propose the use of independent Proximal Policy Optimisation as a decentralised and effective solution to the online MMRP, demonstrating reduced travel times and more equitable and fair outcomes for transportation users, and increased profitability for transportation providers. The MMRP framework and learning algorithms offer a principled foundation for competitive, multimodal routing in modern urban transportation networks.