Human-in-the-Loop Learning for Dynamic Congestion Games

Today mobile users learn and share their traffic observations via crowdsourcing platforms (e.g., Google Maps and Waze). Yet such platforms simply cater to selfish users’ myopic interests to recommend the shortest path, and do not encourage enough users to travel and learn other paths for future others. Prior studies focus on one-shot congestion games without considering users’ information learning, while our work studies how users learn and alter traffic conditions on stochastic paths in a human-in-the-loop manner. In a typical parallel routing network with one deterministic path and multiple stochastic paths, our analysis shows that the myopic routing policy (used by Google Maps and Waze) leads to severe under-exploration of stochastic paths. This results in a price of anarchy (PoA) greater than 2, as compared to the socially optimal policy achieved through optimal exploration-exploitation tradeoff in minimizing the long-term social cost. Besides, the myopic policy fails to ensure the correct learning convergence about users’ traffic hazard beliefs. To address this, we focus on informational (non-monetary) mechanisms as they are easier to implement than pricing. We first show that existing information-hiding mechanisms and deterministic path-recommendation mechanisms in Bayesian persuasion literature do not work with even $\text{PoA}=\infty$. Accordingly, we propose a new combined hiding and probabilistic recommendation (CHAR) mechanism to hide all information from a selected user group and provide state-dependent probabilistic recommendations to the other user group. Our CHAR mechanism successfully ensures PoA less than $\frac{5}{4}$, which cannot be further reduced by any other informational (non-monetary) mechanism. Besides the parallel network, we further extend our analysis and CHAR mechanism to more general linear path graphs with multiple intermediate nodes, and we prove that the PoA results remain unchanged. Additionally, we carry out experiments with real-world datasets to further extend our routing graphs and verify the close-to-optimal performance of our CHAR mechanism.