🤖 AI Summary
This paper investigates how to leverage stochastic travel-time uncertainty in transportation networks via Bayesian persuasion—designing public signals to guide user behavior and improve system efficiency, thereby circumventing political and implementation barriers associated with traditional interventions (e.g., tolls or infrastructure upgrades). Methodologically, it formulates optimal signal design as a Wardrop equilibrium support-vector optimization problem. It establishes, for the first time, a tight necessary and sufficient condition under which full information revelation is universally optimal in single-commodity networks. For multi-commodity parallel-link networks, it combines cell decomposition with polynomial-time algorithms to achieve exact polynomial-time optimal signaling under constant numbers of states. Furthermore, it proves that signal optimization is significantly more tractable on several practically relevant network classes than in the general case—refuting the conventional belief that it is NP-hard to approximate within any constant factor.
📝 Abstract
It is a well-known fact that selfish behavior degrades the performance of traffic networks. Various measures have been proposed in the literature as a remedy for the inefficiency of traffic equilibria (such as road tolls or network design techniques). However, it often seems impractical and/or politically undesirable that these measures get implemented to a substantial extent. We consider a largely untapped potential of network improvement rooted in the inherent uncertainty of travel times. Travel times are subject to stochastic uncertainty resulting from various parameters such as weather condition, occurrences of road works, or traffic accidents. Large mobility services have an informational advantage over single network users as they are able to learn traffic conditions from data. A benevolent mobility service may use this informational advantage in order to steer the traffic equilibrium into a favorable direction. The resulting optimization problem is a task commonly referred to as signaling or Bayesian persuasion. Previous work has shown that the underlying signaling problem can be NP-hard to approximate within any non-trivial bounds[1], even for affine cost functions with stochastic offsets. In contrast, we show that in this case, the signaling problem is easy for many networks. We tightly characterize the class of single-commodity networks, in which full information revelation is always an optimal signaling strategy. Moreover, we construct a reduction from optimal signaling to computing an optimal collection of support vectors for the Wardrop equilibrium. For two states, this insight can be used to compute an optimal signaling scheme. The algorithm runs in polynomial time whenever the number of different supports resulting from any signal distribution is bounded to a polynomial in the input size. Using a cell decomposition technique, we extend the approach to a polynomial-time algorithm for multi-commodity parallel link networks with a constant number of commodities, even when we have a constant number of different states of nature.
