Public Signals in Affine Network Congestion Games with Uncertain Free-Flow Times

Travel times in road networks are subject to stochastic uncertainty resulting from various parameters. A benevolent mobility service provider observing the actual travel times from data may use its informational advantage to steer the traffic equilibrium in a favorable direction through a processs known as signaling or Bayesian persuasion. Previous work has shown that the underlying signaling problem can be NP-hard to approximate better than [Formula: see text], even for static Wardrop flows with affine cost functions with stochastic offsets. In contrast, we show that in this case, the signaling problem is easy for many networks. First, we tightly characterize the class of single-commodity networks in which full information revelation is always an optimal signaling strategy. Second, we construct a reduction from optimal signaling to computing an optimal collection of active edges for the Wardrop equilibrium. For two states, this allows us to efficiently compute an optimal signaling scheme whenever the number of different active edge sets is bounded by a polynomial in the input size. Using a cell decomposition technique, we extend the approach to a polynomial-time algorithm for multicommodity parallel-edge networks provided that both the number of commodities and states are constant. Funding: This work was supported by Deutsche Forschungsgemeinschaft EXC-2046/1 [Grant 390685689] and Ho 3831/9-1 [Grant 514505843].