We study a novel approach to information design in the standard traffic model of network congestion games. It captures the natural condition that the demand is unknown to the users of the network. A principal (e.g., a mobility service) commits to a signaling strategy, observes the realized demand and sends a (public) signal to agents (i.e., users of the network). Based on the induced belief about the demand, the users then form an equilibrium. We consider the algorithmic goal of the principal: Compute a signaling scheme that minimizes the expected total cost of the induced equilibrium. We concentrate on single-commodity networks and affine cost functions, for which we obtain the following results. First, we devise a fully polynomial-time approximation scheme (FPTAS) for the case that the demand can only take two values. It relies on several structural properties of the cost of the induced equilibrium as a function of the updated belief about the distribution of demands. We show that this function is piecewise linear for any number of demands, and monotonic for two demands. Second, we give a complete characterization of the graph structures for which it is optimal to fully reveal the information about the realized demand. This signaling scheme turns out to be optimal for all cost functions and probability distributions over demands if and only if the graph is series-parallel. Third, we propose an algorithm that computes the optimal signaling scheme for any number of demands whose time complexity is polynomial in the number of supports that occur in a Wardrop equilibrium for some demand. Finally, we conduct a computational study that tests this algorithm on real-world instances.

翻译：我们提出了一种在网络拥塞博弈标准交通模型中进行信息设计的新方法。该方法捕捉了网络用户需求未知的自然条件。一个主体（例如移动出行服务）承诺采用一种信号策略，观察实现的需求，并向参与者（即网络用户）发送（公共）信号。用户随后基于对需求的诱导信念形成均衡。我们考虑主体的算法目标：计算一种信号方案，以最小化诱导均衡的期望总成本。我们聚焦于单商品网络和仿射成本函数，并得到以下结果。首先，针对需求仅能取两个值的情况，我们设计了一个完全多项式时间近似方案（FPTAS）。该方案依赖于诱导均衡成本作为需求分布更新信念函数的若干结构性质。我们证明了该函数对于任意数量需求是分段线性的，且对于两个需求是单调的。其次，我们针对最优策略为完全揭示实现需求信息的图结构给出了完整刻画。当且仅当图是串并联结构时，该信号方案对所有成本函数和需求概率分布均为最优。第三，我们提出了一种算法，可计算任意数量需求的最优信号方案，其时间复杂度关于某需求下沃德罗普均衡中出现支撑点的数量呈多项式级。最后，我们开展了计算研究，在真实世界实例上测试了该算法。