We study optimal information provision in transportation networks when users are strategic and the network state is uncertain. An omniscient planner observes the network state and discloses information to the users with the goal of minimizing the expected travel time at the user equilibrium. Public signal policies, including full-information disclosure, are known to be inefficient in achieving optimality. For this reason, we focus on private signals and restrict without loss of generality the analysis to signals that coincide with path recommendations that satisfy obedience constraints, namely users have no incentive in deviating from the received recommendation according to their posterior belief. We first formulate the general problem and analyze its properties for arbitrary network topologies and delay functions. Then, we consider the case of two parallel links with affine delay functions, and provide sufficient conditions under which optimality can be achieved by information design. Interestingly, we observe that the system benefits from uncertainty, namely it is easier for the planner to achieve optimality when the variance of the uncertain parameters is large. We then provide an example where optimality can be achieved even if the sufficient conditions for optimality are not met.

翻译：我们研究了当用户具有策略性且网络状态不确定时，交通网络中的最优信息提供问题。一个全知规划者观察网络状态并向用户披露信息，目标是在用户均衡状态下最小化期望出行时间。已知公开信号策略（包括完全信息揭示）在实现最优性方面效率低下。为此，我们聚焦于私有信号，并在不失一般性的前提下将分析限制在与满足约束服从条件的路径推荐相一致的信号上，即用户没有动机根据其后验信念偏离所收到的推荐。我们首先阐述了该一般性问题，并分析了其在任意网络拓扑结构和延迟函数下的性质。随后，我们考虑了具有仿射延迟函数的两条平行链路的情况，并给出了通过信息设计能够实现最优性的充分条件。有趣的是，我们观察到系统会受益于不确定性，即当不确定参数的方差较大时，规划者更容易实现最优性。最后，我们给出了一个即使未能满足最优性的充分条件也能实现最优性的例子。