This paper considers Bayesian persuasion for routing games where information about the uncertain state of the network is provided by a traffic information system (TIS) using public signals. In this setup, the TIS commits to a signalling scheme and participants form a posterior belief about the state of the network based on prior beliefs and the received signal. They subsequently select routes minimizing their individual expected travel time under their posterior beliefs, giving rise to a Wardrop equilibrium. We investigate how the TIS can infer the prior beliefs held by the participants by designing suitable signalling schemes, and observing the equilibrium flows under different signals. We show that under mild conditions a signalling scheme that allows for exact inference of the prior exists. We then provide an iterative algorithm that finds such a scheme in a finite number of steps. We show that schemes designed by our algorithm are robust, in the sense that they can still identify the prior after a small enough perturbation. We also investigate the case where the population is divided among multiple priors, and give conditions under which the fraction associated to each prior can be identified. Several examples illustrate our results.

翻译：本文研究路线博弈中的贝叶斯说服问题，其中交通信息系统（TIS）通过公开信号提供关于网络不确定状态的信息。在该设定中，TIS承诺采用一种信号方案，参与者根据先验信念和接收到的信号形成关于网络状态的后验信念。随后，参与者根据其后验信念选择能最小化个人期望出行时间的路径，由此产生Wardrop均衡。我们探讨TIS如何通过设计适当的信号方案，并观察不同信号下的均衡流量，来推断参与者持有的先验信念。研究表明，在温和条件下，存在一种能够精确推断先验的信号方案。我们进一步提出一种迭代算法，可在有限步数内找到该方案。所设计的方案具有鲁棒性——即便经过足够小的扰动，仍能识别先验分布。此外，我们研究了群体存在多种先验分布的情形，并给出了可识别每种先验对应比例的充分条件。多个算例验证了上述结论。