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 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. Finally, we show how in the simplified 2-road, 2-state case such a scheme can be constructed without the need for a sequential procedure. Several examples illustrate our results.

中文翻译：

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使用公共信号推断路由游戏的先验

本文考虑了用于路由游戏的贝叶斯说服，其中有关网络不确定状态的信息由使用公共信号的交通信息系统 (TIS) 提供。在此设置中，TIS 致力于信令方案，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。他们随后根据他们的后验信念选择最小化他们个人预期旅行时间的路线，从而产生 Wardrop 均衡。我们研究了 TIS 如何通过设计合适的信号方案并观察不同信号下的平衡流来推断参与者持有的先验信念。我们表明，在温和条件下，存在允许精确推断先验的信令方案。然后，我们提供了一种迭代算法，可以在有限的步骤中找到这样的方案。最后，我们展示了如何在简化的 2-road, 2-state 情况下构建这样的方案，而无需顺序过程。几个例子说明了我们的结果。