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

Inferring the prior in routing games using public signalling