Targeted Bayesian Persuasion in a Basic Selfish Routing Game

Travellers are selfish and make routing choices maximizing their own utility, which inevitably leads to congestion and inefficiency in the traffic network. However, travellers’ route choices are affected by the availability and accuracy of travel information. This raises the question: How can the central planner reduce the congestion of the traffic network by designing the information environment for travellers? We approach this question in the framework of Bayesian persuasion. We consider a basic selfish routing game with one risky route and one safe route, wherein the central planner conducts Bayesian persuasion (by sending noisy signals) to a fraction of travellers and no information to the rest of travellers. We first identify travellers’ equilibrium route choice given a certain persuasion strategy. Then, with the objective of minimizing total congestion cost, we decide the optimal persuasion policy, which includes the optimal percentage of travellers that should be targeted by Bayesian persuasion (persuasion coverage) and the optimal information accuracy. We find that first-best outcome can be restored under certain situations by leveraging both the instruments of persuasion coverage and information accuracy.