On Routing Drivers through Persuasion in the Long Run

We formulate and study multi-stage Bayesian persuasion framework for routing games in parallel networks with affine latency functions in two scenarios. The heterogeneous scenario contains a fixed fraction of drivers who do not participate in persuasion. The homogeneous scenario allows the sender to use time-varying route recommendation strategies while all agents participate in the persuasion. The routing decisions of participating drivers are governed by the recommendations received as well as mistrust in the sender. The mistrust dynamic is governed by the collective historical experience of all drivers with the quality of recommendations. In the heterogeneous setting, we propose a reasonable dynamic used by the non-participating drivers for estimating the mistrust of the participating drivers. We establish convergence of the estimate to the actual mistrust, and study convergence of induced link flows by simulation. For time varying recommendation strategy, we identify a sufficient condition for convergence of link flows.