On the Stability of Optimal Bayesian Persuasion Strategy under a Mistrust Dynamics in Routing Games

Abstract

We extend the conventional framework of Algorithmic Bayesian Persuasion (ABP) for non-atomic routing games in two directions. First, we consider the setting where a fraction of agents do not participate in persuasion but induce externality on the agents which do. We formulate natural notions of Bayesian Wardrop equilibrium and incentive compatibility constraints for such a heterogeneous setting, and discuss convexity of computing optimal Bayesian persuasion strategy. Second, motivated by classical regret-based dynamics for learning correlated equilibria, we postulate a mistrust dynamics that tracks the time average of the agents’ perception of the degree to which the recommendation under persuasion strategy is not optimal, and hence also influences the extent to which the agents follow the recommendation. We establish convergence of the link flows induced by such a dynamical process to the link flows resulting from all agents following the persuasion-based recommendations. Simulation case study using data from the Los Angeles area is used to illustrate the methodological contributions.