Robust Trust

Abstract: An agent chooses an action using her private information combined with recommendations from an informed but potentially misaligned adviser. With a known alignment probability, the adviser reports his signal truthfully; with remaining probability, the adviser can send an arbitrary message. We characterize the decision rule that maximizes the agent's worst-case expected payoff. Every optimal rule admits a trust region representation in belief space: advice is taken at face value when it induces a posterior within the trust region; otherwise, the agent acts as if the posterior were on the trust region's boundary. We derive thresholds on the alignment probability above which the adviser's presence strictly benefits the agent and fully characterize the solution in binary-state as well as binary-action environments.