Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response

Classic mechanism/information design imposes the assumption that agents are $\textit{fully rational}$, meaning each of them always selects the action that maximizes her expected utility. Yet many empirical evidence suggests that human decisions may deviate from this fully rationality assumption. In this work, we attempt to relax the fully rationality assumption with $\textit{bounded rationality}$. Specifically, we formulate the bounded rationality of an agent by adopting the quantal response model (McKelvey and Palfrey, 1995). We develop a theory of rationality-robust information design in the canonical setting of Bayesian persuasion (Kamenica and Gentzkow, 2011) with binary receiver action. We first identify conditions under which the optimal signaling scheme structure for a fully rational receiver remains optimal or approximately optimal for a boundedly rational receiver. In practice, it might be costly for the designer to estimate the degree of the receiver's bounded rationality level. Motivated by this practical consideration, we then study the existence and construction of $\textit{robust}$ signaling schemes when there is uncertainty about the receiver's bounded rationality level.