Persuading Risk-Conscious Agents : A Geometric Approach

We consider a persuasion problem between a sender and a non-expected utility maximizing receiver whose utility may be nonlinear in her belief; we call such receivers risk-conscious. Such utility models arise, for example, when the receiver exhibits sensitivity to the variance of the payoff on choosing an action (e.g., uncertainty-aversion when waiting for a service). Due to this nonlinearity, the revelation principle fails and action recommendations no longer suffice for optimal persuasion. To overcome this challenge, we develop an optimization framework using the underlying geometry of the persuasion problem to pose it as a convex optimization program. We use this approach to analyze the setting of binary persuasion, where the receiver has two actions and the sender prefers one of them over the other in every state. Under a mild convexity assumption, we reduce the persuasion problem to a linear program, and establish a canonical basis for the set of signals in an optimal signaling scheme. The signals in this canonical set either reveal the state, or induce in the receiver uncertainty between two states. Finally, we apply our methods to optimally share waiting time information in a queueing system with uncertainty-averse customers