Persuading Risk-Conscious Agents: A Geometric Approach

TL;DR

This paper develops a geometric convex optimization framework to determine optimal persuasion strategies for risk-conscious agents with nonlinear utilities, addressing limitations of traditional methods.

Contribution

It introduces a novel geometric approach to solve persuasion problems with nonlinear utilities, including conditions for full persuasion and a reduction to linear programming in binary cases.

Findings

Convex optimization framework for nonlinear utility persuasion

Conditions for achieving full persuasion

Binary persuasion reduces to a linear program

Abstract

We consider a persuasion problem between a sender and a receiver whose utility may be nonlinear in her belief; we call such receivers risk-conscious. Such utility models arise when the receiver exhibits systematic biases away from expected-utility-maximization, such as uncertainty aversion (e.g., from sensitivity to the variance of the waiting time for a service). Due to this nonlinearity, the standard approach to finding the optimal persuasion mechanism using revelation principle fails. To overcome this difficulty, we use the underlying geometry of the problem to develop a convex optimization framework to find the optimal persuasion mechanism. We define the notion of full persuasion and use our framework to characterize conditions under which full persuasion can be achieved. We use our approach to study binary persuasion, where the receiver has two actions and the sender strictly prefers one of them at every state. Under a convexity assumption, we show that the binary persuasion problem reduces to a linear program, and establish a canonical set of signals where each signal either reveals the state or induces in the receiver uncertainty between two states. Finally, we discuss the broader applicability of our methods to more general contexts, and illustrate our methodology by studying information sharing of waiting times in service systems.