Persuading Risk-Conscious Agents: A Geometric Approach

43 Pages Posted: 13 Jun 2019 Last revised: 11 May 2020

See all articles by Jerry Anunrojwong

Jerry Anunrojwong

Columbia University - Columbia Business School

Krishnamurthy Iyer

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering

David Lingenbrink

Cornell University

Date Written: May 10, 2020

Abstract

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.

Keywords: Bayesian persuasion, non-expected utility maximizers, revelation principle

JEL Classification: C70, D4, D82, D83

Suggested Citation

Anunrojwong, Jerry and Iyer, Krishnamurthy and Lingenbrink, David, Persuading Risk-Conscious Agents: A Geometric Approach (May 10, 2020). Available at SSRN: https://ssrn.com/abstract=3386273 or http://dx.doi.org/10.2139/ssrn.3386273

Jerry Anunrojwong

Columbia University - Columbia Business School ( email )

3022 Broadway
New York, NY 10027
United States

HOME PAGE: http://jerryanunroj.github.io/

Krishnamurthy Iyer (Contact Author)

University of Minnesota - Twin Cities - Department of Industrial and Systems Engineering ( email )

111 Church St SE
Minneapolis, MN 55455
United States

David Lingenbrink

Cornell University ( email )

Ithaca, NY 14853
United States

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