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- Title
Persuading Risk-Conscious Agents: A Geometric Approach.
- Authors
Anunrojwong, Jerry; Iyer, Krishnamurthy; Lingenbrink, David
- Abstract
A Convex Programming Framework for Information Design Under Realistic Human Behavior Platform markets and services typically have additional relevant information in comparison with their users. Information design studies how the sharing of this information can be leveraged by the platform to influence user behavior and obtain desirable outcomes. Previous research has studied information design assuming that the users act to maximize their expected utility, but this assumption does not always hold in reality. Instead, people often exhibit biases and deviations from expected utility maximization. In "Persuading Risk-Conscious Agents: A Geometric Approach," Anunrojwong, Iyer, and Lingenbrink study information design with "risk-conscious" agents whose utility functions may depend nonlinearly on their beliefs. They provide a convex programming approach for solving for the optimal persuasion mechanism and establish their structural properties in different settings. They illustrate their approach in an application involving the sharing of waiting-time information in a queueing system. Overall, this work contributes to the study of information design under realistic models of human behavior. We consider a persuasion problem between a sender and a receiver where utility may be nonlinear in the latter's 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). Because of 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 we illustrate our methodology by studying information sharing of waiting times in service systems. Funding: The second and the third authors gratefully acknowledge support from the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grants CMMI-1633920 and CMMI-2002156]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2023.2438.
- Subjects
NATIONAL Science Foundation (U.S.); GEOMETRIC approach; EXPECTED utility; INFORMATION design; CONVEX programming; UTILITY functions; UTILITY theory; RISK sharing
- Publication
Operations Research, 2024, Vol 72, Issue 1, p151
- ISSN
0030-364X
- Publication type
Article
- DOI
10.1287/opre.2023.2438