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Motivated by practical concerns in applying information design to markets and service systems, we consider a persuasion problem between a sender and a receiver where the receiver may not be an expected utility maximizer. In particular, the receiver’s utility may be non-linear in her belief; we deem such receivers as risk-conscious. Such utility models arise, for example, when the receiver exhibits sensitivity to the variability and the risk in the payoff on choosing an action (e.g., waiting time for a service). In the presence of such non-linearity, the standard approach of using revelation-principle style arguments fails to characterize the set of signals needed in the optimal signaling scheme. Our main contribution is to provide a theoretical framework, using results from convex analysis, to overcome this technical challenge. In particular, in general persuasion settings with risk-conscious agents, we prove that the sender’s problem can be reduced to a convex optimization program. Furthermore, using this characterization, we obtain a bound on the number of signals needed in the optimal signaling scheme. We apply our methods to study a specific setting, namely binary per-suasion, where the receiver has two possible actions (0 and 1), and the sender always prefers the receiver taking action 1. Under a mild convexity assumption on the receiver’s utility and using a geometric approach,we show that the convex program can be further reduced to a linear program. Furthermore, this linear program yields a canonical construction of the set of signals needed in an optimal signaling mechanism. In particular, this canonical set of signals only involves signals that fully reveal the state and signals that induce uncertainty between two states.We illustrate our results in the setting of signaling wait time information in an unobservable queue with customers whose utilities depend on the variance of their waiting times.
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This content will become publicly available on July 7, 2026
Leakage-Robust Bayesian Persuasion
This paper introduces the concept of leakage-robust Bayesian persuasion. Situated between public Bayesian persuasion and private Bayesian persuasion, leakage-robust persuasion considers a setting where one or more signals privately communicated by a sender to the receivers may be leaked. We study the design of leakage-robust Bayesian persuasion schemes and quantify the price of robustness using two formalisms: - The first notion, k-worst-case persuasiveness, requires a signaling scheme to remain persuasive as long as each receiver observes no more than k leaked signals from other receivers. We quantify the Price of Robust Persuasiveness (PoRPk)— i.e., the gap in sender's utility as compared to the optimal private persuasion scheme—as Θ(min{2k,n}) for supermodular sender utilities and Θ(k) for submodular or XOS sender utilities, where n is the number of receivers. This result also establishes that in some instances, Θ(log k) leakages are sufficient for the utility of the optimal leakage-robust persuasion to degenerate to that of public persuasion. - The second notion, expected downstream utility robustness, relaxes the persuasiveness requirement and instead considers the impact on sender's utility resulting from receivers best responding to their observations. By quantifying the Price of Robust Downstream Utility (PoRU) as the gap between the sender's expected utility over the randomness in the leakage pattern as compared to private persuasion, our results show that, over several natural and structured distributions of leakage patterns, PoRU improves PoRP to Θ(k) or even Θ(1), where k is the maximum number of leaked signals observable to each receiver across leakage patterns in the distribution. En route to these results, we show that subsampling and masking serve as general-purpose algorithmic paradigms for transforming any private persuasion signaling scheme to one that is leakage-robust, with minmax optimal loss in sender's utility. A full version of this paper can be found at https://arxiv.org/abs/2411.16624.
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- Award ID(s):
- 2022448
- PAR ID:
- 10631072
- Publisher / Repository:
- Twenty-Sixth ACM Conference on Economics and Computation (EC 2025)
- Date Published:
- Format(s):
- Medium: X
- Location:
- Stanford, California
- Sponsoring Org:
- National Science Foundation
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