Designing Inferable Signaling Schemes for Bayesian Persuasion

2025-10-01

AI Summary

This paper studies Bayesian persuasion under *inferable commitment*, where the receiver does not know the sender’s signaling mechanism and must infer it through repeated interactions. To address this inferability challenge, we propose two novel mechanism design approaches: (1) a stochastic gradient descent (SGD) algorithm guided by the sender’s utility, and (2) an optimization framework incorporating bounded-rational receiver models. Our theoretical analysis characterizes how signal-space structure and action discriminability affect persuasion performance, and establishes sample complexity bounds for approximating the fully committed benchmark. Empirically, on a security alert application, our methods yield more concise signals, improve distinguishability of optimal actions, and achieve rapid convergence with SGD—even under limited interaction—attaining performance close to the full-commitment optimum. The core contribution is the first systematic formulation of inferable Bayesian persuasion, accompanied by a design paradigm that delivers both rigorous theoretical guarantees and strong practical efficacy.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

In Bayesian persuasion, an informed sender, who observes a state, commits to a randomized signaling scheme that guides a self-interested receiver's actions. Classical models assume the receiver knows the commitment. We, instead, study the setting where the receiver infers the scheme from repeated interactions. We bound the sender's performance loss relative to the known-commitment case by a term that grows with the signal space size and shrinks as the receiver's optimal actions become more distinct. We then lower bound the samples required for the sender to approximately achieve their known-commitment performance in the inference setting. We show that the sender requires more samples in persuasion compared to the leader in a Stackelberg game, which includes commitment but lacks signaling. Motivated by these bounds, we propose two methods for designing inferable signaling schemes, one being stochastic gradient descent (SGD) on the sender's inference-setting utility, and the other being optimization with a boundedly-rational receiver model. SGD performs best in low-interaction regimes, but modeling the receiver as boundedly-rational and tuning the rationality constant still provides a flexible method for designing inferable schemes. Finally, we apply SGD to a safety alert example and show it to find schemes that have fewer signals and make citizens' optimal actions more distinct compared to the known-commitment case.

Problem

• Studies receiver inferring signaling schemes from repeated interactions in Bayesian persuasion
• Bounds sender's performance loss and required samples for known-commitment performance
• Proposes methods for designing inferable schemes using SGD and bounded rationality

Innovation

• Uses stochastic gradient descent for signaling scheme optimization
• Models receiver as boundedly-rational for scheme design
• Applies gradient methods to improve action distinctiveness