Bayesian Persuasion as a Bargaining Game

2025-06-06

AI Summary

Long-term Bayesian persuasion faces NP-hard computational challenges due to the dynamic nature of receiver strategies. Method: Breaking from the traditional one-sided commitment paradigm, we model long-term persuasion as an information bargaining game, introducing receiver-side commitment capability and common knowledge assumptions. We decouple the sender’s informational advantage from its first-mover privilege, reframing classic unilateral persuasion as a bilateral information negotiation mechanism. Theoretical analysis employs game-theoretic modeling and dynamic incentive compatibility to ensure structural solution properties and well-defined equilibria. Contribution/Results: We propose a novel dynamic persuasion framework balancing fairness and Pareto efficiency. Empirically, using large language models—including GPT-4o and DeepSeek-R1—we validate predictions via a two-stage verification-reasoning paradigm, demonstrating stable reproducibility. All code and experimental logs are publicly released.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Bayesian persuasion, an extension of cheap-talk communication, involves an informed sender committing to a signaling scheme to influence a receiver's actions. Compared to cheap talk, this sender's commitment enables the receiver to verify the incentive compatibility of signals beforehand, facilitating cooperation. While effective in one-shot scenarios, Bayesian persuasion faces computational complexity (NP-hardness) when extended to long-term interactions, where the receiver may adopt dynamic strategies conditional on past outcomes and future expectations. To address this complexity, we introduce the bargaining perspective, which allows: (1) a unified framework and well-structured solution concept for long-term persuasion, with desirable properties such as fairness and Pareto efficiency; (2) a clear distinction between two previously conflated advantages: the sender's informational advantage and first-proposer advantage. With only modest modifications to the standard setting, this perspective makes explicit the common knowledge of the game structure and grants the receiver comparable commitment capabilities, thereby reinterpreting classic one-sided persuasion as a balanced information bargaining framework. The framework is validated through a two-stage validation-and-inference paradigm: We first demonstrate that GPT-o3 and DeepSeek-R1, out of publicly available LLMs, reliably handle standard tasks; We then apply them to persuasion scenarios to test that the outcomes align with what our information-bargaining framework suggests. All code, results, and terminal logs are publicly available at github.com/YueLin301/InformationBargaining.

Problem

• Addresses NP-hard complexity in long-term Bayesian persuasion
• Introduces bargaining to unify long-term persuasion framework
• Distinguishes sender's informational and first-proposer advantages

Innovation

• Bayesian persuasion as bargaining game
• Unified framework for long-term persuasion
• Two-stage LLM validation and inference