Information Bargaining: Bilateral Commitment in Bayesian Persuasion

TL;DR

This paper introduces an information bargaining framework for long-term Bayesian persuasion, addressing computational challenges and clarifying the roles of informational and propositional advantages, validated through large language models.

Contribution

It proposes a novel bargaining perspective that unifies long-term Bayesian persuasion analysis and distinguishes key strategic advantages, with validation via large language models.

Findings

Framework enables fair and efficient long-term persuasion strategies.

Large language models reliably handle persuasion scenarios within this framework.

The approach clarifies the roles of information and proposer advantages in strategic communication.

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.