Information Bargaining: Bilateral Commitment in Bayesian Persuasion

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.