Title: Information Bargaining: Bilateral Commitment in Bayesian Persuasion
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: Information Bargaining, Bayesian Persuasion, Bargaining Games, Fairness, Large Language Models

Abstract: Bayesian persuasion studies how an informed sender can influence a receiver’s actions through committed signaling schemes. While effective in one-shot settings, extending Bayesian persuasion to real-world long-term interactions becomes NP-hard.
A separate empirical mismatch is also evident, where people tend to be much more truthful in practice than the signaling scheme predicted by Bayesian persuasion equilibria.
To address these issues, we first prove that long-term Bayesian persuasion can be decomposed into a bargaining stage and a realization stage while preserving optimality and equilibria. This decomposition disentangles the previously conflated informational and first-mover advantages of the sender. Based on the results, we establish a unified, realistic, and fairness-oriented framework called \emph{information bargaining}. 
Variants of bargaining-game settings and their associated solution concepts, such as the Nash cooperative bargaining model and the Nash bargaining solution, can be applied directly to persuasion games to yield more realistic models.
To validate our framework, we identify and employ capable reasoning LLMs that can solve persuasion game equilibria effectively. In long-term persuasion task variants and in the corresponding bargaining game variants, these capable LLMs demonstrate that they reach the same equilibrium.

TL;DR: We show that variants of bargaining-game settings and their corresponding solution concepts can be applied to persuasion games to create more realistic persuasion models, thereby introducing fairness and Pareto optimality.