Persuading Agents in Opinion Formation Games

2025-09-09

AI Summary

This paper studies how a sender can optimally design an information structure via Bayesian persuasion to influence the equilibrium opinions of $n$ agents governed by the Friedkin-Johnsen (FJ) opinion dynamics model, where agents hold prior beliefs and initial opinions are driven by an unknown state of the world. Method: We jointly model opinion formation and information design, introducing Bayesian persuasion into the FJ dynamics for the first time. The sender partially reveals the state to steer the resulting public opinion equilibrium. Contribution/Results: We characterize the solvability boundary under constant-rank information structures. For subadditive objectives, we establish a polynomial-time $n$-approximation algorithm; for additive objectives, achieving an $n^{1-c}$-approximation is NP-hard. We develop efficient exact and approximation algorithms for interval-valued utility functions and prove the optimality of simple threshold policies across multiple objective classes.

Technology Category

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

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Prominent opinion formation models such as the one by Friedkin and Johnsen (FJ) concentrate on the effects of peer pressure on public opinions. In practice, opinion formation is also based on information about the state of the world and persuasion efforts. In this paper, we analyze an approach of Bayesian persuasion in the FJ model. There is an unknown state of the world that influences the preconceptions of n agents. A sender S can (partially) reveal information about the state to all agents. The agents update their preconceptions, and an equilibrium of public opinions emerges. We propose algorithms for the sender to reveal information in order to optimize various aspects of the emerging equilibrium. For many natural sender objectives, we show that there are simple optimal strategies. We then focus on a general class of range-based objectives with desired opinion ranges for each agent. We provide efficient algorithms in several cases, e.g., when the matrix of preconceptions in all states has constant rank, or when there is only a polynomial number of range combinations that lead to positive value for S. This generalizes, e.g., instances with a constant number of states and/or agents, or instances with a logarithmic number of ranges. In general, we show that subadditive range-based objectives allow a simple n-approximation, and even for additive ones, obtaining an $n^{1-c}$-approximation is NP-hard, for any constant $c > 0$.

Problem

• Optimizing Bayesian persuasion strategies in Friedkin-Johnsen opinion formation model
• Designing algorithms to reveal information for desired equilibrium outcomes
• Addressing computational complexity of range-based persuasion objectives

Innovation

• Bayesian persuasion in Friedkin-Johnsen opinion model
• Algorithms optimize sender's information revelation strategies
• Efficient solutions for range-based opinion objectives