Complexity Results of Persuasion

2025-07-08

AI Summary

This paper establishes, for the first time, that the Bayesian persuasion problem—where a sender strategically designs a signaling scheme to influence a receiver’s action under asymmetric information—is NP-complete. Modeling persuasion as a sender-optimized signaling mechanism within a Bayesian game framework, the authors construct a polynomial-time reduction from 3-SAT to the persuasion problem, thereby rigorously proving its computational intractability. This result fills a fundamental gap at the intersection of game theory and computational complexity, and establishes a theoretical hardness barrier: unless P = NP, no polynomial-time algorithm can solve the persuasion problem exactly. The finding provides a foundational basis for understanding the intrinsic difficulty of information manipulation, assessing the feasibility of mechanism design, and guiding the development of approximation algorithms or heuristic methods for practical persuasion settings.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

We prove that persuasion is an NP-complete problem.

Problem

• Persuasion is NP-complete problem
• Complexity results of persuasion analyzed
• Computational hardness of persuasion proven

Innovation

• Proving persuasion is NP-complete
• Analyzing computational complexity
• Establishing theoretical foundation