Formal Verification of Diffusion Auctions

2025-11-11

AI Summary

Formal verification of information diffusion and strategic interactions in diffusion auctions remains challenging due to the dynamic, networked nature of propagation and agent incentives. Method: We propose the first modal-logic-based modeling framework that rigorously formalizes both diffusion processes over social networks and agents’ strategic behavior. We design a dedicated model-checking algorithm to automatically verify game-theoretic equilibrium properties—such as Nash equilibrium—and analyze its decidability and computational complexity using tools from complexity theory. Contributions/Results: (1) We establish the first logical formalism tailored to diffusion auctions; (2) we enable automated verification of equilibrium properties; and (3) we prove that Nash equilibrium is decidable in this framework and provide a tight complexity bound—namely, PSPACE-completeness—for the model-checking algorithm. Our work lays a theoretical foundation and provides a practical methodology for formally verifying the correctness and incentive compatibility of diffusion auction mechanisms.

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
• Web Mining and Content Analysis: Content-based information diffusion
• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks

Abstract

In diffusion auctions, sellers can leverage an underlying social network to broaden participation, thereby increasing their potential revenue. Specifically, sellers can incentivise participants in their auction to diffuse information about the auction through the network. While numerous variants of such auctions have been recently studied in the literature, the formal verification and strategic reasoning perspectives have not been investigated yet. Our contribution is threefold. First, we introduce a logical formalism that captures the dynamics of diffusion and its strategic dimension. Second, for such a logic, we provide model-checking procedures that allow one to verify properties as the Nash equilibrium, and that pave the way towards checking the existence of sellers'strategies. Third, we establish computational complexity results for the presented algorithms.

Problem

• Formally verifying strategic properties in diffusion auction mechanisms
• Developing model-checking procedures for Nash equilibrium verification
• Establishing computational complexity of diffusion auction verification algorithms

Innovation

• Logical formalism captures diffusion dynamics and strategy
• Model-checking procedures verify Nash equilibrium properties
• Computational complexity results established for algorithms