Efficient Shapley-Based Influence Attribution in Social Networks

2026-05-27

AI Summary

This work addresses the problem of fairly evaluating the individual contributions of seed users in social networks prior to information diffusion, a critical need for budget allocation, influencer pricing, and credit assignment under privacy constraints. Building upon cooperative game theory, we propose the first ex ante influence attribution framework based on the Shapley value. Theoretical analysis reveals that exact computation is feasible in polynomial time for single-step activation models, whereas the multi-step diffusion setting is #P-hard. To tackle this intractability, we develop an efficient approximation algorithm with formal theoretical guarantees. Extensive experiments on both real-world and synthetic networks demonstrate the effectiveness and scalability of our approach, offering a practical and equitable solution for ex ante influence attribution.

Abstract

The ubiquity of social platforms has reshaped the way information, behaviors, and advertisements diffuse across networks, with influence propagation often initiated by a small set of ``seed'' users. While much of the literature emphasizes optimizing seed selection to maximize spread, a critical yet underexplored question remains: how to fairly estimate the contributions of individual seeds ``ex-ante'', i.e., before the diffusion process occurs? This capability is essential for budget allocation, influencer pricing, and fair, privacy-preserving credit distribution under uncertainty, without relying on ex-post cascade logs that capture only a single execution of influence propagation. We introduce a framework for ex-ante influence attribution based on Shapley values from cooperative game theory, which capture each seed's marginal impact in a principled and equitable manner. Adapting Shapley values to influence propagation raises unique computational challenges due to the stochastic nature of diffusion and the intricate dependencies across network structures. To address these challenges, we design polynomial-time algorithms for the special case of single-step activation that is of independent practical interest, establish a sharp tractability boundary by proving $\#P$-hardness for any propagation beyond one step, and develop approximation algorithms with provable guarantees for the standard IC model as well as time-bounded variants. Empirical evaluation on real-world and synthetic networks demonstrates that our methods are both efficient and effective, offering a practical mechanism for ex-ante influence attribution.

Problem

• influence attribution
• Shapley values
• social networks
• ex-ante estimation
• seed contribution

Innovation

• Shapley value
• influence attribution
• social networks
• ex-ante estimation
• computational tractability