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.