Open problems for the Shapley Royalty Share framework: strategic robustness, semivalue foundations, scalable estimation, and economic design of generative-AI copyright royalties

The Shapley Royalty Share (SRS) framework of Wang, Deng, Chiba-Okobe, Barak, and Su (2024) proposes compensating copyright owners proportionally to their contribution to AI-generated content: the utility of a coalition of data sources is the log-likelihood that a counterfactual generative model trained only on that coalition's data would produce the content in question, and each owner's royalty share is the normalized Shapley value of this cooperative game. The paper's own limitations and future-work discussion indicate that the open problems it states remain unresolved: (a) robustness to strategic manipulation such as data replication, merging/splitting of datasets, and injection of non-copyrighted or AI-generated data; (b) an axiomatically justified payoff rule within the semivalue class for ratio-based royalty distribution; (c) game-theoretically grounded revenue division between AI developers and copyright owners beyond the preliminary permission-structure model; (d) efficient Shapley estimation for large numbers of owners in generative settings; (e) treatment of owners who cannot or will not negotiate (e.g., orphan works); and (f) the effect of learning stochasticity on the estimates, which the paper asserts is minimal in the per-source setting it studies while acknowledging that royalty shares become potentially noisy for very small data sources. Later literature has sharpened the threats (adversarial attacks that inflate attribution-based compensation; results showing semivalue-based valuation is gameable) and made partial progress on scalable estimation and uncertainty quantification, but no component is closed. Together, these directions chart the completion of SRS into a deployable, strategically robust, and axiomatically grounded royalty mechanism.

Background

Generative AI systems are trained on large corpora of text, images, and other media that are partly copyrighted, and rightsholders increasingly demand compensation rather than relying on fair-use doctrine. A licensing-market alternative needs (i) a metric for each training-data source's contribution to a given AI-generated item and (ii) a payout rule that turns these metrics into payments that owners will accept as fair.

The SRS framework (Wang, Deng, Chiba-Okobe, Barak, and Su, 2024, arXiv:2404.13964) provides both. Suppose $n$ copyright owners hold datasets $D^{(1)},\dots,D^{(n)}$, and a deployed model trained on all of them generates a content item $x^{(\mathrm{gen})}$ (an artwork, a logo, a passage of text). For a coalition $S$ of owners, the utility is the log-likelihood $v(S)=\mathbb{E}_{\mathcal{A}}\big[\log p_S(x^{(\mathrm{gen})})\big]$ that a counterfactual model trained only on $\bigcup_{i\in S}D^{(i)}$ would generate the same content, with the expectation taken over the stochastic learning algorithm $\mathcal{A}$; a relative variant uses the log-likelihood ratio against a reference model. Each owner's royalty share is then the Shapley value of this game, normalized by the sum over owners. The Shapley value is the classical cooperative-game-theory solution concept that assigns each player the weighted average of its marginal contributions $v(S\cup\{i\})-v(S)$ over all coalitions $S$, and is the unique payoff rule satisfying efficiency (payoffs sum to the total worth of the grand coalition), symmetry, the dummy-player property, and linearity.

Because the total revenue of a coalition is unknown in this market — only the ratios of contribution make sense — the framework pays Shapley-value ratios, and the efficiency axiom loses its meaning in the normalized, ratio-based formulation. Semivalues, a generalization introduced by Dubey, Neyman, and Weber (1981) that drops the efficiency axiom, were therefore suggested as the class within which a suitable payoff rule should be sought, but no axiomatic characterization adapted to ratio-based royalty distribution exists.

A second concern is strategic behavior. A copyright owner can duplicate its data, split or merge datasets, or pad them with non-copyrighted or AI-generated images to inflate its estimated Shapley share. Replication-robust payoff allocation for machine-learning data markets (Han, Wooldridge, Rogers, Ohrimenko, and Tschiatschek, 2020) addresses replication for Shapley-type values, but — as the source paper itself notes — not for Shapley-value ratios, which is what SRS pays out.

Third, the framework is computationally and statistically demanding. Exact Shapley computation requires evaluating $2^n$ coalition utilities, each entailing retraining a generative model; Monte Carlo approximation and single-run attribution methods mitigate but do not resolve this at scale. Because learning algorithms are stochastic, each utility evaluation is a random realization of this expectation, so the Shapley value must be estimated and the variance behavior of that estimate is not characterized when each data source is small. Fourth, the framework's economics is incomplete: a preliminary extension models the split between AI developers and copyright owners via a permission structure (a cooperative-game device, representable as a directed graph in which edges encode which players a coalition must include to be valid), but no optimal revenue-division analysis exists, and owners who cannot or will not negotiate (orphan works; very many small owners) are outside the framework, which the authors suggest might be handled by combining SRS with lawful-content-generation methods such as rejection sampling (generating content with a model trained only on non-copyrighted data and discarding outputs too close to copyrighted material).

Problem Statement

Complete the Shapley Royalty Share (SRS) framework of Wang, Deng, Chiba-Okobe, Barak, and Su (2024) into a deployable royalty mechanism for generative AI by resolving the open problems its authors state. The paper poses the following as separate future-work directions and limitations; together they concern a compensation mechanism, based on Shapley-type attribution of AI-generated content to training-data sources, that is strategically robust, axiomatically justified, computationally scalable, economically complete, and statistically reliable, all within the SRS setting (generative models; log-likelihood-based coalition utilities; ratio payoffs). The six parts are self-contained sub-problems, and any one of them can be answered on its own. Concretely, determine:

(a) A payoff rule (or detection mechanism) for the SRS log-likelihood game that is robust to strategic manipulation by data owners — duplicating data, merging or splitting datasets, and injecting non-copyrighted or AI-generated data to inflate their Shapley-based royalty share. Existing replication-robust solution concepts cover Shapley values, not the ratio payoffs SRS distributes.

(b) A payoff rule within the semivalue class, with axiomatic foundations, suited to ratio-based royalty distribution, replacing the heuristic use of normalized Shapley values for which the efficiency axiom loses meaning.

(c) A game-theoretically grounded division of revenue between AI developers and copyright owners — going beyond the source's preliminary permission-structure model — that accounts for the developers' computational resources, algorithm design, and engineering expertise.

(d) Efficient and accurate estimation of the Shapley(-ratio) payoffs when exact computation requires retraining generative models on $2^n$ data coalitions and the number of (especially small) copyright owners is large.

(e) An extension handling copyright owners who cannot or will not negotiate (orphan works; very many small owners).

(f) A rigorous characterization of the effect of learning stochasticity on Shapley value estimates in this setting. The source asserts that this impact is minimal when each player possesses a data source, but also notes that for very small data sources the royalty share would be minimal and potentially noisy due to the stochastic nature of AI model training; the characterization is needed precisely where that minimality assertion no longer holds — when data sources are small or fine-tuning introduces high variance.

References

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