Creator Incentives in Recommender Systems: A Cooperative Game-Theoretic Approach for Stable and Fair Collaboration in Multi-Agent Bandits

We propose a new framework for meritocratic fairness in budgeted combinatorial multi-armed bandits with full-bandit feedback (BCMAB-FBF). Unlike semi-bandit feedback, the contribution of individual arms is not received in full-bandit feedback, making the setting significantly more challenging. To compute arm contributions in BCMAB-FBF, we first extend the Shapley value, a classical solution concept from cooperative game theory, to the $K$-Shapley value, which captures the marginal contribution of an agent restricted to a set of size at most $K$. We show that $K$-Shapley value is a unique solution concept that satisfies Symmetry, Linearity, Null player, and efficiency properties. We next propose K-SVFair-FBF, a fairness-aware bandit algorithm that adaptively estimates $K$-Shapley value with unknown valuation function. Unlike standard bandit literature on full bandit feedback, K-SVFair-FBF not only learns the valuation function under full feedback setting but also mitigates the noise arising from Monte Carlo approximations. Theoretically, we prove that K-SVFair-FBF achieves $O(T^{3/4})$ regret bound on fairness regret. Through experiments on federated learning and social influence maximization datasets, we demonstrate that our approach achieves fairness and performs more effectively than existing baselines.

We propose incentive-aligned mechanisms for in-context credit assignment: the task of assigning credit for AI-generated content among creators whose intellectual property appears in the context window. Our approach is based on the least core solution concept from cooperative game theory, which distributes value in a way that is as stable as possible by ensuring that no subset of creators is significantly under-compensated relative to the value they could generate on their own. We develop algorithms for approximating the least core, which leverage novel routines for constraint seeding and constraint separation. On a web retrieval credit assignment task, we find that our approaches approximate the least core using an order of magnitude fewer LLM calls compared to alternative methods.

Game-theoretic attribution explains a model by assigning credit to its features or training examples. The least core has attracted interest as an alternative to Shapley-style averaging because it can expose players that cause substantial harm in rare, high-value contexts. However, least-core allocations are generally nonunique, and the choice of allocation can affect the resulting explanation. In this study, we investigate how payoff selection and coalition sampling affect least-core attribution. Our experiments show that selector choice matters for distinguishing useful and harmful contributions, and that sampling can degrade harmful-player identification across the tested selectors even when useful players remain well identified. These observations motivate efficient computation with all coalition constraints and a well-defined selector. We introduce entropic least core (ELC), a smooth approximation whose unique minimizer follows a continuous path along the temperature to the nucleolus, a classical refinement of the least core. Our experiments show that ELC approximates the nucleolus faster than an LP-based nucleolus solver while retaining small payoff errors, with further GPU acceleration at larger problem sizes. In the tested full-coalition contextual-distractor games, ELC matches the minimum-norm selector in identification accuracy and more accurately ranks distractors by harm.