NashHybrid: Bridging Accuracy and Fairness in Collaborative Filtering via a Parametric Nash Bargaining–Welfare Trade-of

Classical recommender systems treat the accuracy–fairness trade-off as an afterthought, correcting it with post-hoc re-ranking. NashHybrid eliminates this two-stage design by embedding the trade-off directly inside the scoring function. The paper observes that two existing Nash criteria — the Nash Bargaining Solution (NBS) and Nash Social Welfare (NSW) — represent opposite extremes of this spectrum: NBS concentrates on high-surplus popular items (Coverage ≈ 34%, lower NDCG), while NSW distributes attention across the latent factor space (Coverage ≈ 5%, higher NDCG).

The central theoretical contribution is Theorem 1: the NashHybrid score traces a monotone Pareto frontier — Coverage is strictly decreasing in λ and Precision strictly increasing, with the Corollary that an interior optimum λ* ∈ (0,1) maximises NDCG. This is the first closed-form, game-theoretically grounded accuracy–fairness frontier in the recommender systems literature. No external fairness constraint, no re-ranking pipeline — just a single parameter.

Empirically, the ablation over λ ∈ {0.0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0} on ML-100K confirms every prediction of the theorem. The optimal NDCG@10 = 0.032 is achieved at λ* = 0.4, strictly interior to the frontier, which means neither pure NBS nor pure NSW is individually optimal — a strong empirical argument for the hybrid.