Adaptive competitive balance regulation in professional sports leagues via graph attention networks and proximal policy optimization

Sustaining competitive balance underpins both the commercial vitality and fan engagement of professional sports leagues, yet most regulatory regimes still rely on static rules that cannot track shifting competitive dynamics. We present an integrated framework that couples graph attention networks (GATs) with proximal policy optimization (PPO) for adaptive, data-driven regulatory policy design. The league is cast as a weighted directed graph in which clubs are nodes and edges encode match outcomes, financial flows, and dominance relations. A multi-layer GAT encoder distills this graph into a compact state vector that retains relational patterns across structural scales, and a PPO agent acts on that vector to optimize multi-instrument regulatory actions-salary caps, revenue-sharing ratios, and draft lottery parameters-over multi-season horizons. A composite reward balances competitive parity, revenue preservation, and policy stability. In simulation experiments calibrated to twenty seasons of English Premier League (EPL) and National Basketball Association (NBA) data, the proposed GAT-PPO framework attains competitive balance improvement rates of 32.7% (95% CI: [30.3%, 35.1%]) and 22.1% (95% CI: [19.9%, 24.3%]), respectively, outperforming fixed-rule baselines and ablated variants at statistically significant levels (paired t-test, p < 0.01, Bonferroni-corrected). To remove any ambiguity about comparability, every baseline is evaluated under the same simulator, the same observation frequency, the same state-space dimensionality, and the same five random seeds; this fairness protocol is detailed in Sect. 4.1. Interpretability analysis shows context-sensitive regulatory behavior: interventions intensify under severe imbalance and relax once parity overshoots the target. All results derive from a calibrated simulation environment with bounded-rational agent assumptions. We do not treat "simulation-based" as the endpoint of validation. Instead, we propose and partially execute a three-stage real-world validation pathway: (i) distributional face-validity checks against twenty seasons of historical EPL and NBA data using Kolmogorov-Smirnov tests on RSD, HHI, and Gini indices; (ii) directional concordance backtesting against four documented regulatory interventions (NBA 2011 CBA reform, EPL 2013 FFP introduction, NBA 2017 apron rule, EPL 2018 PSR tightening); and (iii) zero-shot transfer to a third league (MLB) outside the training distribution. Together these findings demonstrate the practical promise of pairing graph-structured deep learning with sequential decision-making for league governance.