NEXIM: A Nash Equilibrium-Based Framework for Stable Explainable AI in Medical Applications

Reliable explanations are important for trustworthy medical applications of artificial intelligence (AI), but attribution-based explanations can vary across model randomization and small analytic changes. We present NEXIM (Nash Equilibrium-based Explainability and Interpretability Model), implemented here as an accuracy-constrained, equilibrium-inspired model-selection framework that jointly evaluates held-out prediction error, explanation stability, and cross-model connectivity. The implementation evaluated ten GradientBoostingRegressor models per prediction horizon, differing only by random seed (0-9), using a fixed 75/25 patient split. Kernel SHAP attribution vectors were compared using Spearman rank correlation, and graph connectivity summarized whether each model belonged to a dense explanation-similarity region. Candidate models within 0.02 Montreal Cognitive Assessment points of the best root mean squared error (RMSE) were ranked using a multiplicative Explanation Equilibrium Score. In longitudinal Parkinson's Progression Markers Initiative data, NEXIM selected the RMSE-optimal model at the one- and three-year horizons. At the two-year horizon, it selected Model 4 rather than the RMSE-only Model 8, increasing scaled stability from 0.8757 to 0.8847 and normalized graph connectivity from 0.889 to 1.000 while increasing RMSE by only 0.0014. The two models retained the same top-20 feature set but differed modestly in feature order, illustrating that NEXIM primarily acted as a reproducibility screen rather than identifying clinically contradictory explanations. Stability and consensus are treated as reproducibility criteria, not evidence of causal faithfulness, clinical usefulness, or improved patient outcomes. NEXIM may therefore serve as a governance checkpoint for model refresh and documentation, but external validation, stronger model-family baselines, and prospective clinical evaluation remain necessary.