MultKAN-Nash: Strategic Multi-Agent Disaster Response using MultKAN and Nash Equilibriums

Climate disasters require coordination among stakeholders with competing objectives. Emergency responders prioritize rapid coverage, relief coordinators aim for resource efficiency, and affected populations seek timely access to aid. However, existing approaches often fail to balance these goals while maintaining interpretability for decision-making in high-stakes settings. We present MultKAN-Nash, a game-theoretic framework that combines Kolmogorov Arnold Networks (KAN) with Nash equilibrium and Multiplicative Weights (MW) learning to improve disaster response coordination. The framework models emergency operations as a strategic game in which agent utilities are learned from flood scenarios in Bangladesh using KAN. MultKAN attains strong utility prediction performance R2 = 0.9661, ranking competitively among 9 baselines. The complete system achieved a coordination efficiency of 90.11%, equitable resource allocation (Gini = 0.099), and convergence within 10 MW iterations. Ablation studies on 200 scenarios show that the Nash equilibrium contributes the most to performance (+0.099), followed by MW learning (+0.073), with MultKAN providing a smaller yet positive effect (+0.011) despite high predictive accuracy. The learned B-splines capture interpretable patterns, such as exponential disaster impact, capacity saturation, and threshold flood dynamics, offering explainable insights for humanitarian decision-making. Overall, the findings indicate that game-theoretic coordination structures can outperform pure predictive accuracy in multiagent systems, suggesting broader applications of interpretable strategic learning in crisis management.