Game-Theoretic Resilience Framework for Cyber-Physical Microgrids using Multi-Agent Reinforcement Learning

The increasing reliance on cyber physical infrastructure in modern power systems has amplified the risk of targeted cyber attacks, necessitating robust and adaptive resilience strategies. This paper presents a mathematically rigorous game theoretic framework to evaluate and enhance microgrid resilience using a combination of quantitative resilience metrics Load Served Ratio LSR, Critical Load Resilience CLR, Topological Survivability Score TSS, and DER Resilience Score DRS. These are integrated into a unified payoff matrix using the Analytic Hierarchy Process AHP to assess attack defense interactions. The framework is formalized as a finite horizon Markov Decision Process MDP with formal convergence guarantees and computational complexity bounds. Three case studies are developed 1. static attacks analyzed via Nash equilibrium, 2. severe attacks incorporating high impact strategies, and 3. adaptive attacks using Stackelberg games, regret matching, softmax heuristics, and Multi Agent Q Learning. Rigorous theoretical analysis provides convergence proofs with explicit rates , PAC learning sample complexity bounds, and computational complexity analysis. The framework is tested on an enhanced IEEE 33bus distribution system with DERs and control switches, demonstrating the effectiveness of adaptive and strategic defenses in improving cyber physical resilience with statistically significant improvements of 18.7% 2.1% over static approaches.