Cyber-attacks have increasingly threatened the secure and economical operation of microgrids, raising serious concerns for grid operators. In response, this paper introduces a new framework designed for the dynamic reconfiguration of interconnected microgrids, aiming to improve both system resilience and cost-effectiveness. The proposed approach leverages distributed energy resources to mitigate the impacts of cyber intrusions, such as line disconnections or generator failures. To achieve secure and cost-effective operation, an optimization model is developed as a single-objective problem using the sum-weight method. The model applies Stackelberg game theory to detect and mitigate false data injection attacks targeting advanced metering infrastructure. This framework aims to strengthen the resilience and reliability of multi-microgrids. The proposed method was validated on a 33-bus network within the PRINCE microgrid at the Polytechnic University of Bari. The key contributions include a real-time game-theoretic reconfiguration strategy, joint optimization of cost and reliability considering voltage deviation and short-circuit level, and simulation-based validation under cyber-attack scenarios.