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In this paper, we present a market-based resilient power management procedure for electrical distribution systems consisting of multiple cooperative MiroGrids (MGs). Distributed optimization is used to find the optimal resource allocation for the multiple MG system, while maintaining the local and global constraints, including keeping the voltage levels of the micro-sources within bounds. The proposed method is based on probabilistic reasoning in order to consider the uncertainty of the decision model in preparation for expected extreme events and in case of unit failure, to improve the resiliency of the system. Basically, the power management problem formulation is a multiobjective optimization problem, which is solved using the concept of Nash Bargaining Solution (NBS). The simulation results show that the proposed method is able to improve the resiliency of the system and prepare it for extreme events and unit failure, by increasing power reserve and modifying the operating point of the system to maintain voltage and power constraints across the MGs. [ABSTRACT FROM AUTHOR]