This paper proposes a decentralized model of energy cooperation between microgrids, in which decisions are made locally, at the level of the microgrid community. Each microgrid is modeled as an autonomous agent that adopts a Hawk or Dove strategy, depending on the level of energy stored in the battery and its role in the energy trading process. The interactions between selling and buying microgrids are modeled through an evolutionary algorithm. An individual in the algorithm population is represented as an energy trading matrix that encodes the amounts of energy traded between the selling and buying microgrids. The population evolution is achieved by recombination and mutation operators. Recombination uses a specialized operator for matrix structures, and mutation is applied to the matrix elements according to a Gaussian distribution. The evaluation of an individual is made with a multi-criteria fitness function that considers the seller profit, the degree of energy stability at the community level, penalties for energy imbalance at the community level and for the degradation of microgrids batteries. The method was tested on a simulated scenario with 100 microgrids, each with its own selling and buying thresholds, to reflect a realistic environment with variable storage characteristics of microgrids batteries. By applying the algorithm on this scenario, 95 out of the 100 microgrids reached a stable energy state. This result confirms the effectiveness of the proposed model in achieving energy balance both at the individual level, for each microgrid, and at the level of the entire community.