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Power distribution networks that include distributed generation need new control strategies based on distributed and hierarchical structures. For these systems, a replicator dynamics strategy for dynamic resource allocation in the dispatch of distributed generators in a microgrid is presented. This approach uses the characteristics of a defined subsystem in order to offer a simple algorithm with optimal and feasible solutions even in cases where other methods do not satisfy the problem's constraints. To compare the performance of the replicator dynamics strategy and to analyze the optimality of the obtained solutions, a market multiagent-based scheme is adapted. The results are implemented in a simulation model for different scenarios to show the applicability of the proposed strategy.