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A cost assignment model is proposed for the expansion of electrical transmission systems, based on the cooperation and interaction principles that are the foundation of the cooperative game theory. A solution algorithm is proposed that considers the development of independent cooperative games for each expansion segment and whose final assignment can be obtained by any game theory solution method (Kernel, Nucleolus, Shapley Value, etc.). The Kernel method was chosen because it has both equilibrium and transparency characteristics in the computation of final assignments. The model accepts both the technical (load nature, generation levels, etc.) and economic (power station marginal costs, etc.) variables that characterize the network to be analyzed. Cost assignment will depend both on the capacity economic use and the noncoincident maximum use of the expansion lines, made by individual and group agents.