This work presents the study of some cost allocation methodologies in a competitive framework and proposes algorithms to reactive cost allocation among transmission consumers. Among the studied methodologies, e.g. Nucleolus, Decomposition Principle and Shapley Value, the Aumann-Shapley methodology will be shown to be the most adequate in sharing the cost of reactive support, due to its basis in marginal cost compatible with and economic competitive framework. Optimization techniques are very important to Aumann- Shapley methodology application, because the supplied Lagrange multipliers are extremely important to the evaluation of reactive power marginal cost, carried out in Aumann-Shapley cost allocation. Besides that, an interior point algorithm will be presented, which is used to obtain Lagrange multipliers and to determine the reactive support total cost. Afterwards, two algorithms will be presented to reactive power support cost allocation, one to be applied in a deterministic case and the other to a stochastic case, where contingencies in a electric network are taken into account. The proposed method is illustrated in studies with two electric test systems: one composed by 24 buses and other by 1653 buses.