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The Nash equilibrium and competition equilibrium have been widely studied in the electric power market up to now. In this paper, it is explained that the Nash equilibrium can be achieved by using marginal cost pricing and the competition equilibrium can be performed by using accounting cost pricing based on the model of the power market system. The comparison between the Nash equilibrium and competition equilibrium indicates that surplus and unfair allocation of market benefits may be obtained by the Nash equilibrium, and the competition equilibrium realizes the optimization in economics with maximum market efficiency and fairness for market benefit allocations while the optimization in mathematics is achieved by the Nash equilibrium. There is sameness between the Nash equilibrium and competition equilibrium at the point when the power network characteristics are disregarded. The case study is made on a IEEE 30-bus system, and the calculation results indicate that it is the key issue to perform the competition equilibrium by using accounting cost pricing.

Comparing competition equilibrium with nash equilibrium in electric power market