| Summary: | In smart grid, the non-cooperative game is a popular method to model the profit competitions among utility companies, however, this game model requires the complete information of the utility companies, which are difficult to be implemented considering the privateness. Bayesian game is an efficient method in solving the incomplete information game problem. This paper formulates an incomplete information game for the pricing strategy of the utility companies. From a practical standpoint, the substitution elasticity among the utility companies is private, and thus the Bayesian game is applied to study the retail price of the competing utility companies. Then, the Bayesian Nash equilibrium is studied and obtained by the wellknown fictitious play algorithm in symmetric case. Additionally, we consider the consumer's response to balance the electricity market. When the electricity energy is imbalance, we take the action purchasing the regulation service from the consumers rather than the spinning reserve from the generator set to reduce the financial cost. The illustrative examples are shown to verify the efficiency of the designed model. Specifically, the utility companies can maximize their profits by the Bayesian game with the incomplete information, and the change of the profit with market demand disruptions can be obtained.
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