At present, there are mainly two kinds of transaction modes in the power market: bilateral negotiation mode and centralized bidding mode. Bilateral negotiation mode means users' purchases power directly from power plants, whereas centralized bidding mode means power plants and power users conduct power transactions through a Power Trading Center. This paper adopts evolutionary game theory to model this mechanism and explores the behavioral patterns of different entities at equilibrium. This paper is organized as follows. First, we build an evolutionary game model of this mechanism. Then, we discuss the existence and stability of equilibrium outcomes. Furthermore, we compare the equilibrium results under different conditions. We find that different market supply‐demand conditions lead to different equilibrium outcomes. Besides, we find that the bilateral negotiation mode does not necessarily improve the overall profit of the power market. When the demand exceeds the supply in the centralized bidding market, introducing the bilateral negotiation mode would reduce the overall market profit. In addition, the increase of the bidding heterogeneity leads to the increase of profits of power plants in the market. © 2021 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.