In the restructured environment of electricity market, firstly the generating companies and the customers are looking for maximizing their profit and secondly independent system operator is looking for the stability of the power network and maximizing social welfare. In this paper, a one way auction in the electricity market for the generator companies is considered in both perfect and imperfect competition cases. A new model is provided to use the historical data of power market in the state of competition with imperfect information in which two probability functions were simultaneously used for the estimation of required information about each generator company. Nash equilibrium in the game theory is used to find the stability point in the biding strategy of generator companies. The effect of network conditions like limitation of transmission lines, network load, maximum generation of each generator company and the imperfect estimation of information about other competitors on the profit of generator companies and also on the market power of the generators in two mentioned competition methods were shown in the numerical simulation.