It has been a basic model for the present electric power industry that more than two generators compete, and thereby the market clearing price and the generation schedules are determined through the bid process. In order for this paradigm to be applicable to real electric power systems and markets, it is necessary to reflect many physical and economic constraints related to frequency and transmission in the dispatching schedule. The paper presents an approach to deriving a Nash bargaining solution in a competitive electricity market where multiple generators are playing with the system operator who mitigates the transmission congestion to minimize the total transaction cost. In this study, we take the effect of the line flows and the role of system operator into the Game. Finally, a case study has been demonstrated to verify the proposed cooperative game.