Data envelopment analysis (DEA) mainly utilizes envelopment technology to replace production function in microeconomics. Based on this replacement, DEA is a widely used mathematical programming approach for evaluating the relative efficiency of decision making units (DMUs) in organizations. Evaluating the efficiency of DMUs that have two-stage network structures is so important in management and control. The resulting two stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. In this Paper we develops Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. With a new breakdown point, the new model is obtained which by providing example, the results of these models are investigated. Among these results can be pointed to the changing efficiency by changing the breakdown point.