Abstract: In data envelopment analysis (DEA), the cross-efficiency evaluation is an effective method for ranking decision making units (DMUs), which is performed with peer-evaluation and self-evaluation. From different points of view, various secondary goals have been proposed such as the aggressive model and the benevolent model. Yet different secondary goal models lead to different cross-efficiency evaluation. In this paper, the cooperative game theory is used to choose the secondary goal model between the targeted aggressive model and the targeted benevolent model and then evaluate all DMUs. Specifically, it is assumed that a cooperative game is developed among all DMUs. Given a coalition of some DMUs, a DMU in this coalition will make the best appraisal of each DMU in the same coalition based on the targeted benevolent model, and choose the targeted aggressive model to evaluate the other DMUs which do not belong to the coalition. Further, each DMU is evaluated with its Shapley value in the cooperative game. Finally, an example is presented to show that the proposed method can make full use of the minimum cross-efficiency and the maximum cross-efficiency and it is a comprehensive, fair and reasonable ranking method.

Key words: data envelopment analysis (DEA), cross-efficiency, cooperative games, Shapley value