Determination of the weights for the ultimate cross efficiency using Shapley value in cooperative game

This paper firstly revisits the cross efficiency evaluation method which is an extension tool of data envelopment analysis (DEA), then analyzes the potential flaws which happens when the ultimate average cross efficiency scores are used. In this paper, we consider the DMUs as the players in a cooperative game, where the characteristic function values of coalitions are defined to compute the Shapley value of each DMU, and the common weights associate with the imputation of the Shapley values are used to determine the ultimate cross efficiency scores. In the end, an empirical example is illustrated to examine the validity of the proposed method, and we also point out some further research directions in future.