M. Amiri - Ph.D Student, Faculty of athematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.
A. Ashrafi - Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, Iran.

Ranking decision making units (DMUs) is an important topic in data en-velopment analysis (DEA). When efficient DMUs or inefficient DMUs have the same efficiency score, the traditional DEA model usually fails to rank all DMUs. For the sake of comparing and improving the discrimination power of DMUs, some proposed approaches use cooperative game theory for rank-ing DMUs. In this paper, communication game theory, which includes a transferable utility cooperative game and an undirected graph describing limited cooperation between players, can be used to rank DMUs. The idea is that the ranking of DMUs can be done by measuring the effect of remov-ing a subset of DMUs on the total share of the remaining DMUs obtained by the reference frontier share model. In the proposed approach, the play-ers are the DMUs, and the characteristic function measures the increase and decrease in the total share of each DMU. The current paper considers the total share for efficient and inefficient DMUs to rank all DMUs. The proposed approach has been tested on several datasets and compared with the results of the previous ranking methods, which sometimes coincide. In the empirical study, a complete ranking of DMUs is useful and reasonable.

Data Envelopment Analysis, Communication game, Myerson value, Reference frontier share model