A bargaining game model for performance assessment in network DEA considering sub-networks: a real case study in banking

Several network-data envelopment analysis (DEA) performance assessment models have been proposed in the literature; however, the conflicts between stages and insufficient number of decision-making units (DMUs) challenge the researchers. In this paper, a novel game-DEA model is proposed for efficiency assessment of network structure DMUs. We propose a two-stage modeling, where in the first stage network is divided into several sub-networks; we at the same time categorize input variables to measure efficiency of sub-networks within each input category. In the second stage, we calculate efficiency of the network by aggregating efficiency scores of sub-networks within each category. In this way, the issue of insufficient number of DMUs when there are many input/output variables can be handled as well. One of the main contributions of this paper is assuming each category and stage as a player in Nash bargaining game. Using the concept borrowed from Nash bargaining game model, the proposed game-DEA model tries to maximize distances of efficiency scores of each player form their corresponding breakdown points. The usefulness of the model is presented using a real case study to measure the efficiency of bank branches.