A Bargaining Game model for performance assessment in network DEA considering sub-networks: A real case study in Banking

Reza Mahmoudi, Ali Emrouznejad, Morteza Rasti-Barzoki

Research output: Contribution to journalArticlepeer-review


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.
Original languageEnglish
Pages (from-to)6429–6447
Number of pages19
JournalNeural Computing and Applications
Early online date7 Apr 2018
Publication statusPublished - 7 Oct 2019

Bibliographical note

© The Author(s) 2018. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.


  • Data envelopment analysis
  • Network DEA
  • Game DEA
  • Bargaining game
  • Performance assessment
  • Additional inputs
  • Banking


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