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

Abstract

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.

Sustainability in the evaluation of bus rapid transportation projects considering both managers and passengers perspectives: A triple-level efficiency evaluation approach

“…( 1,..., ) i i n  are positive parameters of the model, called breakdown points. The breakdown point is a value of utility that a player is considered as a minimum acceptable level of utility for itself (Mahmoudi et al, 2019a;Mahmoudi et al, 2018). Indeed, the utility of the player must be at least as large as its breakdown point, otherwise, the player will withdraw from the game (Mahmoudi et al, 2014).…”

Efficiency decomposition in a three-stage network structure: Cooperative DEA, Nash bargaining game models and conic relaxations

“…In other words, each stage's weights are independent of the weights of the other stages, while there exist structures where stages' weights may depend on the weights of other stages [20]. To overcome this issue, we utilize Nash bargaining game approach that has been used in several network DEA models [31,39,45]. First, let us briefly discuss this approach.…”

“…However, to calculate the overall efficiency in the three-stage structure with external inputs and outputs, their proposed method has neglected the existence of intermediate products. Using the concept borrowed from Nash bargaining game, Mahmoudi et al [31] also handled insufficient number of DMUs and inputs issue in the network structure.…”

Performance evaluation of thermal power plants considering CO2 emission: A multistage PCA, clustering, game theory and data envelopment analysis

“…There is a variety of game-DEA models in the literature proposed for different purposes (Cook et al, 2010). Mahmoudi et al (2018a) developed a game-DEA approach to evaluate the performance of DMUs in a case that inputs have been categorized into different groups.…”

“……, ). The proposed game-DEA model byMahmoudi et al (2018a) to evaluate the 1 m performance of a set of DMUs when inputs are categorized into two different types, is as follows:…”