Optimization of the dynamic network data envelopment analysis (DNDEA) model ‌based on the game theory in the capital market

Data envelopment analysis (DEA) is a widely-used method in measuring the relative efficiency of sets of homogeneous decision-making units with the same inputs and outputs. In classical DEA models, the whole system is usually considered as a decision-making unit (DMU) to calculate its efficiency, and the communication of separate processes within the system is ignored. However, the internal communication of different sectors of a decision-making unit can have various structures that cause complexity in evaluating its efficiency. To this end, the Network DEA (NDEA) model is developed using communication variables to communicate the internal structures of the decision-making units, in which the production process has two or more stages and considers according to the communication of the internal sectors and sub-units of a decision-making unit as a network structure, and the efficiency of each internal process and the whole process is calculated independently. Therefore, the present research aimed to evaluate the efficiency and ultimately rank the decision-making units and it thus used the dynamic network data envelopment analysis (DNDEA) model using game theory to examine and solve a problem of capital market investors, which was the correct selection of stocks in the efficient companies compared to the stocks of companies with low-efficiency. After developing the proposed model, the performance of 25 active companies in the petrochemical industry was evaluated for three years of 2016-2018 and the efficiency of each stage was calculated along with their overall efficiency. The results indicated that the proposed model had solved the shortcomings of the previous models and the new approach to the evaluation of efficiency in the stock market could provide a more accurate understanding of the performance and efficiency of active companies in this field.