Efficiency evaluation of sustainability indicators in a two-stage network structure: a Nash bargaining game approach

Nowadays, economic planning and policymaking toward economic growth and development require special attention to the energy and the environment, and their relationship with economic indicators. In this regard, the relationship of energy–environment–economy–equity (E4) is considered as a network to evaluate the performance of countries applying network-DEA models. In this regard, a two-stage network structure has been applied for efficiency evaluation of units. So that all the outputs of the first stage are considered as the inputs of the second stage. Due to multiple optimal weights, and consequently flexibility in the overall efficiency decomposition of the two stages, this study develops a Nash bargaining game model to evaluate the efficiency of the network structure to achieve a fair efficiency decomposition for both stages. In the bargaining game, the achievable minimum efficiency is used as a breaking point in each stage, and finally, the whole efficiency can be obtained. Using the data of selected developing countries in 2018, the bargaining results show that 6 countries had the highest score in the first stage, and two countries in the second stage. According to the results, although some countries have high rankings in terms of energy, economic, and environmental efficiency, but in the second stage, which focus on economic equity, only two countries show the highest efficiency. Therefore, in examining the performance of countries in terms of the four indicators, the results will be different, and it is appropriate for policymakers to consider the criterion of equity along with other criteria for better planning and decision making.