Nash bargaining game model for two parallel stages process evaluation with shared inputs

Data envelopment analysis is a non-parametric technique for evaluating peer decision making units (DMUs) with using multiple inputs to produce multiple outputs. In the real world, DMUs usually have complex structures. One of these structures is a two-stage process with intermediate measures. In this structure, there are two stages and each stage uses inputs to produce outputs, separately where the outputs of the first stage are the inputs for the second stage. Cooperative model such as centralized model and non-cooperative model are game theoretic approaches to evaluate two-stage processes. Non-cooperative model supposes that one of the stages is the leader and another stage is the follower, whereas in the centralized model, both stages are evaluated simultaneously. In this paper, we propose a game theoretic model based on the Nash bargaining game to calculate weights when parallel stages with shared inputs compete to reach a high efficiency in the competitive strategy. Two data sets including the bank branches and thermal power plants in Iran are used to show the abilities of proposed model. This model can be applied in other processes such as supply chain, manufacturing and public service units.