Efficiency Decomposition for the Relational Two-Stage Network DEA Approach with Satisfaction Degree

In this paper, we draw upon the relevant Nash bargaining game theory to decompose the efficiencies for the relational two-stage data envelopment analysis model (DEA). The primary objective of this proposal is to facilitate an equitable efficiency decomposition, thereby rendering the efficiency ratings of the two stages of the decision-making unit (DMU) more judicious and gratifying. To start with, a decentralized DEA model, known as the leader-follower model, is introduced to handle the scenario wherein the two unions of the DMU proffer decisions in a sequential order. Then, a concept of satisfaction degree that each union garners from efficiency decomposition is delineated. Furthermore, the resolution extrapolated from the proposed model is characterized as a Pareto optimal solution, thus providing ample incentive for both parties to willingly acquiesce. Based on the proposed models with the empirical analysis, we find that the Nash solution for a specific stage is computed as the geometric mean of the efficiency scores obtained when assuming the roles of leader and follower in that particular stage.