Two-Stage Cooperative/Non-Cooperative Game DEA Model with Decision Preference: A Case of Chinese Industrial System

Decision preference, the most common constraint in the decision-making process, is essential in efficiency evaluation and decision making. Therefore, quantitatively setting the weight of decision-making preference is critical to the field of data envelopment analysis (DEA) efficiency research. This study introduces a decision preference between desirable and undesirable outputs, the order and ratio of the decision preference between sub-stages, and constructs a two-stage cooperative/noncooperative game DEA model. The model is used to evaluate and compare the efficiency of the Chinese regional industrial system over the period 2011–2015 from the perspective of a two-stage cooperative/noncooperative game. Research on introducing desirable/undesirable output preference relation constraints reveals the following: (1) In the noncooperative game evaluation framework that considers undesirable outputs, (i) determining a set of common optimal output preference weights can help decision makers verify the initial subjective decision preference or quantitatively set better decision preference weights to obtain more reliable evaluation results, and that (ii) the method of setting the proportion preference weights between stages based on the perspective of output proportion can effectively avoid the efficiency deviation of the input proportion method in the disposal of undesirable outputs. (2) The efficiency of the Chinese industrial system (i) under the non-cooperative game relationship during the study period is mainly affected by low pollution control efficiency components, in conformity to the “Cannikin Law,” and (ii) there are marked differences in the overall efficiency and substage efficiency of China's industries under the cooperative game relationship; and the imbalance in industrial development among regions is significant.