关键词: 合作博弈, 协调策略, CIS值, 交叉效率

Abstract: Considering the complexity and close connection of real production process, it is difficult for a single-stage evaluation to reflect the real situation. It is necessary to open the “black box” to scientifically measure the efficiency value of each stage and the overall efficiency value. The related researches on two-stage efficiency decomposition and evaluation can be mainly divided into three categories. The first category is to reconstruct the evaluation model by combining with other related theories, such as cooperative game, non-cooperative game, bargaining model, expectation theory, regret theory, etc. The second type is to give the corresponding cross-efficiency model according to the different attitude tendencies of decision makers, such as benevolent attitude, neutral attitude and so on. The third is to establish the corresponding two-stage efficiency evaluation model for different representation forms of input-output information, such as probabilistic linguistic terms, interval numbers, etc. However, the research on cross-efficiency of two stages is not sufficient, especially when shared input and independent inputs in each sub-stage exist. In addition, it is of great significance to consider the coordination between the stage and the whole process to avoid extreme differentiation between them. At the same time, we also need to pay attention to the association relationship between the evaluated subjects which cannot be neglected in the actual evaluation. But most of the existing related research ignores the impact of such factors on the evaluation results.
Under this background, this paper establishes an evaluation and aggregation method based on global coordination and the concept of game solution, and applies it to practical problem to verify its feasibility and effectiveness. Firstly, from a neutral point of view, a coordination variable is introduced to avoid the extreme differentiation between the whole process and the sub-stage, so as to realize the screening of multiple optimal weight vectors. In addition, considering that the solution concept of cooperative game is very suitable to describe the interactive characteristics of decision-making units, the CIS value is chosen to effectively describe the relevance between pieces of the evaluation information, and the weighted aggregation of efficiency information is realized. Finally, combined with the problem of industrial environmental efficiency evaluation, based on the establishment of the two-stage evaluation index system of industrial environment, the comprehensive evaluation of the overall and stage efficiency of industrial environment is carried out among thirteen provinces and cities in China.
The proposed models consider the coordination between the local and the whole, as well as the association relationship between the evaluated subjects. By introducing the solution concept in cooperative game theory, this paper realizes the reasonable aggregation of multi-dimensional evaluation information. The contrastive analysis and practical application results of industrial environmental efficiency evaluation show that the models established in this paper can scientifically and effectively evaluate the efficiency of two-stage network structure, and can realize the full sorting of decision-making units, which provides a new modeling idea for two-stage efficiency evaluation. Meanwhile, the proposed models have strong applicability and operability in practical applications, such as supplier evaluation, energy efficiency evaluation, bank risk assessment, etc., which can provide useful and scientific reference information for managers to make relevant decisions.
In the future, the fusion mechanism of the cross-evaluation information of decision-making units in game theory under different interactive and competitive environments will be one of the research directions that need to be deeply explored. In addition, efficiency evaluation is often carried out in complex environments in practice. Fully considering the uncertain characteristics of data such as randomness, fuzziness and roughness will further improve the practical flexibility and application scope of interactive evaluation method.

Key words: cooperative game, coordination strategy, CIS value, cross-efficiency