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

摘要： 在对复杂环境下的生产过程进行效率评价时,需要考虑局部与整体大联盟间的均衡以及被评价主体间的关联关系,而现有大多数相关研究忽视了此类因素对评价结果的影响。在此背景下,本文建立了基于合作博弈与整体协调策略的交互决策方法,并通过具体实践应用验证了模型的可行性与有效性。首先,从决策者的中立角度出发,引入双协调变量及偏好系数以尽量避免整体与阶段间的极端分化现象。通过双协调度的加权偏离最小化来实现多重最优权重向量的进一步筛选。此外,针对简单算术平均在集结多维评价信息时的不足,考虑到合作博弈的解概念契合于决策单元交互特征的描述,选择利用CIS值来有效刻画评价信息间的关联性,并据此实现效率信息的加权集结。最后,通过对比分析指出本文所建综合模型的优势,并将其应用于工业环境效率评价,为管理者在相关方面的决策提供参考和借鉴。

关键词: 合作博弈, 协调策略, CIS值, 交叉效率