基于博弈DEA的竞争战略识别研究

Competitive Strategy Identification Based on Game DEA

针对竞争状态下的决策单元效率评价问题,引入Nash均衡思想,在自互评体系下构造了Nash均衡约束参数,构建了博弈效率DEA模型,提出了两阶段博弈交叉效率DEA模型及其算法;在融合内外部评价结果的基础上,提出了一种基于博弈效率权重比和博弈交叉效率矩阵的聚类方法,并应用于竞争战略识别的实证研究。实证结果表明,模型能够实现自互评体系下的Nash均衡求解,效率评价的区分度更高;识别方法与同类战略识别方法相比,更具客观性和解释能力,分类效果更好。

How to identify competitive strategy is one of the important issues in the field of strategic management because most Chinese manufacturing enterprises are searching for strategic position. Nevertheless, addressing the empirical problem is challenging because the problem contains some defects, such as the fuzziness of the strategic concept, lack of operability, the subjectivity of selection for strategic dimensions or variables, and deficiency of the traditional clustering methods. Most of the existing literatures identify a strategy based on strategic drivers from the perspective of the external strategic features, which can not describe strategy implementation process. Data Envelopment Analysis（DEA） can be creatively used to identify competitive strategy, which provides explicit connotation and an objective method. This paper uses the DEA method to extend the current literature from the perspective of external characteristics to the perspective of internal process for the first time. In addition, this study tries to uncover the strategy implementation process. The approach differs from the traditional method based on strategic results.Firstly, we introduce the N-player non-cooperative game, and construct a DEA game efficiency model with Nash equilibrium constraint parameters based on traditional CCR model. In the case where the decision-making units（DMUs） are in competitive relationship, efficiency evaluation of each competing DMU is influenced by other DMUs. An asymptotic searching algorithm is designed in which a virtual minimum efficiency value of DMUs is assigned as the initial value. We show that the algorithm is convergent and a Nash equilibrium point is evident. Secondly, this paper proposes a two-stage DEA game cross-efficiency model to accommodate games in self-and cross-evaluation modes. In the first step, Nash equilibrium constraints are added into the CCR model for restricting options of optimal weights. Thus, a DEA game efficiency model is constructed to obtain each DMU＇s self-evaluated Nash equilibrium point in which each DMU＇s efficiency is not less than the minimum efficiency in the last round of the game. In the second step, the obtained self-evaluated Nash equilibrium efficiency is applied as the replacement of self-evaluated CCR efficiency to modify DEA game cross-efficiency model finding each DMU＇s peer-evaluated Nash equilibrium point in the presence of full competition. Then, Nash equilibrium efficiency of each DMU is derived in self-and cross-evaluation. Finally, this paper combines the internal and external evaluation results, defines a modified integrated distance to measure the similarity between DMUs, and proposes a new clustering method based on game efficiency weight ratio and game cross-efficiency matrix. The internal evaluation means that weight ratio can be used as an indicator to measure DMUs＇ similarity. The external evaluation means that the game cross-efficiency matrix can be used as an indicator to measure DMUs＇ similarity. Then, the proposed approach is applied to the empirical study on identifying competitive strategy of China＇s publicly listed companies in the machinery manufacturing industry. The empirical results show that the Nash equilibrium point is found in self-and cross-evaluation methods, with a higher degree of distinction between effective DMUs. This strategic identification method based on DEA is better than other methods. Therefore, it is an adequate identification method with strong explanatory power and objectivity because it captures the multidimensionality of strategy, takes into account the relative importance of the key decision variables, and allows the incorporation the inherent causality of the definition of strategy. It also resolves the problem of multi-optimal weights, in the case where the DMUs are in a competitive relationship in the DEA model.