Resource Allocation Based on DEA and Non-Cooperative Game

Resource allocation is one of the most important applications of data envelopment analysis (DEA). Usually, the resource to be allocated is directly related to the interests of decision-making units (DMUs), thus the dynamic non-cooperative game is one of the representative behaviours in the allocation process. However, it is rarely considered in the previous DEA-based allocation studies, which may reduce the acceptability of the allocation plan. Therefore, this paper proposes a DEA-based resource allocation method considering the dynamic non-cooperative game behaviours of DMUs. The authors first deduce the efficient allocation set under the framework of variable return to scale (VRS) and build the allocation model subjecting to the allocation set. Then an iteration algorithm based on the concept of the non-cooperative game is provided for generating the optimal allocation plan. Several interesting characteristics of the algorithm are proved, including i) the algorithm is convergent, ii) the optimal allocation plan is a unique Nash equilibrium point, and iii) the optimal allocation plan is unique no matter which positive value the initial allocation takes. Some advantages of the allocation plan have been found. For example, the allocation plan is more balanced, has more incentives and less outliers, compared with other DEA-based allocation plans. Finally, the proposed method is applied to allocate the green credit among the 30 Chinese iron and steel enterprises, and the results highlight the applicability of the allocation method and solution approach. Therefore, the approach can provide decision makers with a useful resource allocation tool from the perspective of dynamic non-cooperative game.

资源配置是数据包络分析（DEA）最重要的应用之一。通常，待配置的资源与决策单元（DMU）的利益直接相关，因此动态非合作博弈是配置过程中的典型行为之一。然而，在以往基于DEA的配置研究中很少考虑到这一点，这可能会降低配置方案的可接受性。因此，本文提出了一种考虑决策单元动态非合作博弈行为的基于DEA的资源配置方法。作者首先在规模报酬可变（VRS）框架下推导出有效配置集，并构建了基于该配置集的配置模型。然后，基于非合作博弈的概念提供了一种迭代算法来生成最优配置方案。证明了该算法的几个有趣特性，包括：i）算法是收敛的；ii）最优配置方案是唯一的纳什均衡点；iii）无论初始配置取何正值，最优配置方案都是唯一的。发现了该配置方案的一些优势。例如，与其他基于DEA的配置方案相比，该配置方案更均衡、更具激励性且异常值更少。最后，将所提方法应用于30家中国钢铁企业的绿色信贷配置，结果凸显了该配置方法和求解方法的适用性。因此，从动态非合作博弈的角度来看，该方法可以为决策者提供一种有用的资源配置工具。