Abstract: Previous research proposed the Game-Fixed Cost Allocation Model (Game-FCAM) that combined game theory and efficiency, but it overlooked the element of equity in the resources allocation process. This article develops a fixed cost allocation model that considers equity, game theory and efficiency. To achieve this goal, we first devise an enhanced general cross-efficiency algorithm that considers equity and cooperative game theory to optimize the conventional Game-FCAM. The outcome of this approach is the Game-Equity Fixed Cost Allocation Model (Game-EFCAM). Based on Game-EFCAM, we further consider multiple resources allocation and propose the Generalized Game-Equity Fixed Cost Allocation Model (Generalized Game-EFCAM) applicable to multiple resources allocation.
Comparing the allocation results of the Generalized Game-EFCAM with ones of other resources allocation schemes, we find that the former better satisfies the requirement of equity and achieves higher resources allocation efficiency. In other words, the proposed model allocates resources from the perspectives of equity and game theory, while maximizing overall efficiency. Qualitative and quantitative analyses both show that the allocation results of the Game-EFCAM are superior to those of the traditional Game-FCAM. In addition, we take the coordination allocation of carbon emission quotas and energy use quotas as an example, and examine the coordination results of different resources allocation schemes. The results show that the correlation between carbon emission quotas and energy use quotas in the Generalized Game-EFCAM is much higher than that in other fixed cost allocation models, indicating that the proposed model has higher coordination and applicability for coordinated allocation and collaborative emissions reduction.
The unique contributions of the proposed Generalized Game-EFCAM are as follows: (1)This paper extends the applicability of cross-efficiency. In previous research, cross-efficiency was based on an equal distribution of weights across units. This paper modifies this approach, allowing cross-efficiency to be applicable to units with different weights. At the same time, the paper combines equity principles to propose a fixed cost allocation model that integrates game theory, equity, and efficiency principles. (2)This paper expands the applicability of allocation models. Previous research typically focused on the allocation of a single fixed cost, with limitations in scenarios involving the allocation of multiple fixed costs, especially synergistic allocation. The Generalized Game-EFCAM proposed in this paper is suitable for scenarios involving the allocation of multiple fixed costs, considering the characteristics of different fixed costs, particularly in the case of synergistic features. In this paper, a two-type fixed-cost allocation example is used to derive the Generalized Game-EFCAM, and the corresponding solution steps and theorems are proposed. (3)This paper uses the pressing problem of carbon emission quotas and energy use quotas allocation in China as an example and applies the Generalized Game-EFCAM to solve the coordination allocation quota of carbon emission rights and energy use rights.
The main advantages of the model presented in this article are as follows. (1)In the process of resources allocation, it comprehensively considers efficiency and equity principles from a game perspective. Therefore, it is more in line with actual demand when allocating resources. (2)It can be applied to multi-resources allocation scenarios, allocating resources from the perspective of maximizing overall resources allocation efficiency, which not only improves resources utilization efficiency but also improves the distribution efficiency. The modelproposed in this article can also be improved in the following aspects. Firstly, this article doesn't set relevant equity standards when proposing equity principles, but adopts the per capita pay ability as the equity principle. In fact, the equity principle can also refer to the Gini coefficient, Theil index, and other indicators when designing. Secondly, the Generalized Game-EFCAM proposed in this article only considers games within one camp. If it is expanded to games between two camps, the model can be modified by considering factors such as benevolence and confrontation. In addition, the Generalized Game-EFCAM proposed in this article is an extension of Game-FCAM. However, the equity principles and multi-resources coordination allocation proposed in this article can also be extended based on other DEA models.

Key words: resources allocation, generalized game equity cross fixed cost allocation model, equity, efficiency

摘要： 过去的研究提出了博弈、效率相结合的博弈交叉固定成本分配模型(Game-FCAM),但是在资源配置过程中却忽略了公平要素。本文对交叉效率算法进行修正,提出了通用交叉效率。并结合公平原则,以各个单元的自身特征为公平要素,提出了一种结合博弈、公平与效率原则的博弈公平交叉固定成本分配模型(Game-EFCAM)。此外,本文还考虑了多种固定成本分摊的情形,提出了广义博弈公平交叉固定成本分配模型(Generalized Game-EFCAM)。最后,本文以中国当前亟需解决的碳排放权和用能权分配为例,应用广义博弈公平交叉固定成本分配模型求解了碳排放权配额与用能权配额的协调分配额度,并讨论了多种资源配置方法的配置效率、配置公平性与配置协调性,证明广义博弈公平交叉固定成本分配模型优于传统博弈交叉固定成本分配模型。

关键词: 资源配置, 广义博弈公平交叉固定成本分配模型, 公平, 效率