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

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