In recent decades, the data envelopment analysis (DEA) model has been applied to various fields. However, the current research on DEA for land utilization efficiency is based on the assumption that each decision making unit (DMU) is independent and does not distinguish different preference to output indexes. Therefore, this paper proposes a new game cross efficiency model which considers the different levels of concern to different output indexes. In the proposed model, the output indexes are divided into several groups and DMUs present their preferences to these groups. Subsequently, this paper develops an algorithm to solve this model and proves the convergence of the algorithm. Then, taking the evaluation of land utilization efficiency as an example, the importance of game cross efficiency and group indexes in evaluations is presented. The output indexes are separated as two classes including economy output indexes and environment output indexes. The land utilization efficiency of cities in Pearl River Delta in 2019 is evaluated by the proposed model. The analysis shows that when there is a significant difference between different groups of output indexes, the ranking result for decision making units is different from the traditional DEA. The model reveals that the efficiency of some cities depends much on some special output indexes.

The study employed the super-efficiency SBM model to measure the digital economy efficiency of 30 provincial-level administrative regions in China from 2013 to 2022. Subsequently, we utilized the coupling coordination degree model to analyze the spatiotemporal coupling and coordination status between the diffusion of the “digital economy” concept and the development of the digital economy, using the Geodetector to explore the driving factors involved. The findings indicate that: (1) From 2013 to 2022, the overall efficiency of the digital economy rose slowly, with slight declines in 2015 and 2022. Among these, Shanghai had the highest average efficiency in the digital economy, while Heilongjiang had the lowest. (2)The diffusion of the “digital economy” concept and its development exhibit a coordinated relationship, with growth rates fluctuating significantly from 2013 to 2017. This has shifted to a slow but steady upward trend in recent years. Spatially, there are noticeable differences between the south and north, as well as between coastal and inland areas. (3) Regarding driving factors, the economic base, government intervention, and communication levels have consistently played significant roles. Later, the impetus from research investment, academic output, and digital finance factors progressively strengthened, creating a mechanism where internal and external elements jointly advance the coupled and coordinated relationship.