The New Model of Game Cross Efficiency DEA With Index Groups and an Application to Land Utilization Efficiency

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.