In the competitive decision-making process, the mutual competition caused by limited resources can help participants improve their decision-making effectiveness. When it comes to rational self-interest, the competing individuals and groups play mutual games with each other from a partial perspective. In other words, they focus only on the games among the related individuals or groups, ignoring the competition between their related groups or included individuals. Thus, the obtained game results could exclude parallel dependence and progressive transformation relationships between individuals and groups. To address these issues, this study first proposes the intragroup and intragroup-to-intergroup game envelopment analysis models that consider multiple subgroups as the link between individuals and groups to further realize the dual game. Next, we prove that the proposed models show Nash and dual Nash equilibrium phenomena under the multi-subgroup environment, which shows the dual stability of the optimal results after the multiple mutual game calculations. Furthermore, the optimization algorithm in the multi-subgroup environment is fused with the aforementioned models to make global decisions for the intragroup individuals and intragroup-to-intergroup subgroups in the same schedule. Finally, this study applies the new methods to make a dynamic evaluation analysis of different country's banking competitiveness. The derived results demonstrate the real effectiveness of the proposed methods.