This article addresses the Edge User Allocation (EUA) problem in edge computing, where the appropriate mapping from users to edge servers (ESs) is crucial for optimizing performance metrics. Game theory is one of the powerful tools used in edge computing for user allocation to edge resources and task offloading. However, this approach takes longer to converge to Pure Nash Equilibrium (PNE), which is called a stable optimal solution. In this article, we propose a grouping technique for ESs, enabling parallel execution of game-theoretic approaches to achieve faster convergence at the PNE. Our contributions include the grouping method, the introduction of parallel Best Response (BR) dynamics for rapid convergence, and proof that the parallel BR dynamics will eventually halt at PNE. We also provide empirical evidence demonstrating its efficiency compared to traditional BR dynamics. This research enhances the scalability and effectiveness of game-theoretic approaches in resolving the EUA problem, offering practical solutions for edge computing scenarios.