The rapid growth of the Internet of Things (IoT) has created a pressing need for efficient service allocation methods to manage the multitude of connected devices. Edge computing has become essential to fulfill the low-latency and high-bandwidth demands of IoT applications. This paper investigates the use of game theory as a framework for optimizing service allocation in edge computing environments. By treating the interactions between IoT devices and edge servers as a strategic game, we propose strategies to achieve optimal allocation and resource utilization. Our approach tackles key challenges such as minimizing latency, improving energy efficiency, and balancing load. Experimental results indicate that game-theoretic methods greatly improve the performance and scalability of IoT systems in edge computing, positioning them a promising solution for future applications.