This paper systematically explores the key applications of game theory in computer algorithms. Confronted with computational problems characterized by multi-agent interactions, distribution, and high interactivity (such as resource allocation, path planning, and security protection), game theory provides a core paradigm through its equilibrium concepts for resolving conflicts between individual rationality and system efficiency. The paper focuses on its application in two major areas: Firstly, in intelligent decision-making and planning (e.g., intelligent traffic flow coordination, multi-robot path planning), where non-cooperative game models are established and learning algorithms are utilized to seek equilibria, effectively enhancing system efficiency and safety. Secondly, in the field of information and security, by constructing attack-defense game models (e.g., information security configuration, AI adversarial scenarios), it provides a theoretical basis for quantifying security strategies and formulating optimal decisions. Finally, this paper summarizes the limitations of current research and offers prospects for future directions such as integration with deep learning and online dynamic games.