This paper is a comprehensive paper that systematically reviews previous studies, emphasizing the importance of game-theoretic scenarios in the social intelligence evaluation of large-scale language models (LLMs)-based social agents. We analyze previous studies on LLM-based social agents by organizing them into three core components: game framework, social agents, and evaluation protocols. The game framework includes various game scenarios ranging from choice-driven games to communication-driven games, while the social agent part explores the synergy effects of agents’ preferences, beliefs, reasoning abilities, interactions, and decision-making. The evaluation protocol covers game-independent and game-specific metrics to evaluate agent performance. Furthermore, we analyze the performance of current social agents in various game scenarios and suggest future research directions, providing insights for advancing the development and evaluation of social agents in game-theoretic scenarios.