Game-theoretic scenarios have become pivotal in evaluating the social intelligence of Large Language Model (LLM)-based social agents. While numerous studies have explored these agents in such settings, there is a lack of a comprehensive survey summarizing the current progress. To address this gap, we systematically review existing research on LLM-based social agents within game-theoretic scenarios. Our survey organizes the findings into three core components: Game Framework, Social Agent, and Evaluation Protocol. The game framework encompasses diverse game scenarios, ranging from choice-focusing to communication-focusing games. The social agent part explores agents' preferences, beliefs, and reasoning abilities, as well as their interactions and synergistic effects on decision-making. The evaluation protocol covers both game-agnostic and game-specific metrics for assessing agent performance. Additionally, we analyze the performance of current social agents across various game scenarios. By reflecting on the current research and identifying future research directions, this survey provides insights to advance the development and evaluation of social agents in game-theoretic scenarios.