FAIRGAME is a framework for recognizing bias in AI agents using game theory. It is used to reveal biased outcomes among AI agents in popular games, based on different LLMs and languages, personality traits of the agents, or strategic knowledge. FAIRGAME enables users to reliably and easily simulate games and scenarios of their choice, systematically discover biases by comparing outcomes between simulation campaigns and game-theoretic predictions, predict novel behaviors that arise from strategic interactions, and enable further research on strategic decision-making using LLM agents.