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This surfaces a unique safety problem when a group of agents forms a coalition and colludes to pursue secondary goals and degrade the joint objective. In this paper, we present Colosseum, a framework for auditing LLM agents' collusive behavior in multi-agent settings. We ground how agents cooperate through a formal multi-agent decision-making framework and measure action-based collusive behavior in actions via regret relative to the cooperative optimum and compare it with communication-based collusive behavior. Colosseum enables audits of LLM agents for collusion under benign settings, different coalition objectives, persuasion tactics, and network topologies. 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