As LLM-based agents become increasingly autonomous and will more freely interact with each other, studying the interplay among them becomes crucial to anticipate emergent phenomena and potential risks. In this work, we provide an in-depth analysis of the interactions among agents within a simulated hierarchical social environment, drawing inspiration from the Stanford Prison Experiment. Leveraging 2,400 conversations across six LLMs (i.e., LLama3, Orca2, Command-r, Mixtral, Mistral2, and gpt4.1) and 240 experimental scenarios, we analyze persuasion and anti-social behavior between a guard and a prisoner agent with differing objectives. We first document model-specific conversational failures in this multi-agent power dynamic context, thereby narrowing our analytic sample to 1,600 conversations. Among models demonstrating successful interaction, we find that goal setting significantly influences persuasiveness but not anti-social behavior. Moreover, agent personas, especially the guard's, substantially impact both successful persuasion by the prisoner and the manifestation of anti-social actions. Notably, we observe the emergence of anti-social conduct even in absence of explicit negative personality prompts. These results have important implications for the development of interactive LLM agents and the ongoing discussion of their societal impact.