Large Language Models (LLMs) demonstrate persuasive capabilities that rival human-level persuasion. While these capabilities can be used for social good, they also present risks of potential misuse. Beyond the concern of how LLMs persuade others, their own susceptibility to persuasion poses a critical alignment challenge, raising questions about robustness, safety, and adherence to ethical principles. To study these dynamics, we introduce Persuade Me If You Can (PMIYC), an automated framework for evaluating persuasiveness and susceptibility to persuasion in multi-agent interactions. Our framework offers a scalable alternative to the costly and time-intensive human annotation process typically used to study persuasion in LLMs. PMIYC automatically conducts multi-turn conversations between Persuader and Persuadee agents, measuring both the effectiveness of and susceptibility to persuasion. Our comprehensive evaluation spans a diverse set of LLMs and persuasion settings (e.g., subjective and misinformation scenarios). We validate the efficacy of our framework through human evaluations and demonstrate alignment with human assessments from prior studies. Through PMIYC, we find that Llama-3.3-70B and GPT-4o exhibit similar persuasive effectiveness, outperforming Claude 3 Haiku by 30%. However, GPT-4o demonstrates over 50% greater resistance to persuasion for misinformation compared to Llama-3.3-70B. Notably, o4-mini emerges as both an effective persuader, and a resistant persuadee. These findings provide empirical insights into the persuasive dynamics of LLMs and contribute to the development of safer AI systems.