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. Moreover, LLMs' susceptibility to persuasion raises concerns about alignment with ethical principles. To study these dynamics, we introduce Persuade Me If You Can (PMIYC), an automated framework for evaluating persuasion through multi-agent interactions. Here, Persuader agents engage in multi-turn conversations with the Persuadee agents, allowing us to measure LLMs' persuasive effectiveness and their susceptibility to persuasion. We conduct comprehensive evaluations across diverse LLMs, ensuring each model is assessed against others in both subjective and misinformation contexts. We validate the efficacy of our framework through human evaluations and show alignment with prior work. PMIYC offers a scalable alternative to human annotation for studying persuasion in LLMs. 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. These findings provide empirical insights into the persuasive dynamics of LLMs and contribute to the development of safer AI systems.