Given the exponential advancement in AI technologies and the potential escalation of harmful effects from recommendation systems, it is crucial to simulate and evaluate these effects early on. Doing so can help prevent possible damage to both societies and technology companies. This paper introduces the Recommender Systems LLMs Playground (RecSysLLMsP), a novel simulation framework leveraging Large Language Models (LLMs) to explore the impacts of different content recommendation setups on user engagement and polarization in social networks. By creating diverse AI agents (AgentPrompts) with descriptive, static, and dynamic attributes, we assess their autonomous behaviour across three scenarios: Plurality, Balanced, and Similarity. Our findings reveal that the Similarity Scenario, which aligns content with user preferences, maximizes engagement while potentially fostering echo chambers. Conversely, the Plurality Scenario promotes diverse interactions but produces mixed engagement results. Our study emphasizes the need for a careful balance in recommender system designs to enhance user satisfaction while mitigating societal polarization. It underscores the unique value and challenges of incorporating LLMs into simulation environments. The benefits of RecSysLLMsP lie in its potential to calculate polarization effects, which is crucial for assessing societal impacts and determining user engagement levels with diverse recommender system setups. This advantage is essential for developing and maintaining a successful business model for social media companies. However, the study's limitations revolve around accurately emulating reality. Future efforts should validate the similarity in behaviour between real humans and AgentPrompts and establish metrics for measuring polarization scores.