Social dilemmas are situations where groups of individuals can benefit from mutual cooperation but conflicting interests impede them from doing so. This type of situations resembles many of humanity's most critical challenges, and discovering mechanisms that facilitate the emergence of cooperative behaviors is still an open problem. In this paper, we study the behavior of self-interested rational agents that learn world models in a multi-agent reinforcement learning (RL) setting and that coexist in environments where social dilemmas can arise. Our simulation results show that groups of agents endowed with world models outperform all the other tested ones when dealing with scenarios where social dilemmas can arise. We exploit the world model architecture to qualitatively assess the learnt dynamics and confirm that each agent's world model is capable to encode information of the behavior of the changing environment and the other agent's actions. This is the first work that shows that world models are crucial for the emergence of complex coordinated behaviors that enable interacting agents to ``understand'' both environmental and social dynamics.