We discuss the Minority Game, a model of heterogeneous, indictive rational agents inspired by the El Farol Bar problem. We derive the exact solution of the model in the limit of infinitely many agents using tools of statistical physics of disordered systems. Our results show that the impact of agents on the collective behavior plays a key role: even though for each agent this effect is very small, the collective behavior crucially depends on whether agents account for it or not.