Nowadays, Internet is becoming the primary source of information, and the use of social networks makes possible to come every day in contact with a great deal of news, much of which turns out to be fake. In recent years, for this reason, more and more fake news has been studied, trying to understand how to recognize them, how they propagate and how they affect people, especially their knowledge. In the first part of this thesis, it is analyzed through kinetic theory how individual's competence varies in the interaction with a fake news, characterized by a degree of falsehood. This analysis shows that, over long periods of time, there is a polarization in agents' knowledge toward the highest degree of competence (those who are perfectly able to discern between true and false news) and toward the lowest degree of competence (those who are unable in any way to recognize the reliability of a news).