Temptation to free-ride is an important aspect of social strategic behavior and a central issue in game theory. Network games with free-riding present multiple Nash Equilibria, in which a fraction of agents cooperate and the others exploit the actions of their peers. Statistical mechanics can help to analyze the organization and the structure of these Nash Equilibria. I will discuss in particular the problem of converging to optimal NE (i.e. those with minimal or maximal density of free-riders), and its connections to the physics of spin-glasses and combinatorial problems