Fluctuations around Nash Equilibria in Game Theory

We investigate the fluctuations induced by irrationality in simple games with a large number of competing players. We show that Nash equilibria in such games are ``weakly'' stable: irrationality propagates and amplifies through players' interactions so that huge fluctuations can results from a small amount of irrationality. In the presence of multiple Nash equilibria, our statistical approach allows to establish which is the globally stable equilibrium. However characteristic times to reach this state can be very large.