Fluctuations around Nash equilibria in game theory

Abstract

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 result from a small amount of irrationality. In the presence of multiple Nash equilibria, our statistical approach allows to establish which is the globally stale equilibrium. However, characteristic times to reach this state can be very large.