  We introduce a simple stochastic dynamics for game theory. It assumes
``local'' rationality in the sense that any player climbs the gradient of his
utility function in the presence of a stochastic force which represents
deviation from rationality in the form of a ``heat bath''. We focus on
particular games of a large number of players with a global interaction which
is typical of economic systems. The stable states of this dynamics coincide
with the Nash equilibria of game theory. We study the gaussian fluctuations
around these equilibria and establish that fluctuations around competitive
equilibria increase with the number of players. In other words, competitive
equilibria are characterized by very broad and uneven distributions among
players. We also develop a small noise expansion which allows to compute a
``free energy'' functional. In particular we discuss the problem of equilibrium
selection when more than one equilibrium state is present.
