  New continuous and stochastic extensions of the minority game, devised as a
fundamental model for a market of competitive agents, are introduced and
studied in the context of statistical physics. The new formulation reproduces
the key features of the original model, without the need for some of its
special assumptions and, most importantly, it demonstrates the crucial role of
stochastic decision-making. Furthermore, this formulation provides the exact
but novel non-linear equations for the dynamics of the system.
