  We study analytically a simple game theoretical model of heterogeneous
interacting agents. We show that the stationary state of the system is
described by the ground state of a disordered spin model which is exactly
solvable within the simple replica symmetric ansatz. Such a stationary state
differs from the Nash equilibrium where each agent maximizes her own utility.
The latter turns out to be characterized by a replica symmetry broken
structure. Numerical results fully agree with our analytic findings.
