Solving ${\bf x} = \mbox{sgn}(A{\bf x} + {\bf b})$. Nash equilibrium of n-player game with binary decisions and linear utilities

Is it possible to solve the equation in the subject line numerically or in a closed form (unlikely)? Any algorithms?

$x_i\in\{+1,-1\}$

$a_{ii}=0$, i.e. all diagonal elements of $A$ are zero.

Dimensionality of $x > 1000$

Thanks

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I don't understand what the question is. –  Ross Millikan Nov 9 '12 at 2:44
Sorry, the question is how to solve the equation in the subject line. This equation arises in an attempt to find N.E. –  Konstantin Nov 9 '12 at 3:57
Reformulated the problem, provided more details. –  Konstantin Nov 9 '12 at 4:15