Solving linear equation with max min function

Question

For a particular problem, I got some equations of the form $a = \min(1-b,0.9)$ $b = \max(\min(1-a,0.7)$, $\min(c, 0.8))$ $c = \max(\min(1-a,0.9)$, $\min(1-c, 0.9)) a,b,c \in [0,1]$ The system has a unique solution $a = 0.23333, b = 0.766666, c = 0.76666$.

Just wondering, how can I solve those equations in a general case.

Answer 1

The system does not have a unique solution. Here are some more, obtained via linearizing the constraints and solving a mixed integer linear programming problem: \begin{matrix} a & b & c\\ \hline 0.2 & 0.8 & 0.8 \\ 0.3 & 0.7 & 0.7 \\ 0.5 & 0.5 & 0.5 \end{matrix}