On-line numerical simulations and analytical calculations will be presented to study a structure of interacting networks with opposite values of their internal degrees of freedom. The problem corresponds to a system of two social groups with different opinions. Evolution of opinions will be truncated to the Ising dynamics with Monte-Carlo bath. It will be shown that not a number of group members but a type and strength of their internal connections decide on the result of inter-group competition. We shall demonstrate how a well known paradigm of statistical physics called the fluctuations-dissipation theorem  can be applied for analysis of this problem.