  This paper studies a special kind of equilibrium termed as "balanced
equilibrium" which arises in the power allocation game defined in
\cite{allocation}. In equilibrium, each country in antagonism has to use all of
its own power to counteract received threats, and the "threats" made to each
adversary just balance out the threats received from that adversary. This paper
establishes conditions on different types of networked international
environments in order for this equilibrium to exist. The paper also links the
existence of this type of equilibrium on structurally balanced graphs to the
Hall's Maximum Matching problem and the Max Flow problem.
