  In this paper two algorithms with the goal of generating the equilibrium set
of the power allocation game first developed in \cite{allocation} are proposed.
Based on the first algorithm, the geometric property of the pure strategy Nash
equilibrium set will be proven to be a collection of convex polytopes. The
second, simulation-based, algorithm is developed to overcome the shortcoming of
the first algorithm in terms of generating the equilibrium set efficiently and
then making policy-relevant predictions based on the set. The second algorithm
will be usefully applied to a real-world case study, which draws on the current
crisis between North Korea and certain key players including the US and China.
