  In this paper, we first devise two algorithms to determine whether or not a
bimatrix game has a strategically equivalent zero-sum game. If so, we propose
an algorithm that computes the strategically equivalent zero-sum game. If a
given bimatrix game is not strategically equivalent to a zero-sum game, we then
propose an approach to compute a zero-sum game whose saddle-point equilibrium
can be mapped to a well-supported approximate Nash equilibrium of the original
game. We conduct extensive numerical simulation to establish the efficacy of
the two algorithms.
