  We develop an approach of variational analysis and generalized
differentiation to conditioning issues for two-person zero-sum matrix games.
Our major results establish precise relationships between a certain condition
measure of the smoothing first-order algorithm proposed by Gilpin et al.
[Proceedings of the 23rd AAAI Conference (2008) pp. 75-82] and the exact bound
of metric regularity for an associated set-valued mapping. In this way we
compute the aforementioned condition measure in terms of the initial matrix
game data.
