Applying Metric Regularity to Compute a Condition Measure of a Smoothing Algorithm for Matrix Games

Abstract

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.