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

TL;DR

This paper uses variational analysis to relate a condition measure of a smoothing algorithm for matrix games to metric regularity, enabling explicit computation from game data.

Contribution

It introduces a novel approach connecting condition measures of smoothing algorithms to metric regularity, providing explicit formulas based on initial game data.

Findings

Established precise relationships between condition measure and metric regularity.

Derived explicit formulas for the condition measure from game data.

Enhanced understanding of the stability of smoothing algorithms in 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.