In this chapter, we examine the evolution of the free market characterized by competing firms. We explore its relationship to random walks, specifically positing that the time-dependent market shares of firms can be modeled as instances of random walks. Our approach complements the multifractal detrended fluctuation analysis (MF-DFA) [2, 6]. More precisely, we propose utilizing market shares for multifractal market analysisMultifractal market analysis among competing firms. This innovative method begins with a partition function directly expressed in terms of market shares, thus eliminating the laborious preparatory work typically associated with traditional MF-DFA. Unlike conventional methodologies that rely on a fluctuation function derived from time series data, our approach streamlines the analysis by directly incorporating market share information. We successfully applied our method to publicly available empirical data. A key outcome of this chapter is the sought-after classification of the spectrum of dimensions, which greatly enhances the applicability of a multifractal description in this context.