In this thesis, we study brand choice problem via the following three perspectives: a company's market share management, introduction of customers with different perspectives, and an analysis of an application domain which is illustrative of these issues. Our contributions following these perspectives include: (1) development of a stochastic differential-jump game (SDJG) model for brand competition in a specific situation wherein market share is modeled by a jump-diffusion process, (2) a robust hierarchical logit/probit model for market heterogeneity, and (3) applications of logit/probit model to the dynamic pricing problem occurring in production-inventory systems with jump events. Our research explores the use of quantitative method of operations research to control the dynamics of market share and provides a precise estimation method to integrate more detail information in discrete brand choice models.