Market Share Analysis with Brand Effect

We investigate the effect of brand in market competition by proposing a variant Hotelling model, with an additional brand effect term modeled by a function of its market area of the form - beta. (Market Area)(q), where beta captures the brand influence and q captures how market share affects the brand. We show that at equilibrium, a company's price is proportional to its market area over the competition intensity with its neighbors, a result that quantitatively reconciles the common belief of a company's pricing power. We also study an interesting "wipe out" phenomenon that only appears when q > 0, which is similar to the "undercut" phenomenon in the Hotelling model, where companies may suddenly lose the entire market area with a small price increment. Our results offer novel insight into market pricing and positioning under competition with brand effect.