  Product cost heterogeneity across firms and loyalty models of customers are
two topics that have garnered limited attention in prior studies on competitive
price discrimination. Costs are generally assumed negligible or equal for all
firms, and loyalty is modeled as an additive bias in customer valuations. We
extend these previous treatments by considering cost asymmetry and a richer
class of loyalty models in a game-theoretic model involving two asymmetric
firms. Here firms may incur different non-negligible product costs, and
customers can have firm-specific loyalty levels. We characterize the effects of
loyalty levels and product cost difference on market outcomes such as prices,
market share and profits. Our analysis and numerical simulations shed new light
on market equilibrium structures arising from the interplay between product
cost difference and loyalty levels.
