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.
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