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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 differentarXiv:2102.09620v1 fatcat:2ubhlok4z5betfwjbxjoyaut6y