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Abstract Conditioning the pricing policies on purchase history is proven to generate a cutthroat price competition enhancing consumer surplus. This result typically relies on a framework where competitors are assumed to be symmetric. This paper demonstrates that under significant asymmetries of competing firms, the strong firm trades off current market share for future market share and the weak firm does the opposite. This inter-temporal market sharing agreement generates unidirectional poaching and entails new and distinctive welfare implications. In particular, if consumers are sufficiently myopic, price discrimination softens price competition in relation to uniform pricing, overturning the conclusion of previous studies.
