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We examine the incentives of horizontally differentiated multinational firms to invest in cybersecurity of their customers’ personal data. Each firm can use price discrimination based on consumers’ purchase history in the presence of switching costs. We show that the firms’ investment choice does not only depend on the level of the cybersecurity cost but also on their markets dominance degrees. Furthermore, we prove the existence of a threshold’s market-share-dominance under which the dominant firm practices the below-cost sale strategy in order to attract its rival’s customers. Finally, we show that the dominant firm is still unable to chase its rival from the market. JEL Codes: F12, F23, F61, L1, L11.