We study competition in data-driven markets, where the cost of quality production decreases in the amount of machine-generated data about user preferences or characteristics. This gives rise to data-driven indirect network effects. We construct a dynamic model of R&D competition, where duopolists repeatedly determine innovation investments. Such markets tip under very mild conditions, moving towards monopoly. After tipping, innovation incentives both for the dominant firm and the competitor are small. We show when a dominant firm can leverage its dominance to a connected market, thereby initiating a domino effect. Market tipping can be avoided if competitors share their user information.