We analyze a dynamic model of repeated innovation where inventors may either be acquired by an incumbent or else resist takeover and challenge for leadership. In the short run, acquisitions always spur innovation because of the invention-for-buyout effect. In the longer run, however, they may stifle it because of a countervailing effect, the entrenchment of monopoly. The latter occurs when the incumbent's dominance depends on past levels of activity and is therefore reinforced by recurrent acquisitions. We show that if the entrenchment effect is sufficiently strong, forward-looking policymakers should prohibit acquisitions in anticipation of the long-run negative impact on innovation. This argument sets out a new theory of harm that can be used to block acquisitions that could otherwise go unchallenged.