How do start-up acquisitions affect the direction of innovation?

A start-up engages in an investment portfolio problem by choosing how much to invest in a "rival" project, which threatens the position of an existing incumbent, and a "non-rival" project. Anticipating its acquisition by the incumbent, the start-up strategically distorts its portfolio of projects to increase the (expected) acquisition rents. Depending on parameters, such a strategic distortion may result in an alignment or a misalignment of the direction in which innovation goes relative to what is socially optimal. Moreover, prohibiting acquisitions may increase or decrease consumer surplus. The more (less) the rival project threatens the incumbent and the less (more) the non-rival project appropriates the social surplus, the more likely is that consumers benefit (suffer) following an acquisition. These results are robust to acquisitions where the acquirer takes over the research facilities of the start-up.