We study competition for acquisition of a start-up and its effect on the innovator's choice for the “direction of innovation”, which determines the fit of the innovation to each acquirer. We show that an initially lower quality firm can acquire innovation and increase its market share, that is, “decreasing dominance” can prevail. The innovator chooses an innovation that better fits the lower-quality firm to intensify the competition for acquisition. The innovation fit gets closer to the lower-quality firm when the initial quality asymmetry is greater, and the innovation's value is smaller. The lower-quality firm is more likely to win the innovation if it is better in integrating the innovation and the firms are less asymmetric. Comparative statics depend critically on which firm is better at integrating innovation. The equilibrium direction of innovation minimizes total and consumer welfare. In a two-period model, the initially lower-quality firm wins the first-period innovation more (less) often than in the case of the one-period model if it is better (worse) in integrating innovation than the higher-quality firm. (joint with Bruno Jullien and Gary Biglaiser)