We present a new approach to endogenizing technological spillovers. Firms choose levels of a cost-reducing innovation from a continuum before they engage in competition for each other's R&D-employees. Successful bids for the competitor's employee then result in higher levels of cost reduction. Finally, firms enter product market competition. We apply the approach to the long-standing debate on the effects of the mode of competition on innovation incentives. We show that incentives to acquire spillovers are stronger and incentives to prevent spillovers are weaker under quantity competition than under price competition. As a result, for a wide range of parameters, price competition gives stronger innovation incentives than quantity competition.