We study a three-stage, asymmetric duopoly game of R&D rivalry. The stages are: (1) development of an innovation; (2) fixed-fee licensing of the innovation; and (3) sale of the final product. We find that major innovations will not be licensed, but that equally efficient firms will tend to license minor innovations. For some innovations, licensing is both privately and socially undesirable. If at least one of the two producers would refuse to license (were it to acquire the innovation), then licensing will not occur; an excluding firm will obtain the innovation. The possibility of licensing may decrease the returns to innovation if the licensee appropriates most of the licensing gains to trade.