The paper considers the problem of whether in a strategic two-stage game duopolistic firms make an overinvestment or underinvestment in R & D when there are their spillovers. We deal with two cases of Cournot quantity and Bertrand price competitions. It is shown that in Cournot (Bertrand) competition each firm has an incentive to use a larger (less) or less (larger) investment than the one required to minimize the costs of investment according as its rival's spillover rate is relatively small or large
