On a Dynamic Model of Cooperative and Noncooperative R and D in Oligopoly with Spillovers

We developed a dynamic model of oligopoly in which firms' R and D investments accumulate as R and D capital and have spillover effects. We showed that there exists a symmetric stable open-loop Nash equilibrium for each of the differential games under noncooperative R and D and cooperative R and D. We then showed that for small spillovers, each firm's R and D investments are larger under R and D competition than under R and D cooperation. We further demonstrated that, in the limit, when the discount rate goes to zero, the stability condition for our dynamic game approaches the stability condition for the static two-stage game in d'Aspremont and Jacquemin (Am Econ Rev 78:1133-1137, 1988). However, we also showed that at the Markov perfect equilibrium, cooperative R and D investments are larger than noncooperative investments for all possible values of spillovers.