We investigate the issue of strategic substitutability/complementarity in differential games. We prove that instantaneous best replies exist if Hamiltonian functions are multiplicative in the control variables. Otherwise, if the Hamiltonians are addively separable w.r.t. controls, a dominant...

We investigate the timing of adoption of product and process innovation by using a differential game in which firms may invest in both activities. We consider horizontal product innovation that reduces product substitutability, and process innovation that reduces marginal cost. First, we...

We investigate a linear state differential oligopoly game with advertising, under either Cournot or Bertrand competition. We show that a unique saddlepoint equilibrium exists in both cases if the marginal cost of advertising is sufficiently low. Then, we prove that Bertrand competition entails...