Persuasive Advertising in Oligopoly: A Linear State Differential Game

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 more intense advertising than Cournot competition. This is due to the fact that enhancing reservation prices is more relevant to firms when market competition is tougher. Ultimately, this may entail that Cournot outperforms Bertrand when it comes to social welfare.