Strategic pricing and advertising in the presence of a counterfeiter

We consider a finite-horizon differential game with a legal producer and a counterfeiter as players. The planning horizon is divided into two periods. In the first period, the legal producer is alone in the market, while in the second both players compete. Each player controls his own retail price and advertising budget. We characterize the equilibrium pricing and advertising strategies of the two players, and assess the impact of the counterfeiter's entry date on these strategies. Further, by contrasting the results of the scenarios with and without counterfeiting, we determine the conditions under which the presence of the illegal producer is beneficial to consumers and even to the legal firm.