Fines Imposed on Counterfeiters and Pocketed by the Genuine Firm. A Differential Game Approach

We consider competition between a legal firm that sells a product protected by IPR (Intellectual Property Rights) laws and a counterfeiter who illegally copies and sells products without the permission of the brand-name producer. Each time the counterfeiter is caught, the payment of a fine proportional to the amount confiscated and to the price of the original goods is imposed. However, fines are pocketed by the legal firm. In this paper a differential game is studied in which both firms compete for prices while the legal firm invests in advertising to increase goodwill and, accordingly, demand. Based on this, a feedback Nash equilibrium is computed and discussed. Unfortunately, the analytical results are too complex to allow an explicit comparison between the payoff of the producer with and without the presence of counterfeiting. However, through some numerical simulations, it is shown that, under specific values for the parameters of the model, the genuine producer can be also better off in the presence of counterfeiting rather than in its absence.