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 intellectual property rights (IPR) 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.

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    The U.S. International Trade Commission (1984, p. vii).

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    Cesareo [3], in her book, identify, analyse and systematize the available research on counterfeiting and piracy published from 1980.

  4. 4.

    From Yao [21]: a pegged-fine counterfeit monitoring regime can be found in several countries. For example, the US Anti-Counterfeiting Consumer Protection Act of 1996, 1136, provides civil fines pegged to the value of the genuine goods. Fines for repeat offences are limited to not more than twice the domestic value of the merchandise as if it had been genuine, based on the manufacturers suggested retail price of the merchandise at the time of seizure. Another example is in Taiwan where the pegged ratio of fines ranges from 500 to 1500 (Taiwan Trademark Act of 1997, Article 66).

  5. 5.

    We denote by \([x]_+=\max (0,x).\)


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The authors thank the anonymous referees who have contributed, with their valuable observations and suggestions, to significantly improve this paper.

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Correspondence to Andrea Di Liddo.

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Biancardi, M., Di Liddo, A. & Villani, G. Fines Imposed on Counterfeiters and Pocketed by the Genuine Firm. A Differential Game Approach. Dyn Games Appl 10, 58–78 (2020).

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  • Differential games
  • Counterfeiting
  • Fines
  • Intellectual property rights
  • Numerical simulations

Mathematics Subject Classification

  • 91A23
  • 91A80

JEL Classification

  • C73
  • D23