Patents, imitation and welfare

Abstract

We consider the effects of product and process patents on profits and welfare. In a duopoly model, we show that if the cost of imitation is not very large, prisoner's dilemma occurs under process patent, thus creating lower profit of each firm under process patent than under product patent. Welfare is higher under process (product) patent for very small (not very small) cost of imitation. Although the possibility of cross-licensing never makes lower welfare under process patent for all costs of imitation, welfare is never lower under product patent under infinitely repeated game.

Keywords:

• Cross-licensing
• Prisoner's dilemma
• Process patent
• Product patent
• Repeated game
• Welfare

Acknowledgements

We would like to thank two anonymous referees of this journal for helpful comments and suggestions that helped to improve the article. The usual disclaimer applies.

Notes

¹Lambertini and Rossini (1998) also show prisoner's dilemma in an innovation game with positive externality. However, in contrast to them, we show prisoner's dilemma without externality and it increases imitative innovation in our article. Further, Bernhofen and Bernhofen (1999) explain that the argument of Lambertini and Rossini (1998) is misleading and show that the parameter configuration that most likely generates the equilibrium with no innovation in Lambertini and Rossini (1988) is least likely to generate prisoner's dilemma. In contrast, prisoner's dilemma in our analysis occurs whenever we have a unique equilibrium under process patent where both firms do imitation.

²This inverse demand function is generated from the utility function U=a(x+y)−((1/2)(x ²+y ²+2gxy)).

³As suggested by a referee, K may also be viewed as the fixed cost of producing the extra product. Thus, this article may also be related to the literature showing welfare reducing competition in presence of fixed costs (see, e.g. von Weizsäcker, 1980; Mankiw and Whinston, 1986; Suzumura and Kiyono, 1987; Okuno-Fujiwara and Suzumura, 1993).

⁴There is a mixed strategy equilibrium when K∈(K ₂, K ₁). However, we concentrate on pure strategy equilibrium only.

⁵Schelling's theory (1960) of ‘focal pints’ suggests that in some situations, players may coordinate on an outcome in which players have a common understanding that this is the obvious one to choose. In the case of multiple equilibria, higher payoffs for both players in an equilibrium than the other may itself achieve the necessary convergence of all players' expectations for the former equilibrium and may make it a focal point; see Dixit and Skeath (1999) for a non-technical discussion on focal points and Furdenberg and Tirole (1991) for a more detailed discussion on this issue.

⁶We find the collusive and the deviation profits of a firm by maximizing Max _q π^co, pdt (q)=Max _q (a−q−gq)q and Max _d π^de, pdt (q)=Max _d (a−d−gq)d. The non-cooperative payoff is given by the profits shows in Section 2.