Debapriya Sen

General licensing schemes for a cost-reducing innovation

Two general forms of standard licensing policies are considered for a non-drastic cost-reducing innovation: (a) combination of an upfront fee and uniform linear royalty, and (b) combination of auction and uniform linear royalty. It is shown that in an oligopoly, the total reduction in the cost due to the innovation for the pre-innovation competitive output forms the lower bound of the payoffs of both outsider and incumbent innovators. Further, the private value of the patent is increasing in the magnitude of the innovation, while the Cournot price and the payoff of any other firm fall below their respective pre-innovation levels. Sufficiently significant innovations from an outsider innovator are licensed exclusively to a single firm. Otherwise, all other firms, except perhaps one, become licensees. The dissemination of the innovation is generally higher with an incumbent innovator compared to an outsider. For both outsider and incumbent innovators, the monopoly does not provide the highest incentive to innovate; for sufficiently insignificant innovations, it is the duopoly that does so, and, the industry size that provides the highest incentive increases with the magnitude of the innovation. Finally, it is argued that significant innovations are more likely to occur when the innovator is an incumbent firm.

Fee versus royalty reconsidered

For an outsider innovator in a Cournot oligopoly, royalty licensing could be superior to both fixed fee and auction. The result depends on a simple fact that has been overlooked in the existing literature, namely, the number of licenses can take only integer values.

Cooperation in R&D: patenting, licensing and contracting

In this paper we review some of the literature on R&D collective arrangements using game theoretical concepts and considering various settings, involving either complete or incomplete contracts. Patent protection, licensing in various industry contexts as well as the role of various factors such as product differentiation, innovation magnitude and asymmetric information are considered. The relation of innovative activity to the intensity of competition is reconsidered and the benefit of various types of cooperative R&D-agreements in presence of externalities are reviewed. The last two sections are devoted to contracting issues.

Technology Transfer Under Returns to Scale

In this paper we consider the licensing of a cost-reducing innovation by an outside innovator that uses optimal combinations of upfront fees and royalties in a Cournot duopoly characterized by non-constant returns to scale. The main conclusion of our theoretical analysis is that incidence of positive royalties and diffusion of innovations are both inversely related to economies of scale. Our analysis provides a plausible explanation of the variation of licensing policies across industries.

When an inefficient competitor makes higher profit than its efficient rival

We consider a Cournot duopoly with strategic delegation, where quantities of firms are chosen by their managers. A firm can offer its manager one of the two incentive contracts: the profit incentive or the revenue incentive. We show that in this setting there are Nash equilibria in which an inefficient firm obtains higher profit than its efficient rival.

Patent licensing in a Cournot oligopoly: General results

Abstract This paper presents a comprehensive analysis of patent licensing in a Cournot oligopoly with general demand and looks at both cases: outside and incumbent innovators. The licensing policies considered are upfront fees, unit royalties and combinations of fees and royalties (FR policies). It is shown that (i) royalties unambiguously ensure full diffusion of the innovation while diffusion is limited under upfront fees, (ii) the Cournot price is higher under royalties compared to upfront fees and the price could even exceed the post-innovation monopoly price, (iii) for generic values of magnitudes of the innovation, when the industry size is relatively large, royalties are superior to upfront fees for the innovator and (iv) for any m , there is always a non empty subset of m -drastic innovations such that for relatively large industry sizes, upfront fee policy results in higher consumer surplus as well as welfare compared to both royalty and FR policies.

Potential games, path independence and Poisson's binomial distribution

This paper provides a simple characterization of potential games in terms of path independence. Using this characterization we propose an algorithm to determine if a finite game is potential or not. We define the storage requirement for our algorithm and provide its upper bound. The number of equations required in this algorithm is lower or equal to the number obtained in the algorithms proposed in the recent literature. We also show that for games with same numbers of players and strategy profiles, the number of equations for our algorithm is maximum when all players have the same number of strategies. The key technique of this paper is to identify an associated Poisson’s binomial distribution with any finite game. This distribution enables us to derive explicit forms of the number of equations, storage requirement and related aspects.

Decreasing Returns, Patent Licensing and Price-Reducing Taxes

Patent licensing agreements among competing firms usually involve royalties which are often considered to be anticompetitive as they raise market prices. In this paper we propose simple tax policies than can alleviate the effect of royalties. Considering a Cournot duopoly where firms produce under decreasing returns and trade a patented technology, we show that the interaction of royalties with decreasing returns may generate the counter-intuitive result that market prices decrease in the magnitude of diseconomies of scale. In such cases there exist progressive quantity taxes on firms that weaken the effect of royalties and lower the market prices. These taxes collect sufficient revenue to compensate firms for their losses. As a result, it is possible to design deficit neutral tax-transfer schemes that strictly Pareto improve the welfare of consumers as well as firms.