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2014 | OriginalPaper | Chapter

23. Patent Licensing: Stackelberg Versus Cournot Models

Authors : Oana Bode, Flávio Ferreira

Published in: Discontinuity and Complexity in Nonlinear Physical Systems

Publisher: Springer International Publishing

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Abstract

In the present study we consider, on one hand, a differentiated Stackelberg model, and, on the other hand, a differentiated Cournot model, when one of the firms engages in an R & D process that gives an endogenous cost-reducing innovation. The aim of this study is two fold. The first is to study the licensing of the cost-reduction in the Stackelberg model. The second is to do a direct comparison between Stackelberg model and Cournot model. We analyse the implications of these types of licensing contracts over the R & D effort, the profits of the firms, the consumer surplus and the social welfare. By using comparative static analysis, we conclude that the degree of the differentiation of the goods assumes a great importance in the results.

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previous chapter In-Plane Free Vibration and Stability of High Speed Rotating Annular Disks and Rings

next chapter Privatization and Government Preferences in a Mixed Duopoly: Stackelberg Versus Cournot

Throughout the paper we use the notation superscript S to refer to the Stackelberg competition.

We note that d ₁ ≃ 0. 732.

Throughout the paper we use the notation subscript nl to refer to the pre-licensing case.

Throughout the paper we will add a ∼ to identify the values we get in the drastic innovation case.

We note that 0 < d₂ < 1 is such that \(d_{2}^{2} - 4d_{2} + 1 = 0\) , i.e. d ₂ ≃ 0.268.

We note that 0 < d₃ < 1 is such that \(d_{3}^{4} + 2d_{3}^{3} + 8d_{3} - 8 = 0\) , i.e. d ₃ ≃ 0.812.

We note that 0 < d₄ < 1 is such that \(d_{4}^{4} - 5d_{4}^{3} - 3d_{4}^{2} + 10d_{4} - 2 = 0\) , i.e. d ₄ ≃ 0.219.

We note that 0 < d₅ < 1 is such that \(7d_{5}^{4} - 13d_{5}^{3} - 9d_{5}^{2} + 28d_{5} - 10 = 0\) , i.e. d ₅ ≃ 0.458.

Throughout the paper, we use the notation subscript l to refer to the two-part tariff licensing case.

We note that 0 < d₆ < 1 is such that \(6d_{6}^{6} - 42d_{6}^{5} + 125d_{6}^{4} - 156d_{6}^{3} + 14d_{6}^{2} + 112d_{6} - 56 = 0,\) i.e. d ₆ ≃ 0.721.

We note that 0 < d₇ < 1 is such that \(6d_{7}^{2} - 18d_{7} + 11 = 0,\) i.e. d ₇ ≃ 0.855.

We note that 0 < d₈ < 1 is such that \(54d_{8}^{10}-99d_{8}^{9}-621d_{8}^{8}+1866d_{8}^{7}-42d_{8}^{6}-4446d_{8}^{5}+3146d_{8}^{4}+3020d_{8}^{3}-3276d_{8}^{2}-344d_{8}+736 = 0,\) i.e. d ₈ ≃ 0.863.

We note that d ₁₀ ≃ 0. 747.

We note that d ₁₁ ≃ 0. 828.

We note that d ₁₂ ≃ 0. 928.

We note that d ₁₃ ≃ 0. 941.

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Title: Patent Licensing: Stackelberg Versus Cournot Models
Authors: Oana Bode
Flávio Ferreira
Publisher: Springer International Publishing
Book: Discontinuity and Complexity in Nonlinear Physical Systems
Print ISBN: 978-3-319-01410-4

Electronic ISBN: 978-3-319-01411-1

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-01411-1_23

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