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Random Walks, Non-Cooperative Games, and the Complex Mathematics of Patent Pricing

Name
Random Walks, Non-Cooperative Games, and the Complex Mathematics of Patent Pricing
Cite
55 Rutgers L. Rev. 1175
Year
2003
Bluebook cite
F. Russell Denton & Paul J. Heald, Random Walks, Non-Cooperative Games, and the Complex Mathematics of Patent Pricing, 55 Rutgers L. Rev. 1175 (2003).
Author
F. Russell Denton & Paul J. Heald
URL
55 RULR 1175
Item Type
article
Summary
“Current patent valuation methods have been described charitably as ‘inappropriate,’ ‘crude,’ ‘inherently unreliable,’ and a ‘guesstimate.’ This article provides a more rational and systematic tool than any we have found in the existing literature or relevant case law. We believe our approach to patent valuation will be useful in improving investment decisions, in facilitating licensing negotiations, and in reducing error costs in litigation.” Id. at 1179.

“The multiplicity of factors that affect patent value over time have rendered an accurate patent license pricing model elusive. Although classical tools of measurement permit the rough estimation of a current value for an invention, no plausible model has yet accounted for the effect of numerous market forces over the life of the patent. Accurate pricing of a patent license, characterized as an option to use an invention for an extended time period, has so far been impossible to achieve. . . .Given that the value of both stock and patented inventions is driven by predictions about future business revenue, the Black-Scholes equation presents a pricing story worthy of further investigation to those interested in pricing patents. . . . The patent pricing metric suggested herein, which we denominate the Denton Variation of the Black-Scholes equation, exploits the similarities between the option to buy stock and the option to develop an invention.
Unfortunately, patent pricing presents a difficulty not present in most stock option deals because merely inquiring about acquiring a license will affect its price. . . . In other words, the relative positions of the patent licensor and licensee affects the price, unlike stock option pricing, which is accomplished without inquiry into the relative bargaining positions of the parties to the deal. . . . The need to model patent pricing as a non-cooperative game adds a layer of complexity to the Denton Variation of Black Scholes, but a realistic model cannot ignore the consequences that flow from the bargaining context.
We conclude that an adequate patent pricing metric must combine probabilistic methods familiar to experts in mathematical finance, quantum mechanics, and statistical climatology, with the strategic assumptions familiar to game theorists.” Id. at 1175-77.

Excerpts and Summaries

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Sunday 01 of February, 2009 21:55:41 GMT
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