Extensions to the Model
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Valuing Interrelated Inventions
Another criticism of these results rests on the measurement of the value of an invention. In reality, the demand curve is insufficient for determining how much social welfare an innovation generates. Green and Scotchmer point out that inventions are often improvements or applications of other inventions. Oftentimes, a patent by itself may not generate any profit at all. For example, Green and Scotchmer note that LASER technology is not profitable by itself, unless combined with ideas for applications. Clearly, the values of related inventions do not summate, but rather interact in some complicated way.
By constructing a two-player game theoretic model of subsequent inventions, Green and Scotchmer explore how patent structure affects where value is captured. Patent structure here is most closely related to Klemperer's idea of patent scope. A broader patent encompasses more possible inventions, so improvements to the technology must be larger before they can be produced without infringing the original patent.
Green and Scotchmer find that when one firm improves on another firm's invention, the two firms must negotiate over how to split the value of the combined product. Altering patent breadth changes the equilibrium bargaining strategies as different "threat points" appear. Because value must be collected by two players, the reward for the combined invention must be larger than in a one-player game. If the second firm takes too much of the profit, the first firm has insufficient incentive to research the original idea.
Even this extension does not fully capture the rich variety of interconnections among innovations. Some inventions (consider the telephone) are extended by an enormous number of other inventions. How should value be distributed among a continuous stream of inventors who build upon preceding patents?
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