“Waiting to Imitate: On the Dynamic Pricing of Knowledge,” E. Henry & C. Ponce (2011)

Reverse engineering is not free – at the very least, it is a tiny bit more costly to reverse engineer if I don’t have a blueprint than if I do. The inventing firm owns the blueprint to their own invention. Is this enough to make patents sometimes unnecessary? It turns out that the answer is yes, if markets in knowledge exist; that is, if I can sell a blueprint, it may not be necessary to give me a patent at all. Why is this?

Henry and Ponce consider a very simple example first. Let there be three firms, one of whom has invented something. If I sell it myself, I earn p1 in profits each year. If two of us are selling, we earn p2<.5p1 profits each in the duopoloy. If three of us all sell, we earn p3<.67p2 in triopoly profits. It costs K to reverse engineer, and K<p3, so in the absence of markets for knowledge, everyone imitates immediately, and all earn triopoly profits. This is the standard "if we don't give patent protection, inventions will be imitated" story.

But what if I can sell knowledge that I hold? Think about what happens in the subgame once two firms have the knowledge: since it is worthwhile for firm 3 to reverse engineer, she will do so unless once of us sells her knowledge for less than K. But since she is going to enter whether she is sold knowledge or not, we are all going to earn triopoly profits going forward. So we should both try to sell her the knowledge we have and earn triopoly profts plus the gains from selling the knowledge – but since we both know this, the knowledge will sell to the third firm for 0 since the two firms already holding knowledge will Bertrand compete it away.

What happens, then, when only one firm, the original inventor, holds knowledge? She sets a price for the knowledge equal to exactly K. The two other firms must be playing a mixed strategy as to when to buy the knowledge (or when to pay K and reverse engineer), since if the other firm will buy knowledge at time t, I know I can immediately buy that knowledge epsilon later for 0 given the logic in the last paragraph. That is, both firms want to get knowledge and start earning profits as early as possible, but they also would love to get the knoweldge for free by waiting until the other firm buys it. Therefore, each firm buys the knowledge at a time dependent on a mixed strategy; precisely, they buy according to an exponential distribution that looks basically the same as the solution to your usual war of attrition game (discounting future profits is essential here, of course). Note that the original inventor earns triopoly profits after a random delay before the first entrant, but monopoly profits until that point, and a profit of K at the time the knowledge is first sold; this is much better for the firm than triopoly profits from time 0 onward, the best case for the imitator, as well as the profits earned in the world without markets for selling knowledge.

What if we increase the number of potential imitators? With more imitators, the delay before the first imitator buys knowledge increases; this is because the profit from entering falls from p3 to pN, where N is the number of potential imitators, and because there are a lot more other imitators that I think may enter before me, letting me get knowledge for free. Under some conditions on K, p1, p2, p3 and p4, inventor expected profit in this knowledge sale market may be equal to monopoly profit forever. Note that this secrecy payoff is better for the inventor than even a patent, since patents involve disclosure of knowledge and last only for a limited time. The authors hypothesize that more well-developed markets for licensing knowledge may explain why secrecy has, over time, become more important for IP protection compared to patents.

A simple proof you can read in the original paper notes that the result does not change if it is possible to change the knowledge sales contract such that I can sell knowledge and make it so the recipient cannot then resell: it turns out that we can ignore this since, in equilibrium, the inventing firm will never want to insist on such a condition. The paper also ignores sequential innovation, but hypothesizes that such chains may make the example above more stark, an intuition that seems reasonable to me. Note also that many of the results above hold even when K, the cost of imitating, is very small.

At the very least, following this result, I expect statements in the theory literature along the lines of “in the absence of patent protection, firms are immediately imitated and profits are Bertrand competed away” to disappear. That is a poor way to discuss interesting issues surrounding patents.

econ.sciences-po.fr/sites/default/files/file/ehenry/carlos.pdf (April 2011 working paper – final version in the October 2011 JPE)

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