Josh Lerner and Jean Tirole (the latter was just awarded a Nobel Prize) write,

Innovations in hardware, software or biotechnology often build on a number of other innovations owned by a diverse set of owners.

Pointer from Joshua Gans. For more on Tirole, see Tyler Cowen and subsequent posts by Alex and Tyler.

Two (or more) firms may hold complementary patents. That is, the value of using firm A’s patented innovation is higher to a licensee who can also use firm B’s patented innovation. Lerner and Tirole ask when a social planner would want these firms to pool their patents, that is to license them together. If you do not care to follow their mathematical analysis, you can skip to the end where they summarize their conclusions.

The situation is a form of the dual-monopoly problem. As I once explained,

suppose that a single company has a monopoly in both peanut butter and jelly. When it sets the price of jelly, it knows that the more jelly it sells the more peanut butter it will sell. Therefore, at the margin, it will tend to want to set a lower price for jelly than if it were just looking at jelly as a stand-alone product.

If you then break up the PB and J monopoly into two separate companies, the incentives of the two separate monopolies will change. The peanut butter company is not going to worry about the fact that higher peanut butter prices will reduce jelly consumption, and the jelly company is not going to worry about the fact that higher jelly prices will reduce peanut butter consumption. The net result of the breakup is that prices to consumers will rise.

This theory goes all the way back to Cournot.

It seems to me that we observe patent pools more often internally than externally. Think of Apple Computer as one gigantic internal patent pool. Or a large pharmaceutical company. It might be easier for one firm to internalize complementary patents than for several firms to get together and pool them.