The KEI Blog has a post on a proposal by the John Edwards campaign to replace patent monopolies with prizes as an innovation incentive in the pharmaceutical industry. A lot of the economics literature on prizes is directed at this particular industry (rather than, say, space), and the debate on "patents vs. prizes". Here's a more detailed article on the proposal. Here's another one. This article expresses a worry that the prizes will be much too small to replace the incentive of patents.
I'm very skeptical of these grand schemes to replace patents with prizes. We'll have to wait to see what the details of the Edwards plan is, but most of the patent-replacing prize ideas have lots of problems. They usually have some kind of government bureaucracy (expensive in itself) to try to determine what the value of the pharmaceuticals are (before or after the fact), and that organization is vulnerable to all sorts of political mischief. That's in contrast to the current space prizes which are difficult to manipulate politically, and too small for the bad guys to bother with. They are extremely expensive if they have any hope of providing an incentive comparable to patents (or simply keeping the details of how the innovation works secret). That is in direct contrast to the X PRIZE style of prizes which are cheap. If they aren't expensive enough ... your innovation and pharmaceutical businesses stagnate. They also tend to be directed towards an entire industry, whether the particular sub-area is appropriate for prizes or not. That's in contrast to the laser-beam focus of the space prizes we have now. Finally, because they are so all-encompassing, they totally lose the major benefit of prizes, which is the publicity and enthusiasm and energy of a sport or game-like competition.
Hopefully this proposal will turn out to be much more like the targeted incentives to break logjams in areas where government contracts and grants have failed, like the X PRIZE, but until I find out otherwise I'll be very skeptical on this one.
One more thought (not original - it's from a memory of one of those economics papers) - it would be much better to start with a pilot program than a grand overhaul that's likely to be economically crippling. Also, it would be much better to have prizes that supplement patents in areas where we really want a breakthrough rather than replace them (perhaps in areas that are technically very difficult, or that don't pay much even though we can agree they would be worthwhile). We want the improvements! Paying more temporarily because of patents is a small price to pay for advances, which you look at it in the long view for the nation or human species. Another variant would be to have a patent-replacing prize that is optional for the company. Then the incentive to innovate would still be there either way.