With the recent discussions on extremely large Mars-related prizes, I thought I'd post more of those old links I've gathered:
The Mars Prize - See pages 10-11. This is a proposed series of Mars-related prizes that lead to a large prize to a human Mars mission. The smaller prizes are intended to build towards the large prize. The idea is similar to one described in "The Case for Mars". Even the small prizes, such as a $500M prize for a Mars robotic orbiter that produces high-resolution imagery of the surface (the idea was before MRO), are much larger than the ones we see in the prize business today.
The Cato Institute has a white paper from 1998 about the economics of going to Mars. It presents The Mars Prize idea is presented as a way to simulate some of the advantages of a market, but the article also tries to come up with a way to do a purely private human Mars mission. It's pretty difficult to do, unless the component systems you are building are useful for other business purposes.
Since the beginning of this blog I've had a link on the right to "A Cold, Dry Cradle", a short story by Gregory Benford that features a human Mars mission inspired by a large Mars prize. I haven't read it, but it looks like Benford's novel The Martian Race is a variant of that story. Here's an excerpt from the novel. Benford is on the Board of Directors of the Mars Society.