Thoughts and some history from Bob Zubrin. The plan, at least as stated by Bob, has a (as Newt would say) “fundamental” flaw in it:

There would be at least two prizes: a $5 billion prize to develop and demonstrate a heavy-lift booster capable of lifting at least 100 tons to low Earth orbit, and a $10 billion prize for the first human mission to Mars. In addition, the winners of these prizes would be given contracts for the purchase by NASA of an additional five copies of their flight systems at a recurring cost of 20 percent of the respective prize per copy.

Prizes should specify the goal, not the means to achieve it. It presumes without evidence the need for an arbitrarily-sized heavy lifter. Bob, if you want to get to Mars, then put out a prize for Mars, but don’t tell people how to do it.