I think auctioning things off would be a huge mistake. Better to use prizes to encourage competition:
- First company to land a probe on the moon gets X number of billion dollars.
- First company to send people around the moon and return them safely gets 2X billion dollars.
NASA would have a certain amount of dollars to put up as prizes, and would be in charge of the objectives, just not how they were accomplished.
The prizes could be substantial and would still be less than the $90 billion NASA will squander attempting to build the Ares V Rocket. The current scheme simply pays out money without requiring results. It also stifles competition by awarding the contract to a single player, the company with the best connections or spin gets the contract. The prize method would reward the fittest competitor that could actually deliver. That would encourage many more to attempt to the actual feat. At the end of the prize-winning phrase one company has a huge amount of technology that was paid for by the prize leaving lots to profit from.
The prizes also encourage frugality; people are a lot less likely waste their money than they are the governments'. And since there is a fixed dollar value at the end, there is no incentive to simply run on with contract overruns because we didn't get the job done. Those that play that game go bankrupt in the prize scenario.
Yes, this would require speculation and investment by private industry. But SpaceX has already proven that the job can be done and done efficiently, and it's probably a lot safer than investing in home mortgages for overpriced property was under capable purchasers. Even if you lost this bet, you'd have something to show for it at the end in the form of patents, equipment, and/or capability. Coming in second place would only mean you lost prize, not the farm (mortgages?).