How we can let banks cheat Geithner's plan

Amid discussions about whether it would be possible for banks to cheat Timothy Geithner's bank plan (by bidding on their own toxic assets with government-subsidized non-recourse loans) it's worth thinking a bit more about why that would be such a bad thing. After all, the banks that own these securities arguably have better access to the (admittedly scarce) supply of information about the assets, so given an appropriate auction structure, the assets should be more accurately priced if the banks are allowed to bid in some way. 

The problem under the current proposal is that banks would have an incentive to bid the price up to exorbitant levels. As I understand the plan, bidders only have to post $0.08 or so for every dollar bid on the assets -- the rest is supplied by the government in the form of a non-recourse loan. So for every dollar a bank were to bid on its own asset, it would essentially receive a $0.92 low-interest loan from the government, and if the value of the asset itself ever fell below the value of the government's loan, the bank could walk away from the asset without repaying the loan at all. Sounds like a sweet deal -- and indeed it would be, for the banks (though not for taxpayers).

Still, it's worth asking whether there might be some way to put banks' potentially superior knowledge about their own assets to use in accurately setting those assets' prices. Of course, banks' better knowledge about these assets might be part of the reason we're facing this pickle in the first place. Banks might correctly believe that these assets are worth more than the very low price set by the market (which has little information and fears the worst) and so no transactions take place. This is arguably why the government needs to provide such large non-recourse loans in the first place, subsidizing the market price to the point that it exceeds the banks' own valuation of the assets. A risk of such subsidies, however, is that they may make the assets too cheap for the bidding institutions, leading to inflated prices, and leaving the government loans unpaid when the assets turn out to be worth less than the loans themselves. 

Is there a way to mitigate this risk of over-subsidizing bids by making use of banks' in-house knowledge about these assets? It seems to me there should be some sort of auction structure that could accomplish this by allowing banks to bid on their own assets. Here's one possibility that occurs to me: 

1. Independent investors first bid on the toxic assets (as under the current plan).

2. The government looks at the top bidder's offer, and, in particular, at the loan it would provide to that bidder for the asset's purchase -- call it loan amount $X.

3. The government then offers the bank (which currently owns the toxic asset) free insurance against the price of the asset in question falling below $X.

4. The bank chooses whether to take the free insurance from the government, or to sell to the top bidder at the offered price. 

It seems to me such a structure would leave everyone better off than the current plan does. Under the current plan, the taxpayer is already on the hook for $X in the event that the asset's value turns out to be below that amount (since the investor will then walk away from the non-recourse loan), so offering that insurance to the bank doesn't cost anything. If the bank chooses to keep the asset and the insurance, rather than take the bidder's offer, the taxpayer also saves the cost of offering the bidder a low-cost loan. Finally, with such insurance, banks could lend again without fear of potential losses from the toxic assets, even if those assets remain on their books. 

There are, I'm sure, other better ways of making use of banks' knowledge to save taxpayers money and accurately set these prices -- any auction theorists out there who feel like chiming in?