Problem with Geithner's plan

As per the new Geithner plan, the Fed is going to partner with private investors and treasury to take care of the toxic assets in the balance sheet of banks. As per the plan, while the treasury and private investors will have equal equity stakes in the assets, the fed will be providing loan to support the rest of the toxic assets. 

The idea is that the treasury and the private investors will bid to set a price for the toxic assets and who ever wins the auction will own it at that price. The assumption is that the auction will help discover the correct price of those assets. 

Now the banks will be provided by the cash instead of the toxic asset and thus cleanse their balance sheets and be solvent again.

Now the plan has lots of negatives at this point:

1) When the private investors are currently not ready to pay more than 30 cents on a dollar, why would they be willing to pay more then that as part of this scheme. Besides there would be no reason why they would be willing to invest money in a scheme where the probability of losing it is very high.

2) The other scenario is that the banks may partner with private investors and have them support the scheme on their behalf so as to cleanse their balance sheet. This would mean that the bank takes money from fed and give it to the private investors to invest for them. This will result in bank losing a tenth of the amount to cleanse their assets. So this is eventually giving the bank a huge empty check from the tax payers money.

3) Now if that is the case, then do other private investors know that this scenario  is evident and is that a incentive for everyone to participate. This is because the payoffs are definitely very high if the scheme goes through.