Here is good description of how an auction for hard-to-price assets might work -- from
Economists Look at Ways to Structure Auctions - WSJ.com:
Auction experts say the best solution would be for the government to bring experienced buyers into the auction process so it wouldn't be the sole buyer. Absent that, there are techniques the government could use to force sellers to disclose what they believe the appropriate prices are, said University of Maryland economist Lawrence Ausubel.
He said he thinks the government should hold an auction in which it announces its intention to buy some of the amount outstanding of a security -- perhaps half. It would then start the process by setting a relatively high price for a security at which presumably all the firms that hold it would want to sell all they own. Then the government would set the price progressively lower until the holders, either by dropping out or reducing their bid sizes, were willing, overall, to sell no more than half of what they own.
The "winners" of the auction would get to sell, but the losers, who were unwilling to sell cheaply, would benefit as well, because the price the government paid in the auction would help establish what a reasonable price for the security is, helping to re-establish the market for such securities. "Once the government establishes some liquidity, the private market may finish the job," said Mr. Ausubel.
Key is price setting. In essence, this is what the OceanTomo IP auctions have been doing for patents. The systemic benefits from these auctions extend far beyond simply serving as a clearinghouse for IP transactions (as important as that is). The auctions give the rest of the market a starting point for private transactions by providing price data. That is not to say that negotiations don't take place without price data. But once a generally accepted reference point has been established, the negotiations run a lot smoother and with less transaction costs.
So, Mr. Ausubel is exactly right. Set up a way to get some generally accepted price points and the market will start to work again. After all, a major cause of illiquidity is the lack of confidence - and that lack of confidence is due to uncertainty - on both price and the ability of your counterparty to fulfill their obligations. Reduce the price uncertainty and you can help reduce the illiquidity.
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