TITLE: Can someone explain Cremer-Mclean's astonishing result in auction theory?
QUESTION [14 upvotes]: In mechanism design/auction theory, there is a famous result by Cremer and Mclean that if agents'/bidders' valuations are even slightly correlated, then all the surplus can be extracted by the principal/auctioneer. This is what makes auction theory without i.i.d. valuations an unpopular research topic even though it's interesting from a practical point of view.
My question is: Can someone explain to me why the Cremer-Mclean result is true?
The original paper is Econometrica 1998, "Full extraction of the surplus in Bayesian and dominant strategy auctions" by Cremer and Mclean.
There is an explanation beginning on page 151 in Vijay Krishna's Auction Theory textbook.

REPLY [5 votes]: The main idea behind the Cremer-McLean result is the following:

When agents values are correlated, after an agent learns her own value is $v$, her posterior on the other agent's values is distinct from the case where it is some over value $v'$.
Given that the two values $v$ and $v'$ induce different posteriors on the other agents' values, we can potentially concoct a bets on the realization of the other agents' values for each of $v$ and $v'$ such that each prefers their own bet.  (And these bets are revenue-neutral for the auction.)
Scale the magnitudes of these bets so that the incentive to obtain the right bet exceeds the incentive to get a good deal in the auction.  Now in the auction the winner can be charged her value.

The conditions under which Cremer-McLean holds specify the conditions under which these bets exist.