Ausubel on Demand Reduction in Auctions
Bidders 1 and 2 want to buy 2 units at v1 and v2 per unit max. Bidder 3 wants 1 unit at v3. All three values are drawn from the [0,1] interval, i. i. d.
In an ascending auction, bidder 3 bids up to v3. Bidder 1 reduces his demand purposely, bidding for only 1 unit. Then, Bidder 2 will decide to do that too. The market will clear at the initial price of 0. And the result will be inefficient if v1 and v2 are not equal, since for efficiency just one of those two bidders should get both units.
Demand Reduction Hungarian auction: The big bundles close out first. Then the smaller unit auction is held. The seller will do better by selling the 3 units in two bundles, of 1 and of 2 units
Suppose Bidder 3 has the highest value. He’ll get the 1. Whoever values the 2-bundle the most will get them. Efficinecy! High revenue!
Suppose bidder 3 has the lowest value and bidder 1 the highest. Bidder 3 will lose, but will give a floor to the winning price. Bidder 1 will bid most for the 2-bundle, and Bidder 2 will get the 1-bundle. So we get efficiency.
Suppose Bidder 3 has the middle value and bidder 1 the highest. He will bid highest for the 1-bundle. Then Bidder 1 will outbid Bidder 2 for the 2-bundle. So we get efficiency.