(Multi-unit auctions) Two units of an object are available. There are n bidders. Bidder i values…

(Multi-unit auctions) Two units of an object are available. There are n bidders. Bidder i values the first unit that she obtains at vi and the second unit at wi, where vi > wi > 0. Each bidder submits two bids; the two highest bids win. Retain the tie-breaking rule in the text. Show that in discriminatory and uniform-price auctions, player i’s action of bidding vi and wi does not dominate all her other actions, whereas in a Vickrey auction it does. (In the case of a Vickrey auction, consider separately the cases in which the other players’ bids are such that player i wins no units, one unit, and two units when her bids are vi and wi.) Goods for which the demand exceeds the supply at the going price are sometimes sold to the people who are willing to wait longest in line. We can model such situations as multi-unit auctions in which each person’s bid is the amount of time she is willing to wait.