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Prerequisites: Chapters 1 and 8.
You are probably familiar with English auctions, where players bid for an item. The one with the highest bid gets the item, and pays his or her bid for it. There are many versions dealing with the details, for example whether bidding increments are required, or whether the players must bid in a special order (usually they do not have to).
An English auction is easy to analyze. A player bids as long as the bid is below the worth of the item to him or her, but does not go above that.
In an attempt to make more money for the item, the auctioneer may impose the following rules:
SHUBIK AUCTION(A, B, n) Two players, Ann and Beth, bid sequentially for an item. The bids must increase in increments of 10 units. Ann starts by bidding 10 units or passing (in which case Beth can get the item for 10 units, or can instead pass as well). If Ann bids 10 units, Beth can bid 20 units or pass, and so on. After one player passes, the other player gets the item for her highest bid, but in contrast to ordinary auctions, the other player still has to pay her highest bid to the auctioneer, but gets nothing in return. There is a maximum number n of rounds. The item has a worth of A units for Ann and of B units for Beth.
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