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Hard · Game Theory & Logic · Quant Trader interview question · game-theory, auctions, revenue-equivalence, expected-value
Two identical items are being auctioned off. In Auction A, it's a standard first-price sealed-bid auction: the highest bidder wins the item and pays their bid. In Auction B, it's an all-pay sealed-bid auction: all bidders pay their bids, regardless of whether they win the item, and the highest bidder wins the item. Assume there are $n$ risk-neutral bidders in both auctions. What can you say about the expected revenue generated by Auction B compared to Auction A?