We are talking about a sealed-bid second-price auction with two bidders. Values are independently and uniformly distributed on [0,1].
Bidder 1 is certain of her value; bidder 2 is completely uncertain of his value.
Find the expected surplus of each bidder if:
(a) Bidder 1 bids truthfully and bidder 2 bids randomly (uniformly on [0,1]).
(b) Bidder 1 bids truthfully and bidder 2 always bids his expected value of 1/2.
(c) How much can bidder 1 hurt bidder 2 in part (b) without hurting herself?
(d) Compare these surpluses with the usual private-value Vickrey auction, where both bidders know their values.
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