Vickrey auction

A Vickrey auction is a silent auction in which the object being sold goes to the highest bidder but for the amount bid by the second-highest bidder. In a normal silent auction prospective buyers place their bids in sealed envelopes and the highest bid wins. This makes it risky for the seller because if the object is highly valuable and all buyers think they are the only ones who recognize this fact, they may offer much less than they think the object is actually worth. However, a Vickrey auction induces people to bid truthfully. Why? Because when all other bids are fixed and unknown to a given bidder, that bidder's optimal strategy is to bid what she thinks the object is worth. Suppose Alice places a bid for an antique vase. Let V be the amount that Alice thinks the vase is actually worth, and B the bid that she actually makes. Let M be the maximum of all other bids. If M is more than V, then Alice should set her bid B less than or equal to V, so that she does not get the vase for more than she thinks it is worth. If M is less than V, then Alice should set B = V, because if she bids any less, she will not get the vase any cheaper, and she may lose it altogether.