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Online auctions often use an equivalent version of Vickrey's second-price auction wherein bidders provide proxy bids for items. A proxy bid is an amount an individual values some item at. The online auction house will bid up the price of the item until the proxy bid for the winner is at the top.
In an English auction, all current bids are visible to all bidders and in a sealed-bid auction, bidders only get to know if their bid was the best. Best/not best auctions are sealed-bid auctions with multiple bids, where the bidders submit their prices like in English auction and get responses about the leadership of their bid. [74]
There are two bidders participating in a first-price sealed-bid auction for an object that has either high quality (value V) or low quality (value 0) to both of them. Each bidder receives a signal that can be either high or low, with probability 1/2. The signal is related to the true value as follows:
Note that with this bidding function, the player with the higher value still wins. We can show that this is the correct equilibrium bidding function in an additional way, by thinking about how a player should maximize his bid given that all other players are bidding using this bidding function. See the page on first-price sealed-bid auction.
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Another variation on the English auction is the open-exit auction, where the bidders must announce that they are dropping out of the bidding and they cannot re-enter. In France , when the last bid has been made in an auction for an art object, a representative of the state can say "Préemption de l'état" ("Pre-emption of the state") and buy ...
A savvy bidder will anticipate this, and reduce their bid accordingly. Bid shading is also used in first-price auctions, where the winning bidder pays the amount of his bid. If a participant bids an amount equal to their value for the good, they would gain nothing by winning the auction, since they are indifferent between the money and the good.
The official can only do one favor and will do the favor to the donor who is giving him the most expensive present. This is a typical model for all-pay auction. To calculate the optimal bid for each donor, we need to normalize the valuations {250, 500, 750} to {0.25, 0.5, 0.75} so that IPV may apply. According to the formula for optimal bid: