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The generalized second-price auction (GSP) is a non-truthful auction mechanism for multiple items. Each bidder places a bid. The highest bidder gets the first slot, the second-highest, the second slot and so on, but the highest bidder pays the price bid by the second-highest bidder, the second-highest pays the price bid by the third-highest, and so on.
Next, the total social value of the original auction excluding A's value is computed as $7 − $5 = $2. Finally, subtract the second value from the first value. Thus, the payment required of A is $6 − $2 = $4. For bidder B: Similar to the above, the best outcome for an auction that excludes bidder B assigns both apples to bidder C for $6.
A classic example is the pair of auction mechanisms: first price auction and second price auction. First-price auction has a variant which is Bayesian-Nash incentive compatible; second-price auction is dominant-strategy-incentive-compatible, which is even stronger than Bayesian-Nash incentive compatible. The two mechanisms fulfill the ...
Second-price sealed-bid auctions (Vickrey auctions) which are the same as first-price sealed-bid auctions except that the winner pays a price equal to the second-highest bid. The logic of this auction type is that the dominant strategy for all bidders is to bid their true valuation. [10] William Vickrey was the first scholar to study second ...
The uniform-price auction does not, however, result in bidders bidding their true valuations as they do in a second-price auction unless each bidder has demand for only a single unit. A generalization of the Vickrey auction that maintains the incentive to bid truthfully is known as the Vickrey–Clarke–Groves (VCG) mechanism.
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Example 1. [1] There are two items for sale and two potential buyers: Alice and Bob, with the following valuations: Alice values each item as 5, and both items as 10 (i.e., her valuation is additive). Bob values each item as 4, and both items as 4 (i.e., his valuation is unit demand). In a SASP, each item is put to a second-price-auction.