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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.
In a first-price auction of a single item, a Nash equilibrium is always efficient, so the PoA and PoS are 1. In a second-price auction, there is a Nash equilibrium in which the agents report truthfully; it is efficient, so the PoS is 1. However, the PoA is unbounded.
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 ...
As shown by Riley and Samuelson (1981), [1] equilibrium bidding in an all pay auction with private information is revenue equivalent to bidding in a sealed high bid or open ascending price auction. In the simplest version, there is complete information.
Usually the system is modeled as a game and the efficiency is some function of the outcomes (e.g. maximum delay in a network, congestion in a transportation system, social welfare in an auction, etc.). Different concepts of equilibrium can be used to model the selfish behavior of the agents, among which the most common is the Nash equilibrium.
In a sealed-bid second-price auction, there is a SBNE with =, i.e., each bidder bids exactly his/her signal. PROOF: The proof takes the point-of-view of Xenia. We assume that she knows that Yakov bids r Y {\displaystyle rY} , but she does not know Y {\displaystyle Y} .
1.2 Equilibrium bidding in the sealed first- and second-price auctions. ... then truthful bidding is a Nash equilibrium of the ascending proxy auction and yields the ...