Strategic Equivalence of Auctions

The idea of strategic equivalence is that some auctions which superficially appear to be quite different from each other actually present bidderss with exactly the same set of alternative choices; hence the Bayesian Nash Equilibrium bidding strategies for the auctions will be the same. The first-price sealed bid and Dutch auctions are strategically equivalent: a function of item values that determines optiml bids in the first-price auction also determines the optimal prices at which to stop the Dutch auction clock. The English and second-price sealed-bid auctions are strategically equivalent when bidders item values for the auctioned item are private and independently drawn from the same probability distribution. In that case, bidders have a dominant strategy to bid their item values in the second-price auction and to drop out of the bidding in the English auction when the standing bid passes their values.