Three Auctions, Three Strategies: English, Dutch and Vickrey

Three formats, three rules

An auction is a mechanism for turning private information — how much each bidder actually values an item — into a public price and a winner, and the rules of the mechanism change how bidders behave. Three classic formats illustrate this cleanly, each with a different rule for the price the winner pays:

English    open, ascending price. Bidders openly outbid each other;
           the last one standing wins, pays their own final bid.

Dutch      open, descending price. Price starts high and falls in
           public until someone accepts it; winner pays that price.

Vickrey    sealed, second-price. Every bidder submits one hidden
           bid; the highest bid wins, but pays the SECOND-highest
           bid, not their own.

Why the Vickrey rule fixes strategy

The sealed second-price rule, formalised by economist William Vickrey in 1961 (work that earned him the 1996 Nobel Memorial Prize in Economic Sciences), produces a remarkably clean result: bidding your true value is a dominant strategy — the best move no matter what anyone else does. Your bid only ever decides whether you win, because the price you pay if you do win is set entirely by someone else's bid. Bid above your true value and you risk winning at a price that exceeds what the item is worth to you; bid below it and you risk losing a purchase that would have been profitable. Bidding exactly your value eliminates both risks simultaneously — no strategic calculation about other bidders is required.

Why English auctions behave almost the same

An open ascending English auction, under simple assumptions, has the same rational stopping point: keep bidding as long as the current price is below your true value, and drop out the instant it exceeds it. The auction naturally stops right where the price reaches the second-highest bidder's own valuation — the winner pays essentially the second-highest value, structurally the same outcome a Vickrey auction reaches directly through its pricing rule, even though the process looks completely different from the bidders' side.

Why first-price formats invite bid-shading

Dutch auctions and ordinary sealed first-price auctions share a rule that changes everything: the winner pays exactly what they bid. Bidding your true value here guarantees zero profit even in the best case, so every rational bidder deliberately shades their bid below their true valuation, trading some probability of winning for a larger margin if they do. How much to shade depends on beliefs about competitors' valuations and how many bidders are competing — more competitors generally means less room to shade, since someone else is more likely to outbid a low offer.

Revenue equivalence, and where it breaks

A landmark result in auction theory, the revenue equivalence theorem, shows that under a specific set of idealised conditions — independent private values (each bidder's valuation is their own private draw, unaffected by others), risk-neutral bidders, and symmetric information — the expected revenue to the seller is identical across all of these formats, including first-price sealed-bid auctions once optimal bid-shading is accounted for. In practice those assumptions rarely hold exactly: bidders may be risk-averse (which tends to raise first-price revenue as bidders shade less to reduce the risk of losing), valuations may be correlated (relevant when bidders share uncertainty about a common, unknown value, as in oil-lease auctions), or bidders may differ systematically in resources — any of which can push real auction revenue away from the idealised equivalence.

Where these formats show up today

Auction theory is not just an academic exercise — governments use ascending and sealed-bid variants to sell radio spectrum licenses worth tens of billions of dollars, art houses run classic English auctions, Dutch flower markets in the Netherlands still use literal descending-price clocks, and online advertising platforms run generalized second-price auctions, a multi-item cousin of Vickrey's rule, billions of times a day to decide which ad appears and what the advertiser pays.

Frequently asked questions

Try it live

Everything above runs in your browser — open Auction Simulator and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.