English and Dutch Auctions

The two open auction formats — the ascending-bid English auction and the descending-price Dutch auction — are usually introduced as the “live” cousins of the two sealed-bid formats, and then quietly dropped on the grounds that each is equivalent to one of them. That framing hides the note’s central point: the two equivalences are not the same kind of claim, and only one of them is safe. The Dutch auction and the first-price sealed-bid auction are strategically equivalent — they are literally the same game written twice, with the same strategy sets and the same map from strategy profiles to outcomes, so every equilibrium of one is an equilibrium of the other regardless of what bidders know or value (Vickrey 1961; Milgrom & Weber 1982, §2.1). The English auction and the second-price sealed-bid auction are only outcome equivalent, and only under private values — because the English auction lets bidders watch each other quit, and under common or affiliated values those drop-out prices are information that changes what everyone bids. One equivalence is structural. The other is contingent, and it breaks exactly where auctions get interesting.

Mental Model: a 2×2 that is not symmetric

The four standard single-object formats are usually laid out on two axes: open versus sealed, and the winner pays her own bid versus somebody else’s. The equivalences are the horizontal arrows.

flowchart LR
    subgraph OPEN["Open (dynamic) formats"]
        DUT["Dutch<br/>descending clock<br/><i>open first-price</i>"]
        ENG["English<br/>ascending clock<br/><i>open second-price</i>"]
    end
    subgraph SEALED["Sealed-bid (static) formats"]
        FPSB["First-price<br/>sealed bid<br/>pay your own bid"]
        SPSB["Second-price / Vickrey<br/>sealed bid<br/>pay the runner-up's bid"]
    end
    DUT ==>|"STRATEGIC equivalence<br/>same strategy sets, same outcome map<br/>holds unconditionally"| FPSB
    ENG -.->|"OUTCOME equivalence<br/>same winner, same price<br/><b>only under private values</b>"| SPSB
    SPSB -.->|"breaks: English reveals<br/>rivals' drop-out prices"| ENG

    style DUT fill:#1f6f43,color:#fff
    style FPSB fill:#1f6f43,color:#fff
    style ENG fill:#7a3b12,color:#fff
    style SPSB fill:#7a3b12,color:#fff

What it shows: the four standard formats and the two claimed equivalences. The insight to take away is the difference in line weight. The solid double line is an identity between games — it needs no assumption at all. The dashed lines are a coincidence of equilibrium outcomes that survives only in the independent-private-values world; the moment a bidder’s estimate of the prize depends on what other bidders know, the English auction and the Vickrey auction stop being the same auction.

Everything below is an unpacking of that asymmetry: first what each format actually does, then why one equivalence is unconditional and the other is not, then what the difference costs in measured revenue, and finally why the “English auction” that theory analyses is not the English auction that Sotheby’s or eBay runs.

The Two Open Formats, Mechanically

The English (ascending) auction

In an ascending-bid or English auction, “the price is successively raised until only one bidder remains, and that bidder wins the object at the final price” (Klemperer, Auction Theory: A Guide to the Literature, §1.2). That one-sentence description hides an enormous amount of institutional variation, and Milgrom and Weber are explicit that the variation matters:

“There are many variants of the English auction. In some, the bids are called by the bidders themselves… In others, the auctioneer calls the bids, and a willing bidder indicates his assent by some slight gesture… Cassady has described yet another variant, used in Japan, in which the price is posted using an electronic display… These three forms of the English auction correspond to three quite different games.” (Milgrom & Weber 1982, §5)

That last sentence is the single most under-quoted line in auction theory. “The English auction” is not one game. It is at least three, and they differ in what a bidder observes and when.

The variant that theory almost always means is the Japanese or button auction. Klemperer calls it “the model most commonly used by auction theorists”: the price rises continuously on a clock, each bidder holds down a button while she wishes to remain active, releasing the button withdraws her irrevocably, and both the clock price and the set of active bidders are continuously visible. Milgrom and Weber adopt exactly this: “We assume that both the price level and the number of active bidders are continuously displayed. We use the term ‘English auction’ to designate this variant.”

Formally, a strategy in the button auction is not a number. It is a family of functions

$b_{i, k} (x_{i} ∣ p_{1}, \dots, p_{k})$

giving the price at which bidder $i$ will release her button, as a function of her own private signal $x_{i}$ , the number $k$ of rivals who have already quit, and the prices $p_{1} \leq \dots \leq p_{k}$ at which they quit (Milgrom & Weber 1982, §5). Reading that object carefully tells you where the second equivalence will fail: a strategy in the English auction is allowed to depend on rivals’ drop-out prices. If the strategy does not need to — because values are private — the extra arguments are dead weight and the game collapses to something simpler. If it does need to, it does not.

sequenceDiagram
    autonumber
    participant C as Clock
    participant B1 as Bidder 1 (signal 0.91)
    participant B2 as Bidder 2 (signal 0.74)
    participant B3 as Bidder 3 (signal 0.38)
    Note over C,B3: All three hold the button at price 0
    C->>B3: price reaches 0.38
    B3--xC: releases button (quits at 0.38)
    Note over B1,B2: both now KNOW bidder 3's signal was 0.38
    Note over B1,B2: under common values they revise their<br/>estimates DOWN and re-plan their quit prices
    C->>B2: price reaches revised quit point
    B2--xC: releases button
    Note over C,B1: one bidder left: auction ends,<br/>bidder 1 pays the price at which bidder 2 quit

What it shows: a three-bidder Japanese button auction. The insight is step 3 — the drop-out of the lowest bidder is a public, credible, quantitative signal. Under private values it is irrelevant to bidders 1 and 2. Under common or affiliated values it is the whole game, and it is information the sealed-bid second-price auction cannot transmit.

Milgrom and Weber describe the equilibrium of this game as proceeding “in two phases. In phase 1, the $n - 2$ bidders with the lowest estimates reveal their signals publicly through their bidding behavior. Then, the last two bidders engage in a second-price auction.” That is a precise and useful picture: an English auction is a public information-revelation phase followed by a two-person second-price auction.

The Dutch (descending) auction

The Dutch or descending-price auction runs the clock the other way. “The auctioneer starts at a very high price, and then lowers the price continuously. The first bidder who calls out that she will accept the current price wins the object at that price” (Klemperer §1.2). Klemperer’s footnote 13 describes the real thing, which is a piece of industrial equipment rather than a metaphor:

“In Dutch flower auctions, the potential buyers all sit in a room at desks with buzzers connected to an electronic clock at the front of the room. The interior of the clock has information about what is being sold and the price at which the auction starts. Once the auction begins, a series of lights around the edge of the clock indicate to what percentage of the original asking price the good has fallen. As soon as one bidder buzzes in, she gets the flowers at the price indicated on the clock.”

Vickrey, writing in 1961, already noted that “a mechanized form of this procedure is actually used in wholesale flower marketing in the Netherlands and has proved very economical of time and effort” (Vickrey 1961, p. 14). Speed is the operational reason the format exists: a descending clock terminates on the first action by any bidder, so the wall-clock time of an auction is bounded by how fast the clock can fall, independent of the number of bidders. An ascending auction, by contrast, cannot end until all but one bidder has acted.

Here is the crucial structural observation, and it is Vickrey’s:

“Each bidder, in attempting to determine at what point he should be prepared to make a bid so as to obtain the greatest expectation of gain, will need to take into account whatever information he has concerning the probable bids that might be made by others… To put in a bid as soon as the price has come down to the full value of the object to the bidder maximizes the probability of obtaining the object, but guarantees that the gain from securing it will be zero; as the announced price is progressively lowered, the possibility of a gain emerges, but as the gain thus sought increases with the lowering of the point at which a bid is to be made, the probability of securing this gain diminishes.” (Vickrey 1961, pp. 14–15)

Nothing in that paragraph mentions time. The Dutch auction looks dynamic, but a bidder’s entire decision problem is a single number chosen before the clock starts moving.

Equivalence One: Dutch ≡ First-Price, Unconditionally

Two games are strategically equivalent when they have the same strategy sets and the same map from strategy profiles to outcomes. Not “the same equilibria under some assumption” — the same game, up to relabelling. This is a far stronger relation than any statement about equilibrium behaviour, and it is what holds between the Dutch auction and the first-price sealed-bid auction.

Milgrom and Weber’s derivation is three sentences long:

“An insight due to Vickrey is that the decision faced by a bidder with a particular valuation is essentially static, i.e. the bidder must choose the price level at which he will claim the object if it has not yet been claimed. The winning bidder will be the one who chooses the highest level, and the price he pays will be equal to that amount. This, of course, is also the way the winner and price are determined in the sealed-bid first-price auction. Thus, the sets of strategies and the mapping from strategies to outcomes are the same for both auction forms. Consequently, the equilibria of the two auction games must coincide.” (Milgrom & Weber 1982, §2.1)

Why is the Dutch bidder’s problem static, when the clock is visibly moving? Because no information arrives while the clock falls. The only event that can occur is another bidder claiming the object, and that event ends the auction. Conditional on the auction still being live at price $p$ , a bidder has learned exactly one thing: nobody has claimed yet. And “nobody has claimed yet” is already implied by the fact that she is still choosing. There is no observation she can condition on that she did not have at time zero. So her strategy set is ${$ a single price at which to buzz $}$ — precisely the strategy set of a sealed first-price bid.

The mapping is equally direct. Highest chosen price wins; winner pays her own chosen price; losers pay nothing. That is the first-price rule, written in a different notation.

Klemperer states the scope of the claim bluntly: “the equivalence of descending and first-price sealed-bid auctions is completely general in single-unit auctions” (Klemperer §1.5). And Milgrom and Weber’s footnote 11 makes explicit exactly how few assumptions it needs:

“The argument concerning the strategic equivalence of the Dutch and first-price auctions does not require any assumptions about the values to the bidders of various outcomes. In particular, it does not require that a bidder know the value of the object to himself.”

That is the whole asymmetry in one footnote. Common values, affiliated signals, risk aversion, asymmetric bidders, budget constraints, bidders who are confused about their own preferences — none of it touches this equivalence, because the equivalence is a fact about the rules, not about the players. Whatever the first-price equilibrium is in a given environment, the Dutch equilibrium is the same one.

What strategic equivalence does not say

It does not say the two formats will produce the same observed behaviour in a laboratory or a marketplace. Strategic equivalence is a statement about the game, and the game is only a model of the institution. Real Dutch and first-price auctions differ in the clock’s descent rate, in whether waiting is psychologically costly, and in how much time bidders have to think. Lucking-Reiley’s 1999 field experiment auctioned collectible trading cards over the Internet in all four formats and reported that the Dutch auction produced roughly 30% higher revenue than the first-price sealed-bid auction — a violation of a theoretical prediction that no assumption about values can rescue, and (as the abstract notes) a reversal of earlier laboratory results, which had found Dutch revenue below first-price. Two field/lab literatures disagreeing in sign about a prediction that theory says is unconditional is a strong hint that the clock’s descent rate is doing work the model does not represent. See the uncertainty callout below.

Uncertain

Verify: the “≈30% higher Dutch revenue” figure and the claimed reversal of prior lab results. Reason: aeaweb.org serves an abstract landing page rather than full text to curl, and I could not locate a readable author mirror of Lucking-Reiley (1999) from this machine (the u.arizona.edu faculty path returns HTTP 404). The figure here comes from the AEA abstract text only; I did not read the paper. To resolve: obtain the AER PDF (JEL 89(5), pp. 1063–1080) and check the revenue tables and the discussion of the earlier laboratory literature (Coppinger–Smith–Titus, Cox–Roberson–Smith). uncertain

Equivalence Two: English ≡ Second-Price, Only Under Private Values

Milgrom and Weber introduce this one with a warning attached:

“The second conclusion is that — in the context of the private values model — the second-price sealed-bid auction and the English auction are equivalent, although in a weaker sense than the ‘strategic equivalence’ of the Dutch and first-price auctions.”

The weaker sense is outcome equivalence, and it is derived rather than structural. The derivation has two halves, and each half is a dominance argument that quietly assumes the bidder already knows her own value:

In the English auction, “if a bidder knows the value of the object to himself, he has a straightforward dominant strategy, which is to bid actively until the price reaches the value of the object to him.”
In the second-price auction, “if a bidder knows the value of the object to himself, then his dominant strategy is to submit a sealed bid equal to that value.”

Both games therefore have a unique dominant-strategy equilibrium; in both, the highest-value bidder wins and pays the second-highest value. Same winner, same price, same expected revenue — hence “equivalent.” But Milgrom and Weber immediately add the disclaimer:

“Note that this argument requires that each bidder know the value of the object to himself. If what is being sold is the right to extract minerals from a property, where the amount of recoverable minerals is unknown, or if it is a work of art, which will be enjoyed by the buyer and then eventually resold for some currently undetermined price, this equivalence result generally does not apply.”

Klemperer draws the same boundary and adds a second, sharper condition:

“However, this equivalence applies only for private values, or if there are just two bidders. With any common components to valuations and more than two bidders, players learn about their values from when other players quit an ascending auction and condition their behaviour on this information.” (Klemperer §1.4)

The two-bidder exception is worth pausing on because it makes the mechanism unmistakable. Milgrom and Weber: “In the English auction with only two bidders, each bidder’s strategy can be completely described by a single number which specifies how high to compete before ceding the contest to the other bidder… Thus, with only two bidders, the English and second-price auctions are strategically equivalent.” With $n = 2$ , nobody ever drops out before the auction ends, so there is no drop-out to observe, so the extra arguments in $b_{i, k} (\cdot ∣ p_{1}, \dots, p_{k})$ never bind. The English auction has an informational channel; with two bidders that channel carries nothing. Add a third bidder and it starts carrying signal.

Why the channel changes the answer

Under affiliated values — roughly, a high signal for one bidder makes high signals for others more likely; formally $f (s \land s^{'}) f (s \lor s^{'}) \geq f (s) f (s^{'})$ , the multivariate analogue of positive correlation with the monotone likelihood ratio property (Levin, Auction Theory, §2.1) — a bidder’s equilibrium quit price is her expected value conditional on being just barely the winner. Extra public information about rivals’ signals shifts that conditional expectation, and the shift is systematically upward relative to the sealed-bid case, because a bidder who observes low drop-outs learns her pessimistic hypothetical was too pessimistic. Milgrom and Weber prove the ranking:

Theorem 11: “The expected price in the English auction is not less than that in the second-price auction.”
Theorem 15: “The expected selling price in the second-price auction is at least as large as in the first-price auction.”

Together: English ≥ second-price ≥ first-price = Dutch under affiliation. This ordering is the linkage principle, which Klemperer states as “the general principle that expected revenue is raised by linking the winner’s payment to information that is affiliated with the winner’s information” (Klemperer §6). Levin’s summary of the intuition is the crispest:

“The winning bidder’s surplus is due to her private information. The more the price paid depends on others’ information (the price depends on all other bidders’ information in an ascending auction with common-value elements, and on one other bidder’s information in a second-price sealed-bid auction), the more closely the price is related to the winner’s information… So the lower is the winner’s information rent.”

Note the corollary the algorithmic game theory text draws for computer scientists: “in such settings, ascending English auctions are ‘better’ (generate more revenue) than the non-adaptive second price auction (which is equivalent to an English auction in private value models).”

The two equivalences side by side

	Dutch ≡ First-price	English ≡ Second-price
Kind of claim	Strategic equivalence — same game	Outcome equivalence — same winner and price in equilibrium
Proof technique	Inspect the rules; no equilibrium reasoning needed	Two separate dominant-strategy arguments
Needs private values?	No	Yes
Needs the bidder to know her own value?	No (Milgrom & Weber fn. 11)	Yes (explicitly)
Needs risk neutrality?	No	No (bidding one’s value is dominant for any monotone utility)
Needs symmetry?	No	No
Survives $n > 2$ with common values?	Yes	No — English strictly beats second-price (M&W Thm 11)
Survives $n = 2$ with common values?	Yes	Yes — nothing to observe, so it is even strategically equivalent
Survives jump bidding?	N/A (no bid sequence exists)	Not as a game; sometimes as an outcome (see below)

Measured: simulating the clocks rather than the order statistics

The temptation when simulating auctions is to skip the mechanism — to “run an English auction” by computing the second-highest value, and “run a Dutch auction” by evaluating the closed-form first-price bid function. That assumes the very equivalences under test. The C program behind this note instead runs both clocks step by step, so that the equivalences are observed rather than asserted. (See Simulating Auctions in C for the harness conventions; the code below is the format layer.)

/* Ascending "Japanese button" clock. Price rises by `tick`; a bidder holds the
 * button while price < value.  The auction stops when one bidder remains, and
 * the price paid is the clock price at which the second-to-last bidder quit. */
static double english_clock(const double *v, int n, double tick){
    int alive = n; double p = 0.0, last_quit = 0.0;
    char out[MAXN]; memset(out, 0, sizeof out);
    while (alive > 1) {
        p += tick;                              /* clock ticks up */
        for (int i = 0; i < n; i++)
            if (!out[i] && v[i] < p) {          /* i releases the button */
                out[i] = 1; alive--; last_quit = p;
                if (alive == 1) break;          /* winner determined */
            }
        if (p > 1.0 + tick) break;              /* safety: values live in [0,1] */
    }
    return last_quit;                           /* == the price the winner pays */
}
 
/* Descending Dutch clock. Price falls by `tick`; bidder i claims the object at
 * her planned stopping price b(v_i) = ((n-1)/n) v_i.  The FIRST claim ends it. */
static double dutch_clock(const double *v, int n, double tick){
    double coef = (double)(n-1)/(double)n;      /* symmetric IPV uniform equilibrium */
    for (double p = 1.0; p > 0.0; p -= tick)
        for (int i = 0; i < n; i++)
            if (coef*v[i] >= p) return p;       /* first buzzer wins at clock price */
    return 0.0;
}

Line by line, the two loops differ in exactly the way the theory says they should. english_clock carries state that accumulates across ticks (out[], alive, last_quit) — bidders are reacting to each other. dutch_clock carries none: the inner test coef*v[i] >= p consults only bidder i’s own pre-computed number. That structural difference is the difference between the two equivalences.

Running 200,000 trials × 10 independent seeds with $n = 5$ bidders and values drawn i.i.d. uniform on $[0, 1]$ , and a clock tick of $1 0^{- 4}$ :

format	mean revenue	sd across seeds	95% CI of the mean	bias vs exact 2/3	sd per trial
English (clock)	0.666600	0.000480	[0.666302, 0.666898]	−0.000066	0.178148
Dutch (clock)	0.666479	0.000243	[0.666329, 0.666630]	−0.000187	0.112755
First-price sealed	0.666529	0.000243	[0.666379, 0.666680]	−0.000137	0.112755
Second-price sealed	0.666550	0.000480	[0.666253, 0.666848]	−0.000116	0.178148
All-pay	0.666230	0.001138	[0.665525, 0.666935]	−0.000437	0.449547

The exact value is $(n - 1) / (n + 1) = 2/3$ ; every confidence interval covers it. But the equivalence result is much stronger than “the means agree.” The harness also checks the outcome of every individual trial:

per-trial outcome identity  Dutch == FirstPrice  : 2000000 / 2000000  (100.0000%)
per-trial outcome identity  English == SecondPrice: 2000000 / 2000000  (100.0000%)

Both hold trial-by-trial, not merely in expectation — which is what “same game” and “same equilibrium outcome” respectively predict under IPV. (The English/second-price identity here is up to one clock tick; the Dutch/first-price identity is exact modulo the clock’s discretisation.)

The per-trial standard deviations in the last column are where the formats stop being interchangeable, and this is the part revenue equivalence never claimed. The English and second-price prices have sd 0.1781; the Dutch and first-price prices have sd 0.1128. The variance ratio is $0.178 1^{2} /0.112 8^{2} = 2.496$ . Vickrey computed that ratio in his Appendix I:

“The variance of the price is greater under the common or progressive type of auction than with the Dutch auction by a factor of $2 N / (N - 1)$ .” (Vickrey 1961, p. 17)

For $N = 5$ that is $10/4 = 2.5$ . The simulation returns 2.496. Vickrey drew the practical conclusion himself: “If we introduce an element of risk aversion for purposes of evaluating these results (but not for deriving the results!), the Dutch auction thus proves slightly superior by reason of the smaller dispersion of the gains to each of the parties.” A risk-averse seller prefers the closed format even when the means are identical.

Measuring the break: the linkage principle has a size

The theory says English beats second-price under affiliation. It does not say by how much, and the honest answer is “usually not very much.” Quint (2016) constructs the cleanest quantified example: a binary state $θ \in {0, 1}$ , equally likely, with common value $v_{i} = θ$ ; each bidder draws a signal $s_{i}$ with density $α s^{α - 1}$ if $θ = 1$ and $α (1 - s)^{α - 1}$ if $θ = 0$ . Larger $α$ makes signals more informative and more correlated. He then compares a full-information button auction (Milgrom–Weber’s English auction — drop-outs observed) with a no-information button auction (their second-price auction — no feedback until the end).

The two equilibrium bid functions are closed-form Bayes updates, and both fit in a few lines of C:

/* no-information (sealed second-price): b(s) = Pr(theta=1 | s(1)=s(2)=s) */
static double q_bid_noinfo(double s, double a, int N){
    double r    = pow(1.0-s, a-1.0)/pow(s, a-1.0);              /* likelihood ratio */
    double tail = pow((1.0-pow(1.0-s,a))/pow(s,a), (double)(N-2));
    return 1.0/(1.0 + r*r*tail);
}
/* full-information (English button): the N-2 observed drop-outs enter the update */
static double q_bid_fullinfo(double s, const double *t, int k, double a){
    double r = pow(1.0-s, a-1.0)/pow(s, a-1.0), prod = 1.0;
    for (int i = 0; i < k; i++)
        prod *= pow(1.0-t[i], a-1.0)/pow(t[i], a-1.0);          /* each quit price */
    return 1.0/(1.0 + r*r*prod);
}

The only difference between the two functions is the for loop: the English bidder multiplies in one likelihood-ratio factor per observed drop-out. That loop is the linkage principle.

Simulating 300,000 trials × 8 seeds and reporting revenue ×1000 (the object is worth exactly 0.5 in expectation, so 500 would mean the seller extracts everything):

$N$	$α$	no-info (second-price)	full-info (English)	linkage lift	Quint’s published value
3	1.5	388.8	393.8	+1.29%	389 → 394, 1.3%
3	2.0	388.1	400.9	+3.32%	388 → 401, 3.3%
3	2.5	415.9	432.0	+3.85%	416 → 432, 3.8%
3	3.0	443.6	458.6	+3.39%	443 → 458, 3.4%
5	2.0	427.8	453.8	+6.07%	428 → 454, 6.1%
7	2.0	445.5	475.9	+6.82%	446 → 476, 6.8%

The right-hand column is Quint’s Tables 1 and 2, reproduced here from an independent C implementation. Agreement is to three significant figures across every cell tested. Across-seed standard deviations are 0.3–0.8 in these units, so the differences are many standard errors wide.

Two lessons. First, the break is real and reproducible: the English auction does raise more than the sealed second-price auction under affiliation, exactly as Theorem 11 says. Second, the break is small — the largest lift found anywhere in Quint’s grid is 6.8%, and it vanishes at both extremes ( $α \to 1$ makes signals uninformative so there are no information rents to compete away; $α \to \infty$ makes signals so correlated that there are none either). Quint is candid that his own example may exaggerate the effect: “this example has one feature that may exaggerate the magnitude of this effect. Here, $θ$ takes only two values, with signal distributions differing dramatically… Another example I tried… generates a revenue difference of only 0.4% when $N = 3$ .”

So the correct statement is not “the English auction raises more money.” It is: the English auction raises weakly more money under affiliation, by an amount that is single-digit percent at best and can be a rounding error. Any real-world revenue difference between ascending and sealed formats larger than that is being driven by something other than the linkage principle — entry, collusion, asymmetry, or risk — and this note’s siblings Revenue Equivalence and The Winner’s Curse take those up.

xychart-beta
    title "Linkage-principle lift (English over sealed second-price), Quint model"
    x-axis "signal informativeness alpha" ["1.5", "2.0", "2.5", "3.0"]
    y-axis "revenue lift %" 0 --> 8
    bar [1.29, 3.32, 3.85, 3.39]
    line [3.09, 6.07, 5.24, 3.38]

What it shows: the measured revenue advantage of observing rivals’ drop-outs, as a function of how informative signals are. Bars are $N = 3$ ; the line is $N = 5$ . The insight is the hump — the benefit is zero when signals carry no information and zero again when they are so informative that everyone already agrees, and it peaks in the middle at a few percent. There is no regime in this model where the choice of ascending versus sealed second-price is worth more than about 7% of revenue.

Jump Bidding: the English auction stops being a clock

The button model assumes bidders can only quit; they cannot raise the price. Real ascending auctions let bidders jump — raise the standing price by far more than the minimum increment. Klemperer notes that “actual behaviour in, for example, takeover battles, often involves jump bidding in which a bidder raises the price very substantially with a single bid,” and gives the equilibrium that explains why (Klemperer §13.3):

“Consider a standard independent private-value English auction with two symmetric players. The following behaviour is an equilibrium: one player bids the price she would bid in a first-price sealed-bid auction; the second player then infers the first player’s actual value and bids that actual value if her own value is higher, but quits the auction otherwise. So the player with the actual higher value wins, but the first player pays the first-price auction price when she wins, while the second player pays the second-highest valuation when she wins.”

Three things are worth extracting. (1) Under IPV this jumping equilibrium is still revenue-equivalent to the smooth clock, because the higher-value bidder still always wins and the lowest type still gets zero — the two conditions of the revenue equivalence theorem (see Revenue Equivalence). Jump bidding does not, by itself, break anything. (2) It is nonetheless not the natural equilibrium under IPV, because “the first bidder may fear that the second may misunderstand the equilibrium and bid up the price when she will anyway lose.” (3) With affiliation it becomes attractive: since Milgrom and Weber show bidders prefer first-price to ascending under affiliation (the mirror image of the seller’s preference), grafting first-price features onto an ascending auction is a Pareto improvement for the bidders, and “Avery (1998) demonstrates that we may therefore expect a jumping equilibrium to be played.” Avery’s own framing, per the published abstract, is that “jump bids serve as correlating devices which select asymmetric bidding functions to be played subsequently, and each possibility of jump bidding provides a Pareto improvement for the bidders from the symmetric equilibrium of a sealed bid, second-price auction.”

Klemperer adds a second, entirely different route to the same behaviour: “If there are costs to making each bid, then jump bidding arises for similar reasons, even with independent private values, see Daniel and Hirshleifer (1995).”

Uncertain

Verify: Avery (1998)‘s formal model and the precise sense in which jump bids “select” an asymmetric continuation equilibrium. Reason: the paper is behind an Oxford Academic paywall (academic.oup.com returns an abstract page only), and no author mirror was reachable from this machine. Everything above is from Klemperer’s §13.3 summary — which I did read in full — plus the publisher’s abstract. Daniel & Hirshleifer (1995) was not consulted at all. To resolve: read Review of Economic Studies 65(2), pp. 185–210. uncertain

Why Real English Auctions Are Not the Clock Model

The button auction is a model. Every deployed ascending auction differs from it in ways that change the game, and several of the differences are large enough to swamp the linkage principle’s few percent.

flowchart TB
    M["Button/clock model<br/>continuous price · all drop-outs visible<br/>· no re-entry · no jumps · known n"]
    M --> D1["Discrete bid increments<br/>winner overpays by up to one increment;<br/>increments are the auctioneer's lever"]
    M --> D2["Proxy bidding (eBay)<br/>you submit a maximum;<br/>the site bids for you — a second-price<br/>auction wearing an ascending UI"]
    M --> D3["Hard close vs. soft close<br/>a fixed deadline creates sniping;<br/>auto-extension does not"]
    M --> D4["Jump bidding<br/>bidders can raise the price,<br/>not only quit"]
    M --> D5["Auctioneer discretion<br/>who is recognised, what increment,<br/>when the hammer falls"]
    M --> D6["Shill bids and reserves<br/>seller-side bids fake a rival;<br/>secret reserves hide the real floor"]
    M --> D7["Unknown / endogenous n<br/>bidders arrive and leave;<br/>anonymous assent hides the count"]
    style M fill:#1f3a6f,color:#fff

What it shows: seven ways the deployed institution departs from the model. The insight: each arrow is a place where a theorem proved about the clock stops applying, and most of them are not exotic — they are the default in every commercially important ascending auction.

Discrete increments. The clock is continuous in theory and quantised in practice. The winner pays the runner-up’s bid plus one increment, so the increment is a revenue instrument the auctioneer controls, and the “efficient allocation at the second-highest value” result becomes approximate. Cramton notes the flip side, which is behavioural: “if one takes the highest bid of the others as the market price, then it is impossible to overbid by more than one bid increment” — a comfort that, as he says, is “flawed, but it may be one reason bidders routinely fall into the trap of the winner’s curse” (Cramton 1998).

Proxy bidding. eBay’s “automatic bidding” asks for a maximum and then bids on your behalf, one increment above the current high bid, up to that maximum. Roth and Ockenfels describe the resulting institution as “a second price auction with a fixed deadline” (Roth & Ockenfels 2002). So the world’s largest ascending auction is, mechanically, a sealed second-price auction with an ascending display — except that it runs for days, and bids arrive over time.

Hard close and sniping. That “over time” is where the model breaks hardest. eBay auctions end at a scheduled time regardless of activity (a hard close); Amazon’s auctions, when Amazon ran them, extended automatically until ten minutes passed with no bid (a soft close). Under the clock model this is an irrelevant implementation detail. It is not:

measure	eBay Computers	eBay Antiques	Amazon Computers	Amazon Antiques
auctions with a last bid in the final 5 minutes	40%	59%	≈3%	≈3%
bidders whose last bid came in the final 5 minutes	9%	16%	≈1%	≈1%
share of all last bids in the final hour	20% (both categories)		7% (both categories)
bids in the final minute, across 240 auctions per site	89		1
bids in the final 10 seconds, across 240 auctions per site	29		0

Source: Roth & Ockenfels, AER 92(4), 2002, 480 auctions and 2,279 bidders sampled October 1999 – January 2000. What it shows: identical proxy-bidding rules, one rule difference at the deadline, and roughly a twentyfold difference in last-minute bidding.

Two further details from that paper close the loop on strategic interpretation. First, more experienced eBay bidders snipe more, and more experienced Amazon bidders snipe less — “the impact of the feedback number on late bidding is highly significantly positive in eBay and (weakly significantly) negative in Amazon,” from which the authors conclude that “last-minute bidding is not simply due to naïve time-dependent bidding. Rather, it responds to the strategic structure of the auction rules in a predictable way.” Second, sniping is more prevalent in Antiques (59%) than Computers (40%) on eBay but not on Amazon — consistent with experts concealing information they would otherwise leak by bidding early. And the follow-up laboratory experiment removed the confound entirely: “In controlled experiments, we find that the difference in the ending rules is sufficient by itself to produce the differences in late bidding observed in the field data” (Ariely, Ockenfels & Roth, RAND 36(4), 2005).

Sniping is the direct negation of the button model. In the button auction, information revelation is the point. A sniper’s entire strategy is to prevent revelation — to bid so late that no rival can respond and no expert’s valuation leaks. Roth and Ockenfels note it is not costless: esnipe.com’s own statistics showed that “on average 4.5 percent of esnipe’s late bids failed to be successfully transmitted in September 2000,” and eBay bidders attempting last-second bids are sometimes rejected as under the current minimum. The equilibrium is a genuine trade-off between the gain from concealment and the risk of not transmitting.

Shill bidding, rings, and the auctioneer. Cramton’s discussion of why the Vickrey auction is rare applies with modifications to any ascending format: “After receiving the bids the seller can submit a fake bid for just under the amount of the highest bid.” In an open ascending auction the seller’s equivalent is a shill who bids up the price and drops out before winning — which is indistinguishable from a genuine rival on the clock. Conversely, ascending auctions are structurally friendlier to bidder collusion, because “in an ascending auction, deviations from collusive agreements can be punished during the auction. In a sealed-bid auction, deviations cannot be punished in the auction” (Cramton, citing Milgrom 1987). The button model has neither shills nor rings.

Unknown and endogenous $n$ . The button model displays the number of active bidders. The “auctioneer calls the bids and a willing bidder indicates assent by some slight gesture, usually in a way that preserves his anonymity” variant does not — Milgrom and Weber list it as one of the three distinct games, and it is the variant most antiques and art auctions actually run. When $n$ is unobserved, the drop-out channel that generates the linkage principle is partly closed.

Failure Modes and Gotchas

Citing “English ≡ second-price” without the private-values qualifier. This is the single most common error, and it is not conservative — it points the wrong way. Under affiliated values the English auction raises strictly more, so a designer who “simplifies” an ascending auction into a sealed Vickrey auction on equivalence grounds is choosing the lower-revenue format. Milgrom and Weber’s Theorem 11 is the citation; the effect size is a few percent (measured above).

Assuming the equivalence direction is symmetric. Dutch ≡ first-price is unconditional; English ≡ second-price is not. It is easy to write “and by the same argument” and be wrong. The Dutch argument is about the rules; the English argument is about equilibrium play under an assumption about values.

Simulating the “English auction” as an order statistic. Computing the second-highest value is correct only in the private-values world where the equivalence holds. It cannot exhibit the linkage principle, because there is no drop-out sequence to observe. The affiliated-values simulation above required actually conditioning on the observed order statistics sig[2..N-1] — the for loop in q_bid_fullinfo — and without it the measured lift is identically zero. If your English-auction simulator never looks at a losing bidder’s quit price, it is a second-price simulator.

Treating the Dutch clock’s speed as irrelevant. Strategic equivalence says the game is the same. It does not say a human plays it the same way at 1 lot/second (Aalsmeer) as with a week to think. Katok and Roth’s experimental work on multi-unit “Dutch” formats and Lucking-Reiley’s field experiment both report Dutch/first-price revenue differences that the theory forbids; the descent rate is the leading suspect. Do not use strategic equivalence to justify swapping the formats in a live market.

Assuming an English auction ends when the second-highest bidder’s value is reached. It ends at the second-highest bidder’s quit price, which equals her value only under private values. Under common values it is her value conditional on being tied for highest — strictly lower, by the winner’s-curse correction (see The Winner’s Curse).

Confusing “Dutch auction” the format with “Dutch auction” the finance term. Klemperer flags this in a footnote: “Confusingly, the second-price sealed-bid auction is sometimes called a Dutch auction by investment bankers.” A uniform-price multi-unit share repurchase or IPO is also routinely called a Dutch auction and is a descending-clock auction in neither mechanism nor spirit. Check which object is meant before citing any result.

Off-by-one-increment in a discrete clock. In the C harness above, the English clock returns last_quit, the price at which the second-to-last bidder released. With tick $h$ , this over-states the true second-highest value by up to $h$ ; the measured bias of $- 6.6 \times 1 0^{- 5}$ at $h = 1 0^{- 4}$ is consistent with that and with Monte Carlo noise. If you shrink the tick to fight this, cost grows as $O (1/ h)$ per trial — 200,000 trials at $h = 1 0^{- 4}$ already costs ~35 s. Use the order statistic when you are testing revenue and the clock when you are testing the mechanism.

Reading revenue equivalence as distribution equivalence. The measured per-trial standard deviations differ by a factor of 1.58 between the ascending and descending formats (2.5× in variance) and by a factor of 4 between all-pay and first-price. Anything a seller or bidder cares about beyond the mean — risk, financing, bankruptcy of the winner — distinguishes formats that revenue equivalence declares identical.

Alternatives and When to Choose Them

Cramton’s 1998 survey is the practitioner’s answer to “ascending or sealed?”, and it begins by conceding the theory is unhelpful: “With neither theory nor experiments providing definitive results, it is easy to conclude that which auction format is best is an empirical matter.” His organising principle is that the ascending format’s defining feature — information flow during bidding — “is a two-edged sword.”

Choose an ascending (English/clock) auction when	Choose a sealed (first-price/Dutch) auction when
Values are affiliated or common: price discovery reduces the winner’s curse and bidders bid more aggressively (Milgrom–Weber; the linkage principle)	Bidders are ex ante asymmetric: a known-strongest bidder can win an ascending auction near zero, whereas a sealed bid forces her to insure against the weak bidder (Maskin–Riley; see Revenue Equivalence)
Efficiency matters and the setting is messy: “In the single-good case, ascending auctions are efficient under general conditions. Efficiency does not rely on symmetry, private values, or other unrealistic assumptions”	Bidders are risk averse: sealed first-price extracts more because bidders trade a lower prize for a higher win probability
Bidder privacy matters less than legitimacy: losers “are given every opportunity to top the winning bid,” and the loss is visibly their own choice	Collusion is the dominant risk: “in an ascending auction, deviations from collusive agreements can be punished during the auction. In a sealed-bid auction, deviations cannot be punished in the auction”
Corruption via bid-leaking is a concern: open bidding “precludes the most frequent form of corruption in first-price sealed-bid auctions: leaking the high bid to a bidder who can then top it”	You need to bind an agent to a budget: in an ascending auction “the bidding team can return to the Board with hard and fast ‘evidence’ supporting their optimistic estimates” and get the budget raised
Bidders’ strategy must be simple enough to be trusted: experiments show ascending auctions beat sealed Vickrey auctions “because the incentive for playing the efficient dominant strategy is clearer to bidders”	Bid evaluation is multi-dimensional (procurement with quality dimensions), or the seller cannot credibly commit to refuse later higher bids
Multiple interdependent items are for sale: the simultaneous ascending auction lets bidders “shift to better values as relative prices change”	Speed and throughput dominate: a descending clock ends on the first action, which is why flower markets clear thousands of lots per morning

Two entries deserve emphasis because they cut against the textbook. First, Cramton’s citation of Kagel, Harstad and Levin (1987) is the empirical wedge in “English ≡ second-price”: even in a pure private-values laboratory setting, where the equivalence theorem is valid, behaviour differs — “experiments demonstrate that ascending auctions perform better than Vickrey auctions, because the incentive for playing the efficient dominant strategy is clearer to bidders. A bidder with a value of $10 c an see pl ain l y inana sce n d in g a u c t i o n t ha t d r o pp in g o u t b e l o w$ 10 is a bad idea, as is bidding beyond $10." T h e t h eor e mi s ab o u t e q u i l ib r i u m; t h ee q u i v a l e n ceo f t h e * in s t i t u t i o n s * a dd i t i o na l l y r e q u i r es t ha t h u man s f in d t h ee q u i l ib r i u m, an d in t h ese a l e d V i c k r ey a u c t i o nman y d o n o t . S eco n d, t h e a sce n d in g f or ma t^{'} s t e n d e n cy t o * r e l a x * b u d g e t co n s t r ain t s mi d - a u c t i o ni s a r e a l, d oc u m e n t e d r e v e n u ec hann e l : in t h e F C C C - b l oc k a u c t i o n, N e x t W a v e " r ai se d esse n t ia l f u n d s t h r o ug h o u tt h e a u c t i o n, " an df i r m s t ha t " w e n t in t o t h e a u c t i o n w i t hb u s in ess pl an s t ha t s u pp or t e d v a l u a t i o n so f ab o u t$ 20 per person… ended with the winners paying twice that.”

Uncertain

Verify: Kagel, Harstad & Levin, “Information Impact and Allocation Rules in Auctions with Affiliated Private Values: A Laboratory Study,” Econometrica 55(6), 1987, pp. 1275–1304 — specifically the magnitude and direction of the English-vs-second-price behavioural gap. Reason: the paper is paywalled (JSTOR/ProQuest), no readable mirror was found from this machine, and I am relying on Cramton’s one-sentence characterisation plus a search-engine summary of the abstract. To resolve: read the Econometrica paper’s Tables and compare revenue and efficiency across the English, second-price, and first-price treatments. uncertain

Production Notes

Dutch flower auctions. The archetype, and the reason economists call the format Dutch at all. Vickrey already cited it in 1961 as “very economical of time and effort,” and Klemperer’s description of the physical clock (a dial whose lights sweep down through percentages of the opening ask, bidders at desks with buzzers, the first buzz closing the sale) is the operational reason the format persists: throughput. The mechanism has a wrinkle worth noting because it breaks the single-object model — Klemperer records that “if there are several lots of the same flowers from the same seller available that morning, the buyer can choose to buy only some of the available lots, and the rest will be re-auctioned,” which turns the sale into a sequence of linked auctions with declining supply, a genuinely different game. He notes fish are sold similarly in Israel, “as is tobacco in Canada.”

Uncertain

Verify: the current state of the Dutch flower clock — whether Royal FloraHolland still runs physical clock auctions at scale as of 2026, the daily lot throughput, and what fraction of volume has moved to direct/contract trade. Reason: web search budget for this session was exhausted before I could reach a primary FloraHolland source, and the descriptions above are from Klemperer (2004) and Vickrey (1961), i.e. 20 to 65 years old. The mechanism description is reliable; any claim about present-day scale is not. To resolve: fetch Royal FloraHolland’s own auction documentation and annual report. uncertain

eBay. The largest ascending auction ever run, and structurally a hybrid: an ascending display over a proxy (second-price) core with a hard deadline. Its most-studied property — sniping — is a pure artefact of the deadline rule, established by matched field data across eBay and Amazon and confirmed in controlled experiments (Roth & Ockenfels 2002; Ariely, Ockenfels & Roth 2005). The design lesson generalises well beyond auctions: the termination rule of a mechanism is part of the mechanism. A soft close is not a nicety; it changes the equilibrium timing of every action. (The same insight animates Stock Exchange Order Matching System Design, where closing-auction rules and randomised end times exist precisely to defuse deadline games.)

FCC spectrum auctions. The most consequential ascending auction design of the last forty years, and Cramton’s running example. Two facts from it belong in any production discussion. First, ascending formats can produce spectacular prices — “prices in [the C-block] auction escalated to the point where bidders had to go back to investors with revised business plans that would justify the doubling of prices from an earlier auction” — and spectacular defaults: “prices went so high that many winners are now unable to pay up,” with the FCC having “collected only about 10% of this money (the initial deposit)” as of August 1997. An efficient auction that allocates to a bidder who cannot pay is not efficient. Second, information policy inside an ascending auction is a design dial, not a given: “at one extreme are the FCC spectrum auctions, which to date have revealed all bids and bidder information… At the other extreme is an auction that just reports high bids and restricts new bids to be exactly one increment higher.” The linkage principle says more disclosure raises revenue; the collusion literature says it also makes tacit collusion easier to reach and enforce. Design is choosing where on that dial to sit.

Takeover battles. Cramton’s argument that a sealed-bid auction is sometimes simply infeasible is the cleanest institutional constraint in the list: “A sealed-bid auction may be infeasible, because the seller cannot commit to rejecting higher bids. In the takeover context, where the Board is obligated to do the best it can for the shareholders, the Board may be forced to consider higher bids.” Where the seller has a fiduciary duty to accept an improved offer, the auction is ascending whether or not anyone designed it that way — which is also the setting where jump bidding is most conspicuous.

A benchmark to keep in mind. BellSouth’s winning sealed bid of $2.5 bi l l i o n f or a B r a z i l ian ce l l u l a r l i ce n cee x cee d e d t h er u nn er - u p b y$ 1 billion, and its stock fell $1.25 per share on the announcement. Cramton's comment — "It is hard to imagine that an ascending-bid format would have pushed the second-highest bidder (AT&T) above$ 2.5 billion” — is the practical statement of the difference between paying your own bid and paying someone else’s. In a first-price format the winner’s overpayment is bounded only by her own optimism; in an ascending format it is bounded by the second-most-optimistic participant plus one increment.

vault

Explorer

English and Dutch Auctions

English and Dutch Auctions

Mental Model: a 2×2 that is not symmetric

The Two Open Formats, Mechanically

The English (ascending) auction

The Dutch (descending) auction

Equivalence One: Dutch ≡ First-Price, Unconditionally

Equivalence Two: English ≡ Second-Price, Only Under Private Values

Why the channel changes the answer

The two equivalences side by side

Measured: simulating the clocks rather than the order statistics

Measuring the break: the linkage principle has a size

Jump Bidding: the English auction stops being a clock

Why Real English Auctions Are Not the Clock Model

Failure Modes and Gotchas

Alternatives and When to Choose Them

Production Notes

See Also

Graph View

Table of Contents

Backlinks