When the Cost Equivalence Theorem Breaks Down in Procurement

The two assumptions that fail most often are the first and the fourth: that there is only one contract, and that suppliers face no capacity limits. Real procurement organisations, public buyers in particular, award many related contracts within a short window. And suppliers are constrained by their workforce, inventory, distribution channels and the revenue they earn outside your tender.

When you relax these two assumptions, buyers tend to prefer a first-price auction over a second-price auction. The reason is price variability. In a second-price auction (and in its dynamic equivalent, the English auction), the award price is set by the most competitive losing bid, so the winner has no influence over the price they actually receive. That price could land a single cent above the winning bid, leaving effectively zero margin. In a first-price auction, by contrast, the margin is known the moment the bid is submitted. That certainty lets suppliers manage their capacity across a series of projects with controlled, predictable margins. So when contracts come in series and capacity is tight, the first-price and Dutch formats are preferred to the second-price and English formats.

This is one of several reasons format choice is never a formality. For a practical map of the designs in play, see our overview of procurement auction formats.

A risk-neutral supplier is indifferent between a certain profit and an uncertain one with the same expected value. A risk-averse supplier is not: it prefers a more certain price outcome, and it will give up some expected margin to avoid the cases where it makes almost nothing on a contract. For exactly the same reason a capacity-constrained supplier dislikes the second-price and English formats, the risk-averse supplier dislikes them too. Both prefer the first-price or Dutch auction.

The mechanism is the same certainty argument seen from the supplier's seat. In a first-price auction, a bidder knows the price it will receive before the auction even starts. In a Dutch auction, it sets its drop-out price, including its desired margin, in advance. That knowledge makes planning and operations easier. The second-price and English formats remove that certainty, because they use losing bids to set the winner's price.

This matters most for smaller bidders. Smaller firms are typically more risk-averse: they are less likely to hold large lines of credit or the financial reserves needed to absorb a thin-margin project. Yet smaller bidders are often a vital source of competition. Choosing an English auction over a first-price auction can quietly push these firms out of the process and weaken the very competition you depend on for a good price. An intelligent buyer keeps that effect in mind when designing the mechanism.

Suppliers lean toward first-price and Dutch formats when the equivalence assumptions fail. What about the buyer? In most cases, buyers lean the same way. A risk-averse buyer wants to avoid the larger cost swings of second-price mechanisms. Consider a buyer who has earmarked a fixed budget for a project: their real concern is staying under that number, not the percentage by which they beat it. And because a buyer's central goal is a genuinely competitive process, the sensible move is to offer suppliers the format they prefer, especially where small bidders are likely to take part.

There is an important exception, and it turns on supplier symmetry. Suppose costs are not drawn independently but are correlated, so that if one supplier's costs are likely to be low, another's probably are too. In that situation a descending-price English auction can outperform the alternatives. Active, open bidding reveals information and reduces each bidder's uncertainty about its own costs, so bidders grow more confident in their estimates and compete more aggressively.

In practice this holds mainly for large, specialised projects where only a handful of firms can perform the work. Building a new school for two thousand students draws far fewer capable bidders than replacing damaged windows at a school of three hundred. A municipality running a competitive process for that large build, with only two or three qualified firms, may find the English auction well suited to squeezing real competition out of a small field. Matching the mechanism to the market is exactly the kind of design question we work on in strategic procurement.

A vivid illustration, adapted from Rieck et al. (2015), shows why format choice can move enormous sums. Imagine a billionaire hires you as their proxy to bid on the Mona Lisa, a once-in-a-lifetime opportunity. Their maximum willingness to pay is $1.5 billion. If you secure the painting below that ceiling, you earn 5% of the difference between the winning price and their ceiling. Two rival bidders are present, with private valuations of $1.0 billion and $0.9 billion, but you cannot see those numbers, and that incomplete information is the heart of the problem.

Under an English (ascending) auction, starting at $0.5 billion and rising in $0.1 billion steps, each rival drops out once the price passes its valuation. The first exits at $1.0 billion, the second at $1.1 billion, and you win at $1.1 billion. Your client's surplus is $400 million, and your commission is 5% of that, or $20 million.

Under a Dutch (descending) auction, starting at $3 billion and falling in $0.1 billion steps, the first to accept wins. You could accept at $1.5 billion, but that earns you nothing, so you wait one more step to $1.4 billion. Your client's surplus is now $100 million and your commission just $5 million. With no information about the others' valuations, most proxies accept at $1.4 billion rather than risk waiting and losing the painting entirely.

The contrast is stark: the English auction clears at $1.1 billion, the Dutch at $1.4 billion, a difference of $0.3 billion, or 27%. The commission swings from $20 million to $5 million. Two features drive the gap: a thin field of bidders and large differences in their valuations. An English auction works well with several bidders holding similar valuations. A Dutch auction can extract higher prices when bidders are few and dispersed, because its pricing rests on expected rather than realised competition. Flip this to the buyer's side of the table, and the lesson is direct: a descending-price (English) procurement auction tends to set the price at the second-lowest bidder, so a buyer should be wary of it when the spread between supplier costs is likely to be wide.

Cost equivalence is the benchmark, not the recommendation. The right choice depends on which bidders your contract attracts, and it has to be weighed against the 3Cs of an effective mechanism, Competition, Comparability and Credibility. Three patterns capture most situations:

• A series of smaller jobs, with a mix of large and small firms. A simple first-price sealed-bid auction will usually beat an English or second-price auction. Smaller bidders are more risk-averse and more exposed to capacity limits, so they prefer the first-price format, and giving them a format they like increases competition.
• A single large project with only a few capable firms. An English (descending) auction can generate competition that a sealed-bid process would lose, lowering the buyer's price. Here a prudent auctioneer also considers a restrictive information rule, or even a Hong Kong style auction, to guard against coordination or collusion among a small set of large firms.
• Several projects with many similar bidders. A second-price sealed-bid auction can work well, because it removes strategic bid-padding: with the margin set by the lowest losing bid, suppliers focus on estimating their true costs rather than scheming over markup. It mainly makes sense when running a series of dynamic auctions would be too slow or complex.

Whatever you choose, the mechanism has to be one you can run transparently and fairly, especially in public procurement. If bidders lose faith in your ability to commit to a credible process, participation drops, competition thins, and costs rise. When multiple items are in play, the same logic extends to how you carve the work into lots, which we cover in lot sizing and competition.

Does the auction format really not matter?
Only in the textbook case. The Cost Equivalence Theorem holds when all five assumptions are satisfied: a single contract, risk-neutral parties, independent costs, no capacity constraints and fixed, costless entry. Those conditions almost never hold together in real procurement, so in practice the format does matter, and choosing the right one is a genuine lever on price.

First-price or English: which should we run?
It depends on contract size and the bidder pool. For a stream of smaller contracts attracting a mix of large and small, risk-averse firms, a first-price sealed-bid auction usually wins. For a single large project with only two or three capable suppliers, an English auction can create competition a sealed bid would miss, ideally paired with a careful information rule.

Why do small suppliers prefer first-price auctions?
Because they are typically more risk-averse and more capacity-constrained. A first-price (or Dutch) auction lets them lock in a known margin before committing, while second-price and English formats leave their winning margin uncertain. Offering the format small bidders prefer keeps them in the race and strengthens your competition.

Competitio has applied game theory and mechanism design to over €35 billion in negotiated volume across 16 industries, with Prof. Dr. Christian Rieck on our scientific advisory board. If you want to match the right auction format to your category and supplier landscape, get in touch with our team.