Strategic Economics

Auction Formats and the Revenue Equivalence Theorem

Learn the four auction formats, the theorem that says they all raise the same money, and the five specific conditions under which that stops being true, so you stop arguing about format and start working the two levers that actually move the price.

  • Expert
  • 15 min total
  • 15 chapters

What decision this helps you make: Which selling process to run (sealed bid, open ascending, descending clock, or a negotiation) and, far more consequentially, how many bidders to recruit and what floor you are genuinely willing to enforce.

What this topic is

There are four standard auction formats. In an English auction the price rises until one bidder is left. In a Dutch auction the price falls until someone accepts. In a first-price sealed bid everyone submits one number and the highest bidder pays what they wrote. In a second-price sealed bid the highest bidder wins but pays the runner-up's number. The revenue equivalence theorem is the result that, under a specific and demanding set of conditions, all four raise exactly the same money on average, and every bidder pays the same amount on average too.

Why it matters

Practitioners spend enormous energy on format. Sealed or open? One round or several? The theorem says that argument is usually worth nothing, and the arithmetic that proves it points at what is worth something: the number of serious bidders in the room and the floor price you will actually walk away over. It also tells you exactly when format does matter, because the theorem's conditions fail in identifiable, checkable ways, and knowing which one fails in your situation tells you which format to pick.

Who should learn it

Founders and owners running a sale process, procurement leads choosing between a tender and a negotiation, marketplace and advertising product teams setting auction rules, and anyone who has been told that a particular bidding format will "maximise value" and wants to know whether that claim can be true.

What you will understand

  • The four formats, and the two pairs that are strategically the same game in different clothing
  • Why shading in a first-price auction exactly cancels the higher price paid, leaving revenue unchanged
  • The five conditions the theorem needs, and what to do when each one fails
  • Why one extra credible bidder is worth more than any format change or reserve you could set

Prerequisites

Common misconception

"An open ascending auction gets a higher price because bidders get carried away." Under the theorem's conditions it does not, and the reasoning behind the belief is backwards: in a first-price sealed bid, bidders know they pay what they write, so they shade below their true value, and the amount they shade is exactly the amount an ascending auction would have left on the table by stopping at the runner-up's number. The two effects cancel. Where an open format genuinely does raise more is when values are partly common rather than private, because watching other people bid tells you something about what the thing is worth. That is a different mechanism from excitement, and it points to a different design.