A reserve too high

The seller refuses anything under 80 and the room tops out at 72. Nobody wins, nobody pays, and the item everyone wanted goes nowhere.

Run with Second-price (Vickrey). Here is that auction, run once.

Step by step

1. collect bids Each bidder submits one sealed bid; private values are never revealed.
2. sort Bids are ranked from highest to lowest. Equal bids keep the order the bidders were listed in, so a tie goes to the first-listed bidder.

   72 >= 61 >= 40

3. apply reserve The seller refuses to sell below the reserve of 80, so these bids are struck out: A (72), B (61), C (40).

   eligible: b_i >= r = 80

4. no sale No bid reached the reserve of 80, so the item is not sold even though the bidders valued it.

   max(b) < r = 80

How it came out

Open this example in the walkthrough

The link carries the whole setup, so you can change a bid and watch what moves — and send the result to somebody else.

Read next

• First-price sealed bid — Highest bid wins and pays its own bid, which rewards shading below your value.
• English (ascending clock) — Price rises until one bidder is left; equivalent to a second-price auction.
• VCG position auction — The same slots to the same bidders, but each winner pays the externality they impose. Truthful.