Honesty is safe

Three bidders all name their true value. The winner pays the runner-up's bid, not their own — which is why nobody gains by lying.

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.

   90 >= 70 >= 45

3. pick winner The highest eligible bid wins the item.

   argmax b_i = A at 90

4. price rule The winner pays the highest competing bid, not their own. Bidding above your value can only make you overpay, and shading below it can only lose the item at a price you would have been happy with, so honesty is the dominant strategy.

   p = max(max(b_-i), r) = max(70, 0) = 70

5. payments A pays 70; the losers pay nothing.

   revenue = 70

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.