First-price sealed bid
Highest bid wins and pays its own bid, which rewards shading below your value.
Bidding your true value is not dominant here. A bidder who knows something about their rivals can do better by bidding something else, and the worked example below shows what and why.
A worked example
The same three bidders, the same private values — 100, 72 and 41 — but here the winner pays their own bid, so each of them bids below what the item is worth to them. A shades to 75.
| Bidder | Worth to them | Bid |
|---|---|---|
| A | 100 | 75 |
| B | 72 | 60 |
| C | 41 | 35 |
What the mechanism does, step by step
- collect bids Each bidder submits one sealed bid; private values are never revealed.
- 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.
75 >= 60 >= 35
- pick winner The highest eligible bid wins the item.
argmax b_i = A at 75
- price rule The winner pays exactly what they bid, so every unit of bid above the runner-up is money left on the table. That is why bidders shade their bids below their true value here, and why the bids you see are not values.
p = b_i = 75
- payments A pays their own bid of 75; the losers pay nothing.
revenue = 75
How it came out
| Winner | A |
|---|---|
| Price paid by the winner | 75 |
| Seller revenue | 75 |
| Value created | 100 |
| Went to whoever valued it most | yes |
| Bidder | Paid | Ended up with |
|---|---|---|
| A | 75 | 25 |
| B | 0 | 0 |
| C | 0 | 0 |
A wins and pays 75, keeping 25. Had A bid their true 100 they would have won and kept nothing, which is why nobody does. Shading is not cheating here; it is the only sensible play, and how far to shade depends on how many rivals there are and what you believe they are worth — the reason first-price auctions are analysed with Bayes-Nash equilibrium rather than a dominant strategy.
The link carries the whole setup, so you can change a bid and watch what moves — and send the result to somebody else.
Settings
| Setting | Default | What it does |
|---|---|---|
| Reserve price | 0 | Bids below the reserve are ineligible; the seller keeps the item. |