Losers pay too
Everyone pays what they bid and only one of them wins anything. Three of these four bidders end the auction underwater.
Run with All-pay auction. Here is that auction, run once.
| Bidder | Worth to them | Bid |
|---|---|---|
| A | 100 | 62 |
| B | 88 | 58 |
| C | 74 | 44 |
| D | 60 | 31 |
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.
62 >= 58 >= 44 >= 31
- pick winner The highest eligible bid wins the item.
argmax b_i = A at 62
- price rule Every bidder who cleared the reserve pays their own bid, win or lose. A losing bid buys nothing, which is why this models lobbying, contests and R&D races.
p_i = b_i for every eligible i; winner pays 62
- payments A pays 62 and takes the item; the losers pay their bids and get nothing: B loses 58, C loses 44, D loses 31.
revenue = 62 + 58 + 44 + 31 = 195
How it came out
| Winner | A |
|---|---|
| Price paid by the winner | 62 |
| Seller revenue | 195 |
| Value created | 100 |
| Went to whoever valued it most | yes |
| Bidder | Paid | Ended up with |
|---|---|---|
| A | 62 | 38 |
| B | 58 | -58 |
| C | 44 | -44 |
| D | 31 | -31 |
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.