Auction Lab

English (ascending clock)

Price rises until one bidder is left; equivalent to a second-price auction.

Bidding your true value is a dominant strategy here: it is at least as good as anything else you could do, whatever the other bidders do.

A worked example

The auction most people picture: a price that climbs while bidders stay in, and each drops out when it passes what the item is worth to them. Same three valuations as before.

BidderWorth to themBid
A100100
B7272
C4141

What the mechanism does, step by step

  1. collect bids Nothing is submitted on paper. Each bidder privately knows the highest price they will keep their hand up to, and the clock is what reveals it.
  2. clock start The clock opens at the reserve of 0 and only ever rises. 3 bidders are willing to pay that much and keep their hands up.
    clock = r = 0
  3. dropout The clock reaches 41, which is exactly C's limit, so C lowers their hand. 2 bidders are still in.
    clock = 41 = b_C
  4. dropout The clock reaches 72, which is exactly B's limit, so B lowers their hand. Only A is still in.
    clock = 72 = b_B
  5. pick winner The clock stops: A is the last bidder with a hand up and takes the item.
    last standing = A
  6. price rule A pays the price at which the last rival dropped out — the second-highest limit in the room — and never their own limit of 100. That is why an ascending clock is the same mechanism as a sealed-bid second-price auction: same winner, same price, and the same reason to be honest about what the item is worth to you.
    p = clock at final dropout = 72
  7. payments A pays 72; everybody who dropped out pays nothing.
    revenue = 72

How it came out

WinnerA
Price paid by the winner72
Seller revenue72
Value created100
Went to whoever valued it mostyes
BidderPaidEnded up with
A7228
B00
C00

A wins at 72 — the point where B gave up — which is exactly what the second-price auction charged for the same three bidders. That is the equivalence worth carrying away: staying in until the price reaches your value is the ascending-clock version of bidding it, and both are dominant. The difference is that this one shows the losing bids as they happen.

Run this auction step by step

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

Settings

SettingDefaultWhat it does
Reserve price0Bids below the reserve are ineligible; the seller keeps the item.

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