← All games
Markets and auctions
First-price sealed-bid auction
A painting is sold by sealed bid. You know what it is worth to you, somewhere between 0 and 100. The other bidder knows their own value, and neither of you knows the other's.
Both write down a bid. The higher bid wins and pays what it bid, so winning is worth your value minus your bid.
What it teaches
When you pay what you bid you must shade below your value, and the right bid is simply what you expect the strongest rival to be worth in exactly those cases where your bid wins.
The usual mistakeBidding your value on the grounds that it is what the item is worth to you, which is correct advice for a
second-price auction and leaves you with exactly zero surplus here.
The checkAsk what you earn in the event that you win. If it is nothing, the bid is too high regardless of how accurate your valuation is.
In the real world
Real world
A lowest-price public tender
Public bodies invite sealed tenders by a deadline and award to the lowest compliant price, and the winner is then held to the price it tendered. The recurring pattern is a winning price that turns out to be too low to deliver on, followed by claims, variations or an abandoned contract, which is what you would expect from a format that rewards whoever shaded hardest against their own costs.
It is the first-price auction with the signs reversed: the winner is paid its own number rather than the runner-up's, so the bid has to be built on beliefs about rivals, and shading is towards cost from above rather than towards value from below.
Real world
Offers over, by the closing date
Scottish residential sales are commonly run as offers over an advertised figure with a closing date. Each interested buyer submits a single written offer through a solicitor, the offers are considered together, and the seller normally accepts the highest, which that buyer then pays in full. Nobody sees anyone else's number, which is why the familiar outcomes are either paying well over the asking price or losing the house by a margin the buyer would gladly have covered.
The winner is held to the figure they wrote down, so the right offer depends on a judgement about how many rivals there are and what they are likely to put in, which is exactly the judgement a second-price rule would make unnecessary.
Real worldContested
Carillion winning work at any price
Carillion went into compulsory liquidation on 15 January 2018 with liabilities reported in the billions against a very small cash balance, having taken on large fixed-price public contracts at prices that could not cover the work. Its chief executive told MPs that with no money to buy competitors the company 'had to win our work organically'. Parliamentary committees blamed 'recklessness, hubris and greed' at the company, and separately criticised the practice of awarding public contracts on lowest price. Inference, not fact: the revealed preference looks like bidding to win cash flow rather than bidding to make a margin, which is a rational response to needing the next contract to fund the last one, and is precisely the shading error a pay-your-bid format punishes last and hardest.
The winner is held to the number it wrote down, so the optimal bid depends on a judgement about rivals rather than on your own costs alone, and a bidder who shades too far wins exactly the contracts it should have lost; under a second-price rule the winner would be paid the runner-up's price and the error would not be self-inflicted in the same way.
Next door on the wall
Second-price sealed-bid auctionThe winner paying their own bid, which makes the equilibrium bid depend on beliefs about rivals rather than on the bidder's value alone. Not on the wall yet.
All-pay auctionLosing bidders paying nothing, which leaves bidders with a positive expected surplus instead of none. Not on the wall yet.
Common-value auctionValues are common rather than private, so winning is itself information and the curse exists. Not on the wall yet.
Dutch auctionThe bid is submitted by stopping a falling clock rather than on paper, which is a difference in presentation and not in strategy, so the two games are formally the same. Not on the wall yet.
Sources
- Vickrey, W. (1961). Journal of Finance 16(1), 8-37.
- Krishna, V. (2002). Academic Press.