Lecture 24: Asymmetric Information - Auctions and the Winner's Curse

What this lecture covers

This final lecture of the course applies the asymmetric-information framework to auctions, where bidders typically do not know how much rivals value the good for sale. It first distinguishes common-value goods, where the item is ultimately worth the same to everyone but bidders only have noisy estimates (an oil well, or a jar of coins whose contents nobody can see), from private-value goods, where each bidder's valuation is genuinely idiosyncratic and unaffected by others' opinions. Using a live in-class auction for jars of coins, it demonstrates the winner's curse: bidders who bid close to their own estimate tend to win only when their estimate happens to be the most inflated one, so winning is itself bad news about how accurate your estimate was.

The lecture then works out the correct way to bid in a common-value auction (shade your estimate down as if you already knew you had the highest guess), before switching to a broader discussion of auction formats. It defines first-price and second-price sealed-bid auctions and open ascending and descending auctions, argues that the descending auction is strategically the same as first-price sealed-bid and the ascending auction is closely related to second-price sealed-bid, and closes with the revenue-equivalence result for private-value auctions. After watching, you should be able to explain why the winner's curse arises, describe how to correct for it, and compare bidding incentives across the four classic auction formats.

Key ideas

• Common value versus private value: in a common-value auction the good is worth the same amount to everyone (though nobody knows exactly how much), while in a private-value auction each bidder's valuation is idiosyncratic and unaffected by others' valuations; most real goods lie somewhere between these extremes.
• The winner's curse: in a common-value auction, if bidders bid close to their own noisy estimate of the good's value, the auction is won by whoever has the largest estimation error, so the winning bid systematically overshoots the true value.
• Correcting for the winner's curse: the right way to bid is to estimate the value conditional on having the highest estimate in the room, not conditional on your own signal alone, which means shading your bid well below your naive estimate.
• First-price sealed-bid auction: everyone submits one bid privately; the highest bidder wins and pays their own bid.
• Second-price sealed-bid (Vickrey) auction: the highest bidder wins but pays the second-highest bid rather than their own.
• Open ascending and descending auctions: in an ascending auction (like eBay) bidders drop out as the price rises until one remains; in a descending auction (a Dutch auction) the price falls from a high starting point until someone accepts it.
• Strategic equivalence across formats: a descending open auction is strategically equivalent to a first-price sealed-bid auction, and an open ascending auction closely parallels a second-price sealed-bid auction, since in each pair the winner effectively pays based on the same information.
• Bidding truthfully in second-price and private-value first-price auctions: bidding your true value is a weakly dominant strategy in a second-price private-value auction, while in a first-price private-value auction you should shade your bid below your value to trade off winning probability against surplus.
• Revenue equivalence: under independent, symmetric, private values, first-price and second-price auctions (and any auction format where the highest-value bidder always wins) yield the same expected revenue to the seller.

Walkthrough

Common value versus private value (11:00)

The lecture opens (mid-session, following an in-class demonstration setup) by distinguishing common-value goods, illustrated with an oil well whose true reserves are the same for every bidder, from private-value goods, illustrated with a consumption good like a cake that has no resale value. It notes that most real goods, such as houses, mix both elements, since a home has both a private consumption value and a common investment/resale value.

The winner's curse demonstrated live (17:45)

Students bid on jars of coins whose true value is unknown to them, and the winning bidder turns out to have bid well above the jar's actual contents. The lecture shows that when bidders bid close to their own estimate, the winner is whichever bidder happened to have the largest overestimate, so the winning bid systematically exceeds the true value; it connects this to historical overbidding in Gulf of Mexico oil-drilling auctions and to overpriced IPOs.

Correcting for the winner's curse (33:21)

Working through the logic of conditional estimation, the lecture argues that a rational bidder should only care about the value of the good in the scenario where they actually win, and winning reveals that their estimate was higher than everyone else's. The correct strategy is therefore to bid as if you already knew your estimate was the highest, which requires shading your estimate down substantially. A second in-class auction on a smaller jar shows bidders shading more but often still not enough.

Four types of auctions and their equivalences (47:05)

The lecture defines first-price sealed-bid, second-price sealed-bid (Vickrey), open ascending, and open descending auctions. It argues that a descending auction is strategically identical to a first-price sealed-bid auction, since each bidder effectively has a private threshold price in mind, and that an open ascending auction closely parallels a second-price sealed-bid auction, since the winner ends up paying roughly the amount of the second-highest bidder's willingness to pay.

Bidding strategy in private-value auctions (55:39)

Switching to pure private-value settings, the lecture shows that bidding your true value is a weakly dominant strategy in a second-price auction, but that in a first-price auction you should shade your bid below your value to trade off a higher chance of winning against a smaller surplus if you win.

Revenue equivalence (1:00:45)

The lecture closes with the revenue equivalence result: under independent, symmetric, private values, first-price and second-price auctions, and indeed any auction format in which the highest-value bidder always wins, generate the same expected revenue for the seller, though the full proof is left for a later course.

Before you watch

• Watch the previous two lectures on asymmetric information and signaling, since this lecture continues the course's final unit on situations where players don't know each other's payoffs.
• Be comfortable with the idea of conditioning beliefs on new information, since the winner's curse correction relies on updating your estimate based on the fact that you won.
• Basic familiarity with expected value and probability distributions is useful for following the discussion of estimation errors.

Check your understanding

1. Why does bidding close to your own estimate in a common-value auction tend to produce a winning bid that overshoots the true value?
2. What does it mean to "bid as if you know you win," and why does this correct the winner's curse?
3. Why is a descending open auction strategically equivalent to a first-price sealed-bid auction?
4. Why is bidding your true value a weakly dominant strategy in a second-price auction but not in a first-price auction?
5. Under what conditions does the lecture claim that first-price and second-price auctions generate the same expected revenue, and what auctions would this revenue-equivalence result cover beyond just these two formats?