ECON90034 Chap.8 Auctions and the NASDAQ Quote Case
Auctions and the NASDAQ Quote Case
Auctions apply game theory to selling. The subject compares four formats, English, Dutch, first-price sealed-bid and second-price sealed-bid, and asks for the optimal bid in each. Truthful bidding is weakly dominant in a second-price auction, with a three-case proof you should be able to write; in a first-price auction with two bidders whose values are uniform, each bids half their value, and you should be able to derive it.
Revenue equivalence says the expected revenue is the same across formats when bidders are risk neutral with independent private values. The winner's curse belongs to common-value auctions. The NASDAQ application shows dealers sustaining wide quotes through repeated interaction. The worked material compares realised and expected revenue for two pairs of bidders and sets up a dealer market with explicit demand and supply.
What this chapter covers
- 01
English, Dutch, first-price and second-price auctions
- 02
Private values and common values
- 03
Truthful bidding in a second-price auction and its proof
- 04
Bid shading in a first-price auction: the two-bidder derivation
- 05
Revenue equivalence and when it holds
- 06
The winner's curse
- 07
NASDAQ dealer quotes as a repeated game
Worked example · free
Comparing first-price and second-price outcomes
- 1First-price: each bids half their value, 0.4 and 0.25; the first bidder wins and pays 0.4.
- 1Second-price: each bids their value; the first bidder wins and pays the second bid, 0.5.
- 1Expected second-price revenue is the average of the lower of two uniform values, 1/3.
- 1Expected first-price revenue is half the average of the higher value, half of 2/3, also 1/3.
Key terms
- Second-price auction
- A sealed-bid auction in which the highest bidder wins and pays the second-highest bid, so bidding one's true value is weakly dominant.
- Bid shading
- Bidding below one's value in a first-price auction, trading a lower chance of winning for a larger gain when winning.
- Revenue equivalence
- The result that, with risk-neutral bidders and independent private values, the standard auction formats give the seller the same expected revenue.
- Winner's curse
- In a common-value auction, the tendency of the winner to have overestimated the item's value, since winning signals that the estimate was the highest.
- Common value
- A value that is the same for every bidder, such as the oil in a field, which bidders know only through their own noisy estimates.
- Dutch auction
- An auction in which the price falls on a clock until a bidder claims the item at the current price; strategically it is a first-price sealed-bid auction.
- Private value
- A valuation known only to the bidder and independent of other bidders' valuations, although the distribution of values is common knowledge.
Auctions and the NASDAQ Quote Case FAQ
Why is bidding your value optimal in a second-price auction?
Your bid only decides whether you win, not what you pay, which is the highest rival bid. Bidding your value wins every time winning is profitable and never wins at a loss, so no other bid does better.
Is bid shading caused by the winner's curse?
No. Shading happens in first-price auctions even with private values, because you pay your own bid. The winner's curse is a separate effect that arises only when the item has a common value.
Which auction raises more money for the seller?
On any one occasion either can. On average, under risk neutrality and independent private values, the four standard formats raise the same expected revenue, which is the revenue equivalence theorem.
How could NASDAQ dealers keep spreads wide without an agreement?
Quoting is repeated every day. If any dealer narrows the spread, the others return to competitive quotes for good, so as long as dealers are patient enough, keeping the wide quotes is worth more than undercutting once.
How does an English auction relate to a second-price auction?
In an open ascending auction the best plan is to stay in until the price passes your value. The winner is the bidder with the highest value, and the price ends just above the second-highest value, the same outcome as a sealed second-price auction with truthful bids.
Exam move
Write the second-price proof from memory until it fits in five lines with all three cases. Derive the half-value bid twice from scratch, writing the probability of winning, the expected payoff and the first-order condition. Then practise revenue comparisons with pairs of values, and finish with the NASDAQ collusion condition, which reuses the grim-trigger logic from the previous chapter.
Finally, for any auction question, name the format, say whether values are private or common, and state the optimal bid before computing anything.
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