MG207
Managerial Economics
Winter Term
Lecture 20 – Auctions & Review
(Varian: Chapter 18)
Agenda
• Part I: Auctions
–
–
–
–
–
Recap: Auctions & Types of Auctions
Private-Value Auctions: Optimal Bidding Strategy
Common-Value Auctions and The Winner’s Curse
Other Types of Auctions
Wrap-up & More-Practice
• Part II: Review & Exam Advice
– Review of the course objectives and material.
– Exam format: What to expect from your exam paper?
– Revision and Exam tips.
Recap: Allocating Goods Through Auctions
•
Auctions are one of the oldest means to allocate goods among individuals.
• Used for more than collectibles:
– Artwork sold at auction houses
– eBay
– Government contracts
– Electricity markets
– Treasury and money market auctions
– Spectrum auctions
– Privatizations
– IPOs (such as Google’s IPO), etc.
•
Auctions are a good idea if you know that there are enough buyers to
compete for your item, but you are uncertain about how much buyers are
willing to pay for it.
3
Recap: Main Auction Formats
•
An auction has rules that specify
– how bidders can submit bids for a good (or a package of goods),
– how the good is allocated among the bidders based on the bids,
– and how much each bidder pays to the auctioneer.
•
Main auction formats:
1. English auction: Oral ascending-bid auction (e.g., fine arts)
– Auction starts at a minimum price set by the seller
– Bidders successively offer higher prices
– Auction stops when no one is willing to exceed the current bid
– The bidder with the last bid wins and pays a price equal to that bid
2. Dutch auction: Oral descending-bid auction (e.g., Dutch flower
market)
– Price starts high and declines
– Auction stops when someone signals they want to buy the good at that price
– Winner pays the price at which she signaled
4
Recap: Main Auction Formats
3. First-price sealed-bid auction (e.g., Government procurement, oil and
gas)
– Bidders simultaneously submit written bids
– Highest bidder wins the item and pays a price equal to his or her bid
4. Second-price sealed-bid auction, also known as Vickrey auction
(e.g., US toll-free numbers, eBay proxy bid)
– Bidders simultaneously submit written bids
– Highest bidder wins the item and pays the second highest bid
– Note: In sealed bid auctions, the seller may also set a reserve price
(minimum price for the item).
5
Two Main Questions & Two Cases
• The question is how to win and what the expected revenue for the seller is.
• Now we examine the effect of rules across the four auction formats:
– Bidders: how to win (optimal bidding strategies)
– Seller: how the rules affect expected revenue.
• We consider two main cases:
– Private-value auctions: Each bidder 𝑖 has a value 𝑣! of winning in the
auction. Only the bidder knows her value, and values are independent
(e.g., JT’s French Toast, JB’s hair).
– Common-value auctions: All bidders have the same exact value for
the object, and they have different information about the value (e.g., oil
tract, treasury bonds).
6
Private-Value Auctions: Optimal Bidding Strategy & Expected Revenue
Valuation, Bid, Payment
•
Before analysing bidding strategies and expected revenues in private-value
auctions, it is useful to distinguish between a bidder’s valuation, her bid, and
the payment made by the winner:
– Valuation (𝑣! ): bidder 𝑖’s value for the object, that is, their private value.
– Bid (𝑏! ): bidder 𝑖’s submitted offer.
– Payment (or price): the amount ultimately paid by the winner.
8
Model of Independent & Private-Value Auctions
•
There are two bidders (or N bidders in the general case).
•
One indivisible object is being auctioned.
•
The value to bidder 𝑖 is 𝑣! (known only to that bidder)
•
Assume that bidders’ valuations 𝑣! are drawn independently and identically
from a uniform distribution, 𝑈[0,1], which is known to all bidders and to the
seller.
•
We will look for the optimal bidding strategy, and the expected revenue for the
seller in four auction formats:
– First-price sealed-bid
– Dutch (descending price)
– English (ascending price)
– Second-price sealed-bid
9
Winning Play with Private Values
•
Assume you value this painting at £100,000:
– What price would you write down in a first-price sealed-bid auction?
First-price
sealed-bid
Auction
10
First-Price Sealed-Bid Auction
•
Let’s consider a first-price sealed-bid auction with private values.
•
Bidders submit sealed bids.
•
Seller opens bids and awards object to the highest bidder who pays her bid.
•
What is the optimal bidding strategy?
– It is never optimal to bid more than your own valuation.
– If the second highest bid was known, it would be optimal to bid just
above that bid (if own valuation is higher).
– Making a higher bid increases the chance of winning but also the
amount you pay if you win.
– A bidder will optimally bid below their own valuation (shading their bid).
– Optimal bid depends on what each bidder thinks that the others will bid.
– Implication: each bidder needs to form beliefs about their rivals’ bids.
11
First-Price Sealed-Bid Auction
•
Let’s see it. Assume:
– There are two bidders.
– (Independent) private values: bidder 𝑖’s valuation is 𝑣!
– Each bidder does not know the other bidder’s valuation.
– Each bidder knows that the other bidder’s valuation is uniformly
distributed on the interval [0,1].
• This means, the probability that bidder 1 attaches to bidder 2’s
valuation being smaller than 𝑥 is 𝑥.
– If a bidder submits the highest bid, he gets the good and his payoff is
the difference between his reservation price and the price paid (which is
his bid). If he doesn’t win, he obtains a payoff of 0.
– Bids have to be equal or greater than 0.
12
First-Price Sealed-Bid Auction
•
Observations:
– A bidder can always guarantee himself a payoff of zero by bidding his
valuation.
– Moreover, bidding above his valuation is dominated by bidding his
valuation since if he wins, he will be paying more than what is worth to
him and thus get a negative payoff.
– Can a bidder do better? Note that bidding slightly below one’s valuation
dominates bidding your valuation:
• If you win you get a strictly positive payoff and if you lose you get zero.
– Therefore, we see that in any equilibrium of this game bidders will
shade their bids below their valuation.
– A bidder’s optimal bid depends on her own valuation: a bidder’s strategy
is given by a bidding function 𝑏! (𝑣! )
– A bidder with a valuation of 0 bids 0, i.e., 𝑏! 0 = 0
13
First-Price Sealed-Bid Auction
•
•
To derive the optimal bidding strategy, we start with two assumptions:
1.
Bidders who have the same valuation submit the same bid.
2.
Bidders each bid a fraction 𝑓 of their valuation:
i.e. 𝑏𝑖(𝑣! ) = 𝑓𝑣!
We look for bidder 1’s optimal bid 𝑏1 when valuation is 𝑣1 (i.e. we look for 𝑓)
–
When does bidder 1 beat the other bidder’s bid given his strategy?
•
–
Only if the other bidder’s valuation is lower: 𝑓𝑣" < 𝑏#
How likely is it that you beat the second bidder’s bid with a bid of 𝑏1?
Pr(𝑤𝑖𝑛) = Pr(𝑏1 > 𝑏2) = Pr(𝑏1 > 𝑓 𝑣2) = Pr(𝑣2 < 𝑏1/𝑓 ) = 𝑏1/𝑓
–
So, Bidder 1’s expected payoff in the auction is:
𝑈1(𝑏1) = 𝑃𝑟𝑜𝑏[𝑏𝑖𝑑𝑑𝑒𝑟$ 𝑤𝑖𝑛𝑠] ∗ (𝑣1 − 𝑏1) =
𝑏1
∗ (𝑣1 − 𝑏1)
𝑓
14
First-Price Sealed-Bid Auction
•
We now find bidder 1’s optimal bid given that he thinks bidder 2 is bidding
only a fraction of his valuation.
•
By differentiating, we have
𝑑𝑈1(𝑏1)
𝑑 𝑏1
1
𝑏1
=
∗ (𝑣1 − 𝑏1) = ∗ (𝑣1 − 𝑏1) − = 0
𝑑𝑏1
𝑑𝑏1 𝑓
𝑓
𝑓
•
The trade-off bidder 1 faces when increasing his bid is an increase in the
probability of winning, but a lower surplus when winning. The optimal bid
would be given by:
1
𝑏1
𝑣1
∗ (𝑣1 − 𝑏1) − = 0 ⇒ 𝑏1 =
𝑓
𝑓
2
–
This implies that 𝑏#∗ = 𝑣1 /2. Bidder 1 bids the same fraction 𝑓 = 1/2
of her valuation.
15
First-Price Sealed-Bid Auction
•
Thus, the optimal strategy for bidder 1 is 𝑏1 (𝑣1) = 𝑣1 /2 . If bidder 1 is
bidding half of his valuation we have found a (Bayes) Nash equilibrium of
this auction.
•
Similarly for bidder 2 it is 𝑏2 (𝑣2) = 𝑣2 /2 .
•
In equilibrium each bidder is bidding half of his valuation. Note that if bidder
1 knows that his rival has a lower valuation, he will expect bidder 2’s
valuation to be 𝑣# /2 on average.
•
So, each bidder’s bid is their expectation of the other bidder’s valuation if
they think their valuation is the highest.
•
We have seen that, for two bidders, 𝑏𝑖 =
•
For N bidders, we can show that the NE bids are:
•
The bidder with highest 𝑣𝑖 wins.
#
𝑣
" 𝑖
𝑏𝑖 =
%&#
%
𝑣𝑖
16
First-Price Sealed-Bid Auction
•
What is the expected revenue for the auctioneer?
– The expected value of the highest 𝑣𝑖 in N independent draws(1) from
%
U[0,1] is
%'#
– Hence, the expected revenue for the seller is
•
%&#
%
%
%'#
=
%&#
%'#
Note: we will see later on that, under certain assumptions, the seller here
receives the same expected revenue as in the English and second-price
sealed-bid auctions in private-value auctions!
(1) If you’d like to see where this comes from, see the Moodle note “For reference: Order statistics for draws from a Uniform Distribution”.
17
Example: Art Dealer (First-price Auction)
•
You are an art dealer and hear about this painting going up for auction.
1st price
Auction
•
You value the painting at £100,000, which is how much you can eventually
get for it from a wealthy buyer.
•
Suppose the probability of winning in a first-price auction with a bid of £𝑏 is
𝑏/200,000.
•
How much should you bid in a first-price sealed-bid auction?
18
Example: Art Dealer (First-price Auction)
Solution
•
Your payoff is the probability of winning times the profit when you win,
100,000 – 𝑏, that is:
𝑏
(100,000 − 𝑏)
200,000
•
We obtain the optimal bid (maximum of this function) by differentiating with
respect to b and equating to zero
𝑏
𝑑 200,000 (100,000 − 𝑏)
𝑑𝑥
•
= 0 ⇒ 𝑏 ∗ = 50,000
The best strategy is to bid on $50,000 (50% of your true value) and win only
25% of the time!
– If you chose to bid your true value, you would win 50% of the time but
get a payoff of zero.
19
Dutch Auctions
•
Auction starts at a very high price.
•
Price is dropped in increments.
•
Auction stops when a bidder steps in and cries “mine.”
•
This bidder wins the object at the price at that point and pays the last price
named by the auctioneer.
•
This is also called descending-price auction.
•
What is the bidder’s optimal bidding strategy?
20
Dutch Auctions
•
What is the bidder’s optimal bidding strategy? How would you bid?
– First, your strategy would be to name a reservation price at which time,
if the auction is still alive, you would cry “mine” and claim the good.
– Clearly you would not want to raise your hand if the current price is at or
above your valuation.
– Once the price has fallen below your valuation, raise your hand just
before you estimate that the next bid will come.
– It depends on their beliefs about the other bidders’ valuations and
bidding strategies.
– When thinking about bidding or waiting until the price is reduced you are
effectively trading off a lower probability of winning if you wait versus a
higher payoff if you get the good at a lower price.
•
So, we see that this is the same trade-off that we face in a sealed-bid first
price auction. In this simplified world, first-price sealed bid and Dutch
auctions are “strategically equivalent” in private-value auctions and
would generate the same price and therefore the same revenue for the
auctioneer.
21
Winning Play with Private Values
•
Assume you value this painting at £100,000:
– When do you stop bidding in an English auction?
– What price would you write down in a Vickrey (2nd price sealed-bid)
auction?
• English Auction
• Second-price
Auction
22
Second-Price Sealed-Bid Auction
•
In our analysis of bidding behavior in a first-price auction with private values
we concluded that bidders would underbid relative to their valuations.
•
Now let’s change the rules and suppose that the good is given to the
highest bidder who pays in exchange a price equal to the secondhighest bid.
•
In a second-price sealed-bid auction, bidders are asked to submit sealed
bids 𝑏1, … , 𝑏𝑛. The bidder who submits the highest bid is awarded the object
and pays the amount of the second highest bid.
•
Suppose that one bidder’s valuation is 𝑣𝑖. She is of course uncertain of the
valuations of competing bidders.
•
How should the bidder bid?
•
We will show that bidding your own valuation (“bidding truthfully”) is actually
a (weakly) dominant strategy.
23
Second-Price Sealed-Bid Auction
Proof that bidding 𝑣𝑖 is a (weakly) dominant strategy:
• Suppose that you are bidding your valuation. Can you profit from raising
your bid?
― Suppose that all other bids are below your valuation. Then raising your bid
doesn’t change the fact that you win and doesn’t change how much you pay (the
second highest bid).
― Suppose that there is one bid that is above your valuation, and you outbid that
bid (𝑏 > 𝑣𝑖 ). Then now you win, and you pay more than your valuation!
•
Can you profit from lowering your bid? Suppose you bid 𝑏 < 𝑣𝑖
― Suppose that there is at least one bid above your valuation. Then by lowering
your bid you still don’t win.
― Suppose that all bids are below your valuation. If you bid your valuation, you get
the good and obtain a positive payoff. If you bid lower than the next highest bid,
then you lose the good and get a zero payoff!
•
How can it be that bidders will bid truthfully?
― In a second-price auction, conditional on winning, the amount you pay does not
depend on your bid.
― As a result, shading your bid can only affect whether you win the object but not
the price you pay if you win.
24
Second-Price Sealed-Bid Auction: Summary
•
Bidders submit sealed bids.
•
Seller opens bids.
•
Highest bidder wins; she pays the 2nd highest bid.
•
What is a buyer’s optimal bidding strategy?
– Each bidder optimally bids her valuation.
– Winner pays the value of the bidder with the second highest valuation.
– Example: Second-price auction with 3 bidders (v1 = 6, v2 = 8, v3 = 3);
bidder 2 wins and pays 6.
– Note: the outcome here is the same as with the English auction
mechanism.
•
Note: This is also known as a Vickrey Auction—the price paid is the
“externality” the highest-value bidder imposes on the bidder with the second
highest bid.
25
English Auction
•
An English Auction starts at zero and price is increased in increments.
•
Bidders stay in (e.g., hold up their hands) or exit.
•
Auction ends when one bidder is left.
•
This last bidder who stays in gets the object.
•
She pays the price at which the second-to-last bidder dropped out.
•
This is also called ascending-price auction.
•
How would you bid?
– First, you would stop bidding once the current bid is at or above your valuation. If
you increase your bid, you risk the possibility that you would win and thus pay
more for the good than your valuation.
– What if the current bid is below your valuation and the auctioneer says “going
once, going twice…”? Yes—raise your bid. If you don’t, you may lose the object
even though buying it at the current price would give you positive surplus. If you
do raise your bid, you might win and still pay less than your valuation.
26
English Auction: Summary & Example
•
If all bidders behave as above, what is the selling price? The object will go
for a price equal to the second highest valuation, just as in the sealed-bid
second-price auctions.
•
In summary, what is a buyer’s optimal bidding strategy?
– Each bidder optimally bids her valuation.
– Winner pays the value of the bidder with the second highest valuation.
– Example: English auction with 3 bidders (v1 = 6, v2 = 8, v3 = 3); bidder 2
wins and pays 6.
•
So, we see that, in the independent private-value benchmark, second-price
sealed-bid auctions and English auctions are “strategically equivalent”,
generating the same price and revenue for the auctioneer.
27
English Auction: Expected Revenue
•
If N bidders with each vi drawn independently from U[0,1], then:
– The highest expected valuation is N/(N+1)
– The second highest expected valuation is (N-1)/(N+1)
•
Seller’s expected revenue is (N-1)/(N+1).
•
Example: with 5 bidders, expected revenue is 4/6=2/3.
1/N+1
1
0
(N-1)/(N+1)
N/N+1
28
English vs. Second-Price Sealed-bid Auctions
•
In both auctions, bidding (up to) their own valuation is a (weakly) dominant
strategy for each bidder, i.e., the strategy is optimal whatever the strategy of
the other bidders!
•
In this sense the second-price auction is equivalent to the English auction:
bidders have a dominant strategy, the bidder with the highest valuation wins
and pays a price that (approximately) equals the 2nd highest valuation.
•
In both auctions the bidder with the highest valuation wins, i.e. the auctions
are efficient.
29
First- or Second-Price Sealed-Bid Auctions?
•
A common, but mistaken, belief: A second-price sealed-bid auction is bad
for the seller as he only receives the second highest bid whereas in the firstprice auction he would get the highest bid (i.e. more money).
•
Revenue Equivalence theorem: Under certain (restrictive!) assumptions
both auction types are equally good, even if values are unknown!
•
That is, the amount of bid-shading in the first-price auction is such that
bidders bid the average value of the second-highest valuation.
30
Revenue Equivalence
•
Despite different bidding behaviour, first-price sealed-bid auctions (and
Dutch Auctions) and second-price sealed-bid auctions (and English
Auctions) yield the same expected revenue for the seller in private-value
auctions.
•
This is however not that surprising once we realise that in our examples, in
a first-price auction your bid is equal to your expectation of the secondhighest bid in the event that you are the highest bidder.
•
Some common auction designs all lead to efficient outcomes and yield the
same revenue, at least on average. Assumptions:
– Bidders know their own valuations.
– Valuations are independently drawn from a common distribution.
– Bidders are risk neutral.
•
Revenue Equivalence Theorem: Any auction game with an equilibrium in
which a bidder with value 0 has an expected payment of 0, and the bidder
with highest valuation wins, has the same expected revenue for the seller.
31
Summary: Optimal Strategy with Private Values
•
Second-price sealed-bid auction and English Auction:
– Bid your true value.
•
First-price sealed-bid auction and Dutch Auction:
– Bid less than your true value.
32
Summary: Expected Revenue with Private
Values
•
Under these assumptions:
– bidders know their valuations
– symmetric bidders
– risk-neutral bidders
– valuations independently drawn from a common distribution.
•
First-price sealed-bid auctions, Dutch Auctions, second-price sealed-bid
auction, and English Auctions yield the same expected revenue for the
seller in private-value auctions.
33
Auctions and Efficiency
•
Which auction types guarantee that the object is awarded to the bidder with
the highest valuation (Pareto efficient outcome)?
•
More generally, English auction with no reserve price, and second-price
sealed-bid auctions are Pareto efficient as the bidder with the highest
valuation wins.
– English auction with no reserve price must be efficient since, if a buyer with a low
valuation was about to buy, the highest valuation buyer would bid higher.
– Second-price sealed-bid auction is Pareto efficient even though no buyer knows
the other buyers’valuations.
•
Beyond the benchmark model, Dutch and first-price sealed-bid auctions
need not be efficient.
– Dutch auction need not be efficient. No buyer knows other buyers’valuations, so
the highest valuation buyer may delay too long and lose to another bidder.
– First-price sealed bid auction need not be efficient. No buyer knows other
buyers’valuations, so the highest valuation buyer may bid too low and lose to
another bidder.
34
Problems with Auctions
•
However, outside the benchmark, even efficiency in English auctions may
fail.
– Bidders can band together (collude), have a representative acquire the
auction item at a low price, and then hold a second, members-only
auction at which the winner pays a higher price.
– When a winning bidder is allowed to drop out, bidders can bid at
multiple levels and then selectively drop out to lower the price they pay.
35
Common-Value Auctions and The Winner’s Curse
Recall, Classification of Auctions
•
Private-value auctions:
– every potential buyer knows for sure her own valuation of the item for
sale
– all these individual valuations are independent of each other.
– (This is the case in all the auctions we have discussed so far).
•
Common-value auctions:
– item for sale has the same value to every potential buyer
– potential buyers differ in their own estimates of this common value.
37
Offshore Oil Leases
•
The U.S. Government, through the U.S.
Minerals Management Service, leases
the rights to particular territories, known
as tracts, for drilling for oil and gas.
•
These rights have been traditionally sold
through auctions.
•
… You are thinking of bidding in one of
these auctions.
•
For simplicity, suppose that it is a firstprice sealed bid auction.
38
Offshore Oil Leases
•
Note that in this case all bidders care about the same thing: how much oil is
there in the field.
•
In this sense the value to all bidders is the same. So, this is a case of
common-value auctions.
– The item for sale has the same value to every potential buyer. Potential buyers
differ in their own estimates of this common value.
•
Of course, the total yield of the field is unknown! You can get estimates
through geological studies, similar oil fields in the area, etc.
– Bidders are uncertain about the common value of the item being auctioned. In a
common value setting, this means they are also unsure about their own
valuation!
•
Of course, other bidders are also obtaining similar estimates!
•
Even though you have an estimate of the value of the field, you would
obtain a more accurate appraisal of the value of the field if you knew the
estimates of your competitors.
39
When Winning is Bad News: Winner’s Curse
•
Suppose that both you and your competitor use the same bidding strategy
as a function of how much oil there is in the part you have investigated.
•
In fact, both of your bidding strategies are such that if you find more oil in
your part you will bid more for the overall tract (and so does your
competitor).
•
Suppose that you win! What does that tell you? It must be that you found
more oil in your part than your competitor.
v1 > v2
•
If you didn’t take into account that you only win when your estimate is high,
it is very likely that you overbid!
40
The Winner’s Curse
•
The item for sale has the same value to every potential buyer.
•
Potential buyers differ in their own estimates of this common value.
•
Bidder i’s estimate is 𝑣!= 𝑣 + 𝜀! where 𝑣 is the common value and 𝜀! is
bidder 𝑖 ’s estimation error.
•
If every bid is truthful, the winner is the bidder with the largest estimation
error.
•
So, a truthful winner on average pays more than the true value—the
winner’s curse.
•
Winner ends up paying too much.
Highest estimate
True value
41
The Winner’s Curse - Example
•
Always bid as though you have the highest signal.
– If you don’t have the highest signal, it does not matter as you will not
win anyway.
– If you do have the highest signal, what is the object worth?
– Shade your bid a lot, as your signal is likely to have been high!
•
Example:
– An object worth £X.
– 9 bidders get noisy unbiased signals: £X-4, £X-3,…,£X+3, £X+4.
– You get the signal £10.
– Unbiased signal so you expect value to be £10. Bid £9?
– If all bidders reason this way, and you win, your signal must have been
£X+4. You bid £X+3, therefore lost £3!
– Instead assume that your signal is the highest. Then, you can infer the
value must be £10 - 4. You should bid less than this number to extract
any surplus.
42
Empirical Evidence of the Winner’s Curse
•
Rational bidders will take into account the additional information that
winning entails and revise their valuations downward.
•
Empirical evidence of the Winner’s Curse in offshore drilling rights:
Hendricks, Kenneth, and Robert H. Porter. “An Empirical Study of an
Auction with Asymmetric Information.”
American Economic Review 78, no. 5 (December 1988): 865-883.
43
Other Auction Formats
Automatic bidding on eBay
• eBay uses a version of a Vickrey auction with automated proxy bidding.
– An automated bidding agent increases the bid as needed, up to a maximum set
by the participant.
– It’s more convenient than manual bidding because you don't need to monitor the
auction as closely.
– When placing your bid, you enter the highest amount you’re willing to pay for an
item. This is your maximum bid and isn’t visible to other bidders or the seller. You
won't necessarily pay your maximum. If no one else bids as high as your
maximum, you’ll pay less.
– If someone bids more than your maximum, we'll let you know in case you want to
bid again.
– In practice, a lot of participants still hold back until the auction is about to close.
•
If, using automatic bidding, bidders submit their maximum bids once during
an auction, eBay becomes a 2nd price auction. (Bidding only once may not
be optimal if bidders learn from observed bids and “sniping” can occur due
to fixed length of auction).
45
The Buy-Now Option
•
Buy-now option: allows bidder to end auction early at a buy-now price
specified by the seller.
•
Puzzle: Why is it used, because it should reduce competition and efficiency.
•
Explanations:
– Risk averse bidders might exercise this option, which can increase
seller revenue.
– Risk averse sellers might profit from this option as it reduces the
volatility of their revenue.
– Bidders are impatient and will pay more if outcome happens sooner.
– Cognitive effort of participation in auction makes bidders willing to pay a
premium for buy-now option.
•
Buy-now options are used frequently. They seem to increase revenue in
private and common value auctions
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Position Auctions
• Each time a user conducts a Google search that shows advertisements,
Alphabet Inc.’s Google has run an automated auction in a fraction of a
second that considers a variety of factors to decide where the ads rank and
how much advertisers pay.
“Google’s decision to use auctions early in the development of its ad
system has helped it generate more money from advertisers and
build the world’s largest advertising business, estimated to bring in
$79 billion last year. The digital-ad industry has largely adopted the
auction format since.” (WSJ, Jan 2017).
•
What is auctioned?
– If a user enters search term into Google, he gets back a list of search results with
regular links and sponsored links.
– Sponsored links are paid advertisements. They are clearly marked as such. The
displayed sponsored links depend on the search keywords.
– When a user clicks on a sponsored link he will go to the webpage of the sponsor.
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Position Auctions
– Only a limited number of ads can be displayed in the search results.
– Positions on top (of the page) are more likely to be clicked than those at the
bottom.
– Advertisers have a higher willingness to pay for the top positions.
– Advertisers pay per click on their link (“pay-per-click” pricing).
•
How does the auction work?
– For a specific keyword, advertisers submit bids stating their maximum willingness
to pay for a click.
– The ad with the highest bid is displayed on top (in the best position).
– The ad with the next highest bid is displayed second and so on.
– If a customer clicks on a sponsored link at position i, the advertiser is charged by
Google an amount equal to the i+1 highest bid, i.e. the bid of an advertiser that is
at position i+1 (this is a slight simplification of the actual rule, which states that
the price is one cent higher).
– If there were only one position this would be a standard second-price auction.
– Thus, we call it a generalised second-price auction (GSP auction)
– Bids can be made and withdrawn any time.
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Wrap-up & Practice
What to Take Away?
•
Auction as a mechanism to allocate goods and can help sellers solve
the problem of unknown potential buyer valuations.
•
Different rules governing auctions and four main types of auction
mechanisms: English auction, Dutch auction, first- and second-price
sealed-bid auctions.
•
Optimal bidding strategies
– Private-value auctions:
• Shade bid in first-price and Dutch auctions, but bid true value in
second-price or English auctions
– Common-value auctions:
• Winner’s curse (winning is bad news) makes everyone bid less
aggressively, and shade even in the second-price auctions
•
In private-value auctions with symmetric, risk-neutral bidders and
independent signals, all four main formats generate the same expected
revenues.
•
The outcomes in English auctions and second-price sealed-bid
auctions are Pareto efficient.
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Practice & Further Reading
•
Practice – Auctions:
– Varian Review Questions and Workout book
– Weekly Assignment: WT–Assignment 9 for Classes in Week 11
(Moodle)
– Additional Lecture Practice examples with solutions in Week 10
(Moodle)
•
Optional Readings (available on Moodle):
– Robert B. Wilson (Nobel 2020): Can auctions guarantee fair
competition?
– Paul Milgrom (Nobel 2020): Can market design create a more
sustainable world?
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Agenda
• Part I: Auctions
–
–
–
–
–
Recap: Auctions & Types of Auctions
Private-Value Auctions: Optimal Bidding Strategy
Common-Value Auctions and The Winner’s Curse
Other Types of Auctions
Wrap-up & More-Practice
• Part II: Review & Exam Advice
– Review of the course objectives and material.
– Exam format: What to expect from your exam paper?
– Revision and Exam tips.
Part II: Review and Exam Advice
•
Review of the WT objectives and material.
•
Exam format: What to expect from your exam paper?
•
Revision and Exam tips.
•
Spring Term Support
Topics Covered during the WT
•
Game Theory: Developing mathematical tools for analysing strategic
interactions.
•
Oligopoly: Examining market structures with few competitors and strategic
decision-making (pricing and output).
•
Externalities: Understanding how economic activities may impose costs or
benefits on third parties not directly involved in a transaction.
•
Public Goods: Examining the optimal and private provision of goods that are
non-excludable and non-rivalrous.
•
Asymmetric Information (Adverse Selection and Moral Hazard): Exploring
how differences in information affect market outcomes.
•
Auctions: Investigating mechanisms for allocation and pricing in competitive
bidding environments.
•
(Optional) Behavioural Economics: Challenging conventional assumptions
by exploring how psychological factors may influence economic decisions.
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Connecting the dots: Market Failures
•
Across these topics, the focus remains on how market mechanisms work—
or fail—to allocate resources efficiently.
•
Market Failures:
• Market Power: firms with market power will set 𝑝 > 𝑀𝐶 , leading to
reduced output and higher prices compared to competitive markets.
• Externalities and Public Goods
• Externalities: External effect on third party not reflected in market
prices. This can lead to under-provision or over-provision compared
to the socially optimal level.
• Public Goods: Nonexclusive, nonrival goods. Private provision of
public good often lead to underprovision due to free riding problem.
• Asymmetric Information: When one party in the transaction has
informational advantage over the other, it can lead to lower trade and, in
extreme cases, some markets may never develop.
55
Connecting the dots: Strategic Behaviour
•
In all the first-term material, economic agents take the actions of the other
agents in their market as given. Each agent optimises against known and
fixed terms.
•
In almost all the second-term material, decision-making becomes strategic
on the part of at least one agent.
•
For example:
– In an Oligopoly, the presence and actions of competitor firms determine
each firm’s marginal revenue function.
– In an auction, each bidder must choose a bid based on beliefs about
other bidders’ valuations and bidding strategies.
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Part II: Review and Exam Advice
•
Review of the WT objectives and material.
•
Exam format: What to expect from your exam paper?
•
Revision and Exam tips.
•
Spring Term Support
Exam: General Remarks
•
Exam Date: 18 May 2026, 14:30 hrs.
•
Exam Length: 3 hours (No reading time).
•
The exam is a closed-book assessment.
•
You are allowed to use permitted calculators.
– Make sure you have a Casio fx-83 or fx-85 calculator for the exam!
•
You must leave the question paper on your desk at the end of the
examination.
– Reason: it contains your answers to Section A (multiple-choice
questions).
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What to expect from your exam paper?
•
The exam contains 16 compulsory questions distributed in two sections.
– Section A (40%): 12 multiple choice questions
• This section is 40% of the exam.
• Each question is worth 3.33%.
• There is only one correct answer per question.
• There is no penalty for wrong answers.
• You must enter your answers in the space provided in the question
paper.
– Section B (60%): 4 compulsory questions.
• Each question from Section B is worth 15%.
• The questions will be analytical, with some scope for discussion.
• The average level of the exam questions will be of a slightly lower
difficulty than the average level of the assignment questions.
• Answers should be justified by showing work in your answer
booklet.
59
What to expect from your exam paper?
•
Example: Spring 2025 Exam
Section A
• 12 compulsory MCQs (AT and WT
material)
• Enter your answers in the space
provided (squares)
• Only one valid answer.
• Total mark: 40% (3.33% each
question)
60
What to expect from your exam paper?
•
Example: Spring 2025 Exam
Section B
• 4 compulsory questions (AT and
WT material)
• A question is a set of parts.
• You should answer ALL questions
and ALL parts (it can include
graphs!)
• Answers should be justified by
showing work in your answer
booklet.
61
Tips to Tackle the Exam
•
Read the questions carefully!
•
Questions are mostly quantitative, but you can be asked about a theoretical
concept or a graph.
•
For section A:
– Check that you are answering all questions.
– If you are unsure about a question, work smart with the answer options:
• Use elimination first. Perhaps some options are inconsistent with basic logic.
• Check for plausibility: e.g., “what should the answer roughly look like?”
(positive/negative, bigger/smaller, zero/non-zero).
– Review your answers. Common traps in quantitative MCQs:
• Mixing up concepts (e.g., substitution vs income effects; price vs quantity)
• Math mistakes-sign errors (especially when rearranging expressions).
– Finally, double-check that (1) you are providing only one answer, (2)
your answer matches your calculations, and (3) you are answering all
12 questions (no penalty for wrong answers!).
62
Tips to Tackle the Exam
•
For section B:
– Don’t jump into writing your answer! Take a few minutes to understand
the problem/model.
– Determine a way to solve it and organise your answer.
– Carry out the procedure you have devised.
– Important: Justify your answers by showing your calculations and the
steps taken to arrive at the final answer.
• Show and explain your calculations (credit can only be given if all workings
are shown!!)
• Show all steps in solving the question and briefly explain them.
• Structured, careful work keeps you from making mistakes, allows you to find
them when you do make them, and may give you partial credit for what you
do know, even if your ultimate answer is incorrect or incomplete.
– Check your answers: does your answer make sense? Are you
answering all questions? Are you answering the specific question or a
different one?
63
Tips to Review for the Exam
•
Ensure that you cover ALL material in the syllabus in preparation for the
exam.
– Every topic on the syllabus is a legitimate examination target.
– Any aspect/concept/model in the course can come up in exam
questions.
•
Do not rely on question spotting strategy.
– Topics and questions vary from year to year.
– Do not assume that topics or specific questions that have come up in
past examinations will occur again.
•
Don’t memorise but understand.
– Make sure you feel comfortable with the models, the assignments, etc.
64
Tips to Review for the Exam
•
The lecture slides and assignment questions are the best guide to the
material covered.
•
Work on the course material & ask yourself to summarise the main
concepts and the main findings of each topic.
– Make sure you understand the concepts and main findings from each
topic by using the course material and the Varian book.
– Try to summarise each topic yourself (e.g., by using concept maps,
summary tables).
– Recall the examples that you have studied and how they relate to the
theory of each chapter.
65
Tips to Review for the Exam
•
Understand the models in the course: why we setup the problem the way
we do, and every step we take in solving for a solution.
•
Check your understanding of each model in different ways
Can you explain its main arguments in a few simple words?
Can you solve the model analytically?
Can you draw the corresponding graphs (if any)?
•
Do you understand the models and solutions intuitively? Can you place
each model in its overall context?
•
Don’t memorise any formulas but understand.
•
Practice, practice, practice (e.g., assignments, quizzes, past exams, etc.)
– If you require extra practice, create your own practice questions by
slightly changing numbers.
•
And don’t forget to ask your questions during the Spring term support.
66
Draft of the Spring Term Support
Spring Term Support
(1) Subject to change. The final version will be announced and published on Moodle well before the
Spring Term on 5th May.
(2) Catherine OH: TBA
Bank Holiday
GOH (Misha, WT)
11:00-11:45, Room: TBA
OH (Misha, WT)
11:45-12:30, Room: TBA
OH (David, AT-WT)
15:00, Room: TBA
GOH (Misha, WT)
11:00-11:45, Room: TBA
OH (Misha, WT)
11:45-12:30, Room: TBA
Review Session (AT, Catherine)
14:00-16:00
CBG.B1.02
OH (David, AT-WT)
12:30, Room: TBA
GOH (Raquel, WT)
10:30-11:15, CKK1.09
OH (Raquel, WT)
11:15-12:00, CKK1.09
GOH (Raquel, WT)
10:30-11:15, SAL.LG.18
OH (Raquel, WT)
11:15-12:00, SAL.LG.18
OH (Hugo, AT)
10:00, online
Zoom link: TBA
Review Session (WT, Raquel)
14:00-16:00
CBG.B1.02
OH (Hugo, AT)
10:00, online
Zoom link: TBA
Moodle-Forum
MG207 Exam,
18 May, 14:30
GOH: Group Office Hours (Drop-in Session)
OH: Office Hours, bookable via LfY
67