Economic network analysis - Part 2

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NETWORKS, CROWDS AND MARKETS – CHAPTER 15
VANI KANDHASAMY, PSGTECH
1

Keyword based advertising
2

Multiple
Advertisers
2

Multiple
Advertisers
Higher slots
are expensive
2

Pricing of Keyword based advertising
3

▪Paying per click
• Based on a cost-per-click (CPC) model
• You only pay when a user actually clicks on the ad
• How a search engine should set the prices per click for different queries?
• Solution 1: Post prices for the keywords
• Problem: So many possible keywords and combinations of keywords, each appealing
to a relatively small number of potential advertisers
• Solution 2: Setting prices through an auction
• Problem: Multiple slots for displaying ads, and some are more valuable than others
3

▪If the advertisers’ valuations are known
• The situation could be represented as a matching market
▪If the advertisers’ valuations are not known
• Encourage truthful bidding Vickrey-Clarke-Groves principle (VCG)
• Generalized Second-Price Auction (GSP)
ad slots items
advertisers buyers
4

Advertising as a matching market
▪Clickthrough rates of the slots - the number of clicks per hour that an ad placed
in that slot will receive
▪Revenues per click of the advertisers - the expected amount of revenue
advertiser receives per user who clicks on the ad
5

▪Clickthrough rates of the slots - the number of clicks per hour that an ad placed
in that slot will receive
▪Revenues per click of the advertisers - the expected amount of revenue
advertiser receives per user who clicks on the ad
Price-setting with known valuations
ri - the clickthrough rate of slot i,
vj - the revenue per click of advertiser j,
ri.vj - the benefit that advertiser j receives from
acquiring slot i (valuations)
5

6

Market
Clearing Prices
6

The Vickrey-Clarke-Groves principle
▪Price-setting with unknown valuations
▪First price auction:
• Bids = revenues per click
• Slots are assigned in decreasing order of bids
• Price per click = Bids
▪Problem: Underbidding, prices are updated extremely frequently
▪Solution: Second-price auction where truthful bidding is a dominant strategy
▪Encouraging Truthful Bidding in Matching Markets
7

The Vickrey-Clarke-Groves principle
▪Price-setting with unknown valuations
▪First price auction:
• Bids = revenues per click
• Slots are assigned in decreasing order of bids
• Price per click = Bids
▪Problem: Underbidding, prices are updated extremely frequently
▪Solution: Second-price auction where truthful bidding is a dominant strategy
▪Encouraging Truthful Bidding in Matching Markets
What is the analogue of the second-price single-item auction for advertising
markets with multiple slots?
7

The VCG principle
▪The bidder who values the item the most gets it and the winner of
the auction is charged an amount equal to the harm she causes the
other bidders by receiving the item
• Suppose the bidders’ values are v1, v2, . . . , vn in decreasing order
• If bidder 1 were not present, the item would have gone to bidder 2, who
values it at v2
• The other bidders still would not get the item, even if bidder 1 weren’t there
• Thus, bidders 2 through n collectively experience a harm of v2 because bidder
1 is there
• This harm of v2 is exactly what bidder 1 is charged
Each individual is charged the harm she causes to the rest of the world
8

The VCG principle in matching markets
Assumptions:
▪Buyer j has a valuation of vij for the item being sold by seller i
▪Each buyer knows her own valuations, but that these valuations are not known to the other buyers
or to the sellers
▪Each buyer only cares which item she receives, not about how the remaining goods are allocated to
the other buyers
▪The buyers have independent, private values
Procedure:
▪Ask buyers to announce valuations for the items
▪Assign items to buyers so as to maximize total valuation(perfect matching/optimal assignment)
▪The price buyer should pay for seller item is the harm she causes to the remaining buyers
9

What prices does the VCG
principle dictate for each
buyer?
10

The harm that the
winner j causes to the
remaining buyers
The total boost in
valuation everyone else
would get if the optimal
matching is done
without buyer j
11

12

13

14

VCG prices
▪Let S denote the set of sellers and B denote the set of buyers.
▪Let 𝑉𝑆
𝐵
denote the maximum total valuation over all possible perfect matchings of sellers and
buyers.
▪Let S − i denote the set of sellers with seller i removed, and let B − j denote the set of buyers
with buyer j removed.
▪If we give item i to j, then the best total valuation the rest of the buyers could get is 𝑉𝑆−𝑖
𝐵−𝑗
▪If buyer j simply didn’t exist, but item i were still an option for everyone else, then the best total
valuation the rest of the buyers could get is 𝑉
𝑆
𝐵−𝑗
▪The total harm caused by buyer j to the rest of the buyers (i.e., the VCG price) pij
15

VCG as a game
▪Players -> buyers/advertisers
▪Strategy -> a set of valuations to
announce
▪Payoff -> valuation - price buyers’
pay
▪Dominant strategy -> truth-telling
16

MARKET CLEARING PRICES
▪Posted prices
▪Ascending auction
VCG PRICES
▪Personalized prices
▪Sealed-bid second-price auction
Maximizes the total valuation obtained by advertisers
17

MARKET CLEARING PRICES
▪Posted prices
▪Ascending auction
VCG PRICES
▪Personalized prices
▪Sealed-bid second-price auction
Maximizes the total valuation obtained by advertisers
But the search engines (sellers) cares about its revenue
17

Generalized second price auction
▪Each advertiser j announces a bid consisting of a single number bj
▪It is up to the advertiser whether or not its bid is equal to its true
valuation per click vj
▪Each slot i is assigned to the ith highest bidder, at a price per click
equal to the (i + 1)st highest bid
Each advertiser who is shown on the results page is paying a
price per click equal to the bid of the advertiser just below
them
18

GSP as game
▪Advertiser -> player
▪Bid -> strategy
▪Revenue minus the price -> payoff
▪Nash equilibria
▪Truth-telling might not constitute a Nash
equilibrium
▪There can be multiple possible equilibria
▪Some of equilibria may produce socially
non optimal assignments
19

Truth-telling may not be an equilibrium
20

X’s Price = 6 X 10 = 60
X’s Payoff = 70 – 60 = 10
20

5
X is underbidding
20

5
X’s Price = 4 X 1 = 4
X’s Payoff = 28 – 4 = 24
X is underbidding
20

Multiple and non-optimal equilibria
21

5
4
2
Advertisers X & Y are
underbidding
21

5
Nash equilibria exists &
assignment is socially
optimal
4
2
underbidding
21

22

3
5
1
underbidding
22

3
Nash equilibria exists &
assignment is not socially
optimal
5
1
underbidding
22

GSP Vs VCG
Get valuation from advertisers
Determine an assignment of slots to
advertisers
Determine prices to be paid by advertisers
23

GSP Vs VCG
advertisers
VCG Price
23

GSP Vs VCG
advertisers
VCG Price
GSP Price
23

GSP Vs VCG
advertisers
VCG Price
GSP Price
Does GSP or VCG provide more revenue to the search engine?
23

GSP Vs VCG
5
4
2
X’s price: 10 X 4 = 40
Y’s price: 4 X 2 = 8
Search engine’s total revenue: 48
What is the revenue to the search engine from the GSP equilibria?
24

GSP Vs VCG
3
5
1
X’s price: 10 X 3 = 30
Y’s price: 4 X 1 = 4
What is the revenue to the search engine from the GSP equilibria?
25

GSP Vs VCG
X’s price: (60 – 24) + (4 – 0) = 40
Y’s price: (4 – 0) = 4
What is the revenue to the search engine from the VCG principle?
26

GSP Vs VCG
Q: Does GSP or VCG provide more revenue to the search engine?
▪ Revenue with 1st equilibrium -> 48
▪Revenue with 2nd equilibrium -> 34
▪Revenue with VCG principle -> 44
A: Depends on which equilibrium of GSP the advertisers use
27

Economic network analysis - Part 2

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