The Structure of Networks
with emphasis on information and social networks
T-214-SINE
Summer 2011
Chapter 15
Ýmir Vigfússon
Sponsored search

How should we set prices?
◦ Lots of different keywords

Should we post prices (like a store)?
◦ Too many keywords and advertisers

What if there were just one ad slot?
◦ Just a single-item auction!
◦ Sealed-bid second-price auction appealing

But we have multiple ad slots
◦ How do we deal with that?
Sponsored search

Ad slots have different characteristics
◦ Diverse clickthrough rates
◦ Some slots more valuable than others

What if we knew the buyers‘ valuations?
◦ Assign buyers to slots
◦ Known as a matching market (Chapter 10)
◦ Let‘s review the properties
Matchings
Matchings

Def: A perfect matching (i) assigns
everybody on the left with someone on
the right, and (ii) no two nodes on the left
are assigned to the same node on the
right

Def: If the neighbors N(S) of some set S of
nodes are fewer than the nodes in S, then
S is constricted set
Matchings
Matchings

Thm: A bipartite graph has a perfect
matching if and only if there is no
constricted set

Constricted sets are the only obstacles to
perfect matchings
Matching markets

Right nodes have a valuation for every
node on the left
◦ How much do you want each item?

Quality of matching assignment = Sum of
the valuations for people get
Matching markets

Buyer‘s payoff = valuation – price paid

Thm: We can always set prices so that if
buyers buy the item they most want, all
items are sold (market clearing prices)
Matching markets

How does this work?
◦ We connect each buyer to the most
preferred seller
◦ Raise prices for items that are in high demand
◦ Repeat, stop when there is a perfect matching
Matching markets

Thm: Market clearing prices always produce
socially optimal outcome
◦ Maximum total valuation of any matching

What about sponsored search?
◦ Use matching markets to handle sponsored
search when valuations are known
Sponsored search

If there is just one ad slot
◦ Run an auction

If we knew the advertisers‘ valuations
◦ Run a matching market (Chapter 10)

What if we don‘t know the valuations?
◦ Want to encourage truthful bidding
 Like in the second-price auctions we looked at
◦ How do we do that?
Sponsored search

(See other slides)