with emphasis on information and social networks T214SINE Summer 2011 Chapter 15 Ýmir Vigfússon Sponsored search How should we set prices Lots of different keywords Should we post prices like a store ID: 247240
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Slide1
The Structure of Networks
with emphasis on information and social networks
T-214-SINE
Summer 2011
Chapter
15
Ýmir VigfússonSlide2
Sponsored search
How should we set prices?Lots of different keywordsShould we post prices (like a store)?Too many keywords and advertisersWhat 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?Slide3
Sponsored search
Ad slots have different characteristicsDiverse clickthrough ratesSome slots more valuable than othersWhat if we knew the buyers‘ valuations?Assign buyers to slots
Known as a matching market (Chapter 10)
Let‘s review the propertiesSlide4
MatchingsSlide5
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 setSlide6
MatchingsSlide7
Matchings
Thm: A bipartite graph has a perfect matching if and only if there is no constricted setConstricted sets are the
only
obstacles to perfect matchingsSlide8
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 getSlide9
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
)Slide10
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 matchingSlide11
Matching markets
Thm: Market clearing prices always produce socially optimal outcomeMaximum total valuation of any matching
What about sponsored search?
Use matching markets to handle sponsored search when
valuations are knownSlide12
Sponsored search
If there is just one ad slotRun an auctionIf we knew the advertisers‘ valuationsRun 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?Slide13
Sponsored search
(See other slides)