The Structure of Networks

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Presentation transcript:

The Structure of Networks with emphasis on information and social networks 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 items 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?