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The Structure of Networks

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

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The Structure of Networks

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  1. The Structure of Networks with emphasis on information and social networks T-214-SINE Summer 2011 Chapter 15 Ýmir Vigfússon

  2. 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?

  3. 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

  4. Matchings

  5. 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

  6. Matchings

  7. 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

  8. 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

  9. 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)

  10. 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

  11. 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

  12. 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?

  13. Sponsored search • (See other slides)

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