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Social Networks 101

Social Networks 101. Prof. Jason Hartline and Prof. Nicole Immorlica. DO NOT OPEN YOUR ENVELOPES!. Lecture Three : How are real markets designed?. Auctions. Dutch flower auctions. AdWords. eBay. US treasury bonds. FCC spectrum license. Sotheby’s. Christie’s. Google IPO.

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Social Networks 101

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  1. Social Networks 101 Prof. Jason Hartline and Prof. Nicole Immorlica

  2. DO NOT OPEN YOUR ENVELOPES!

  3. Lecture Three: How are real markets designed?

  4. Auctions Dutch flower auctions AdWords eBay US treasury bonds FCC spectrum license Sotheby’s Christie’s Google IPO US government contracts(?)

  5. Common auction forms Sealed-bid 1st-price auction • Bidders submit bids in sealed envelopes • Highest bidder wins and pays what he bid Example: government contracts

  6. Example I’d pay 2 pts for that. I’d pay 5 pts for that. 2 pts. 4 pts.

  7. Example 2 pts. 4 pts.

  8. Example I win nothing and pay nothing, my payoff is zero.

  9. Example I win the painting: +5 I pay my bid: -4 My payoff is: +1pt.

  10. Auction questions How should you bid? Who will win? How much money does auctioneer get?

  11. The auction game Experiment (1st price auction): One of your envelopes has a black X on it. In the envelope is a card with a number indicating your value for the item we will sell. You will compete in the auction with exactly one other buyer.

  12. The auction game Experiment (1st price auction): This is the item you want. One other person also wants this item. 1st price: = 5 pts This is your value for the item. We computed your value with an iPhone (uniform [0,6]).

  13. The auction game Experiment (1st price auction): On your card, 1. Write YOUR NAME on your card and how many points you wish to bid. 2. Put the paper in your envelope, pass it to TAs. We will run a 1st price auction to determine the winner and the payments. You will earn the number of points equal to your payoff.

  14. 1st price auction analysis Value 6 5 Payoff is area here. 4 3 Bidder 2’s bid. 2 1 Bid Value Bidder 1 Bidder 2 Win: – Price: 0 Payoff: 0 pts. Win: 5 Price: 2 Payoff: 3 pts.

  15. 1st price auction analysis You would like to bid just above your opponent (if it is less than your value). But you do not know your opponent’s bid. Try to guess it! (based on probabilistic info)

  16. Time for Math Corner

  17. 1st price auction analysis Guess equilibrium bidding strategy. (2 bidders, values uniform [0,1])

  18. Equilibrium bidding strategy Proposed equilibrium: bid(value v) = v/2.

  19. Equilibrium bidding strategies If bidder 1 follows equilibrium and bids b1 = v1/2, what b2 should bidder 2 pick? payoff2 = Pr[win] x (value – bid) = Pr[b2 > b1] x (v2 – b2) = Pr[b2 > v1/2] x (v2 – b2) = Pr[2 b2 > v1] x (v2 – b2) = (2 b2) x (v2– b2) v1 0 1 x

  20. Equilibrium bidding strategies If bidder 1 follows equilibrium and bids b1 = v1/2, what b2 should bidder 2 pick? Maximize payoff2 d [(2 b2) x (v2 – 2 b2)] / db2 = 0 d [(2 b2v2 – 2 (b2)2)] / db2 = 0 2v2 – 4 b2= 0 b2 = v2/2

  21. Equilibrium bidding strategy bid(value v) = v/2. (Both players are playing a best response to each other.)

  22. 1st price auction How did you bid?

  23. Next time back to social networks (for the next 3 weeks)

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