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Social Networks 101 P ROF. J ASON H ARTLINE AND P ROF. N ICOLE I MMORLICA

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DO NOT OPEN YOUR ENVELOPES!

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Lecture Three: How are real markets designed?

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Auctions eBay FCC spectrum license AdWords Christies Sothebys Google IPO Dutch flower auctions US treasury bonds US government contracts(?)

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Common auction forms Sealed-bid 1st-price auction 1.Bidders submit bids in sealed envelopes 2.Highest bidder wins and pays what he bid Example: government contracts

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Example Id pay 2 pts for that. Id pay 5 pts for that. 2 pts.4 pts.

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Example 2 pts.4 pts.

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

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

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

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The auction game Experiment (1 st 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.

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

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The auction game Experiment (1 st 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 1 st price auction to determine the winner and the payments. You will earn the number of points equal to your payoff.

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Win: – Price: 0 Payoff: 0 pts. Win: 5 Price: 2 Payoff: 3 pts. 1 st price auction analysis Bidder 1Bidder 2 Value Bidder 2s bid. Payoff is area here. BidValue

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1 st 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 opponents bid. Try to guess it! (based on probabilistic info)

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Time for

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

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

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Equilibrium bidding strategies payoff 2 = Pr[win] x (value – bid) = Pr[b 2 > b 1 ] x (v 2 – b 2 ) = Pr[b 2 > v 1 /2] x (v 2 – b 2 ) = Pr[2 b 2 > v 1 ] x (v 2 – b 2 ) = (2 b 2 ) x (v 2 – b 2 ) If bidder 1 follows equilibrium and bids b 1 = v 1 /2, what b 2 should bidder 2 pick? 01 x v1v1

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Equilibrium bidding strategies Maximize payoff 2 If bidder 1 follows equilibrium and bids b 1 = v 1 /2, what b 2 should bidder 2 pick? b 2 = v 2 /2 d [(2 b 2 ) x (v 2 – 2 b 2 )] / db 2 = 0 d [(2 b 2 v 2 – 2 (b 2 ) 2 )] / db 2 = 0 2 v 2 – 4 b 2 = 0

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

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1 st price auction How did you bid?

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

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