Economics and computation Week 10 Auctions Prof Pingzhong

Economics and computation Week 10: Auctions Prof. Pingzhong Tang kenshin@tsinghua. edu. cn http: //iiis. tsinghua. edu. cn/~kenshin/ec/ 11/25/2020 Pingzhong Tang 1

The oldest auction? 11/25/2020 Pingzhong Tang 2

Babylon auctions of women for marriage (500 BC) 11/25/2020 Pingzhong Tang 3

Fun facts of Babylon marriage auction • Two groups • Group 1: Men pay women for marriage • Group 2: Women pay men for marriage • Order of auction • In descending order of beauty • Beauty is in the eye of the auctioneer • No outside option • Illegal to get married via any other means • Get-along phase • In case of mutual rejection --- refund and re-auction 11/25/2020 Pingzhong Tang 4

Melbourne Tea Auction 11/25/2020 Pingzhong Tang 5

Dutch flower auction (Aalsmeer) 11/25/2020 Pingzhong Tang 6

Japan Bluefin Tuna Auction • 34 usd (Spain) vs 46 usd (Japan) • Record price: 1. 7 M USD, 220 KG • Fish market = 43 football courts • Largest seafood market 11/25/2020 Pingzhong Tang 7

A common feature • Value decreases quickly, not available for long • Flower, Tuna, Tea • Use auction as a means to • aggregate demand • increase competition 11/25/2020 Pingzhong Tang 8

An e. Bay auction 11/25/2020 Pingzhong Tang 9

A closer look 11/25/2020 Pingzhong Tang 10

Another e. Bay Auction 11/25/2020 Pingzhong Tang 11

Taobao auctions • 珍品拍卖 • http: //paimai. taobao. com/ • 司法拍卖 • http: //sf. taobao. com/ • 公益拍卖 • 手机号拍卖 11/25/2020 Pingzhong Tang 12

珍品拍卖 11/25/2020 Pingzhong Tang 13

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司法拍卖 • Sell frozen, corrupted assets, to compensate loss • “腐败多 上淘宝” 11/25/2020 Pingzhong Tang 15

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Crowd sourcing ≈ all-pay auction Nokia ringtone and Netflix prize IJCAI competition on predicting repeated buyers in Taobao 11/25/2020 Pingzhong Tang 17

Sponsored search: selling advertisement

Sponsored Search 11/25/2020 Pingzhong Tang 19

Google ads 11/25/2020 Pingzhong Tang 20

Ads on Gmail 11/25/2020 Pingzhong Tang 21

Baidu Ads 11/25/2020 Pingzhong Tang 22

FCC wireless spectrum auction (Since 2004, analog digital) 11/25/2020 Pingzhong Tang 23

FCC incentive auction (Upcoming) Broadcast Mobile 11/25/2020 Pingzhong Tang 24

Many others • Priceline. com • For hotel, car • Shanghai Car plate auction • Central China wheat auction • UK milk/dairy auction • The most important format of e-commerce! 11/25/2020 Pingzhong Tang 25

Auctions • What is auction ? • Methods for allocating goods, tasks and resources • Participants: one seller, at least one bidder/buyer • Agreement between seller and bidders • Who gets the good/item? • How much does everyone pay? • Reverse auction: one buyer, multiple sellers • Auction is a direct quasi-linear mechanism

Classification • Selling a single item • Sell an Hermes handbag • Selling multiple identical items • Google advertising • Wheat • Selling multiple distinct items • Wireless spectrum • Airport departure/landing slots 11/25/2020 Pingzhong Tang 27

Single-item auctions 11/25/2020 Pingzhong Tang 28

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Analysis of auctions 11/25/2020 Pingzhong Tang 35

Independent private value (IPV) assumption • Each buyer i has a private valuation vi towards the item • Maximum amount of money i is willing to pay • vi represents buyer’s type, lose generality? • • • vi is drawn from a publicly known distribution F Only buyer i knows the realization of vi Others, including the seller, know F only Valuations are I. I. D Technical assumptions on CDF F • [0, vmax] • Admits a continuous density function, full support 11/25/2020 Pingzhong Tang 36

The induced Bayesian game • Strategy of buyer i • For any realization of vi, specify a bid bi • Formally: si(vi)= bi • Strategy profile: • 11/25/2020 Pingzhong Tang 37

Dominant strategy equilibrium (DSE) 11/25/2020 Pingzhong Tang 38

Bayes Nash equilbrium (BNE) 11/25/2020 Pingzhong Tang 39

Results on second price auction 11/25/2020 Pingzhong Tang 40

Truthfulness • Theorem: Truthfulness (si(vi)=vi) is a dominant strategy in second-price auction. • Proof. One sentence? • Let’s look at a more direct proof 11/25/2020 Pingzhong Tang 41

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Case 1 11/25/2020 Pingzhong Tang 43

Case 2 11/25/2020 Pingzhong Tang 44

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All these auctions are efficient • Item goes to the buyer with the highest value • In other words, these auctions maximize social welfare 11/25/2020 Pingzhong Tang 46

Results on first price auction 11/25/2020 Pingzhong Tang 47

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Solving BNE of first price auction? • Two bidder symmetric uniform • Vickrey. 1950 s. • Two bidder, asymmetric uniform (2010) • http: //econ. haifa. ac. il/~todd/mypapers/kzuniformfinal 1 pdf file. pdf • Two bidder, general case • Open! • Two bidder, sequential case • The deadly-genius lazy bidder: closed-form solution of Bayes Stackberg equilibrium in First price auction. Pingzhong Tang and Zihe Wang 11/25/2020 Pingzhong Tang 54

Which one gives a higher revenue? Which one is better for buyers? 11/25/2020 Pingzhong Tang 55

Revenue equivalence: a first glance • Order statistic of n iid variables • v(1) is the highest value • v(k) is the k-th highest value • Fact: • Two buyers, uniform [0, 1], revenue comparison • 1 st price: ½* v(1) = 1/2*2/3 = 1/3 • 2 nd price: v(2)= 1/3 11/25/2020 Pingzhong Tang 56

Revenue equivalence: a first glance • n buyers, uniform[0, 1] • 1 st price: n-1/n* v(1) = (n-1/n)*(n/n+1)=n-1/n+1 • 2 nd price: v(n) = n-1/n+1 • Exercise: n buyers, iid drawn from F on [0, 1] • Fact: 1 st price auction: si(vi)= E(v(1)| v(1) <vi) • v(1) now denotes first-order statistic of n-1 values • Show revenue equivalence • Question: • How general can this equivalence hold? 11/25/2020 Pingzhong Tang 57

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