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GSP Equilibrium Properties An equilibrium of the simultaneous-movegame (Γ) induced by GSP is locally envyfreeif a player cannot improve his payoff byexchanging bids with the player ranked oneposition above himµ v − p ≥ µ v − pi g(i) i i−1 g(i) i−1
GSP Equilibrium PropertiesLEMMA 1: The outcome of any locally envy-freeequilibrium of auction Γ is a stable assignment.Proof:no advertiser can profitably rematch with a positionassigned to an advertiser below him (equilibrium)µ v − p ≥ µ v − pi g(i) i i+ 1 g(i) i+1
Page 1 and 2: Sponsored Search Auctionsτου Κ
Page 3 and 4: Introduction For example, Apple or
Page 5: Introduction We call each position
Page 8 and 9: Introduction Today, Internet giants
Page 10 and 11: Existing Models Static Vickrey Clar
Page 12 and 13: Static Αssumptions Bidders prefer
Page 14 and 15: Revenue Maximization Result of Myer
Page 16 and 17: Revenue Maximization Surplus Alloca
Page 18 and 19: Revenue Maximization Thus, Virtual
Page 20 and 21: Revenue Maximization Revenue withou
Page 22 and 23: Revenue Maximization Revenue withou
Page 24 and 25: Revenue Maximization Revenue with r
Page 26 and 27: Allocative Efficiency Letxij= 1if b
Page 28 and 29: VCG Dual:k∑min p + qnii= 1 j=1i j
Page 30 and 31: VCG Cons requires solving a computa
Page 32 and 33: GSP Let w1,…,wn be the weights on
Page 34 and 35: GFP not truthful Payoff in general:
Page 36 and 37: GSP not truthful Payoff in general:
Page 38 and 39: VCG PayoffPayoff in general:eachbid
Page 40 and 41: Equilibrium PropertiesGFP: Bayes-Na
Page 42 and 43: GSP Equilibrium Properties Retaliat
Page 46 and 47: GSP Equilibrium Properties Proof (c
Page 48 and 49: GSP Equilibrium PropertiesLEMMA 2:
Page 50 and 51: GSP Equilibrium Properties Proof (c
Page 52 and 53: GSP Equilibrium Properties Proof:Pa
Page 54 and 55: Dynamic Aspects Online Allocation P
Page 56 and 57: Online Allocation Problem LP:
Page 58 and 59: Online Allocation ProblemComplement
Page 60 and 61: Online Allocation Problem Greedy pr
Page 62 and 63: Online Allocation Problem Can we do
Page 64 and 65: Analyzing BALANCE
Page 66 and 67: Worst Case for BALANCE N advertiser
Page 68 and 69: BALANCE Algorithm βj’s as a func
Page 70 and 71: BALANCE Algorithm When k tends to i
Page 72 and 73: BALANCE Algorithm Lemma Proof: Cons
Page 74: Bibliographic NotesG. Demange, D. G

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