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Equilibrium PropertiesGFP: Bayes-Nash symmetric equilibrium argument identical to that of the sealed bid firstprice auction for a single good for symmetricbidders (same distributions) the revenueequivalence theorem implies that revenue from GFPis the same as any other auction that allocatesaccording to bid order. Revenue Equivalence Principle Under certainweak assumptions, for every two Bayesian–Nashimplementations of the same social choice function f, we have that if for some type t’ of player i, theexpected (over the types of the other players)payment of player i is the same in the twomechanisms, then it is the same for every value ofi’s type t.
Equilibrium Properties GSP: Today nothing is known about theBayesian equilibrium of the GSP auction Special Case: CTRs are separable:α = µ βij i jspecial case:α = µ Locally Envy-Free equilibriaiji
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 42 and 43: GSP Equilibrium Properties Retaliat
Page 44 and 45: GSP Equilibrium Properties An equil
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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