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Revenue Maximization Thus, Virtual surplus is truthfulif and only ifϕj(v )jis monotone non-decreasing invj Myerson Mechanism: Given bids b and F (here Bayesian – Nashdistribution), compute ‘virtual bids’: b ′ = ϕ (b ) Run VCG on b’ to get x’ and p’1 Output x=x’ and p with p = ϕ − (p ′)i i ii i i
Revenue Maximization F is the Bayesian – Nash distributionof of the generalized Vickrey(second price) auction (second price)with reserve prices Proof similar with the Vickrey (secondprice) auction (second price) withreserve price for 1 item
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 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 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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