Sponsored Search. Presenter: Lory Al Moakar. Outline. Motivation Problem Definition VCG solution GSP(Generalized Second Price) GSP vs. VCG Is GSP incentive compatible? GSP has a Nash Equilibrium formed of market clearing prices.
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Sponsored Search
Presenter:
Lory Al Moakar
6
a1â€¢
a2â€¢
a3â€¢
â€¢s1
â€¢s2
â€¢s3
2
0
Pj = VN-iM â€“ VN-iM-j
Assume i lies and is assigned slot k â‰ j which is the slot i gets if it does not lie.
= optimal valuation â€“ (total valuation when i gets k) â‰¥ 0
Counterexample:
ïƒ payoff = 28 â€“ 4 = 24 < 30 ïƒ a1 does not have the incentive to lower its bid
ïƒ payoff = 60 â€“ 40 = 20 ïƒ a2 does not have the incentive to lower its bid
ïƒ the advertiser with the highest valuation per click gets the top slot
ïƒ advertiser i gets slot i
1. Construct a set of bids that produces a set of market clearing prices
Consider a set of market clearing prices pj
ïƒ price per click for slot j : pj* = pj / rj
show that p1* ï‚³ p2* ï‚³ p3* â€¦â€¦ï‚³ pM*
Proof:
ïƒ show that pj* ï‚³ pk*
ïƒ Vk* â€“ pk* ï‚³ Vk* â€“ pj* ïƒ pj* ï‚³ pk*
2. These bids form a Nash equilibrium
Show that with the above bids, no advertiser wants to lower his/her bid and no advertiser wants to raise his/her price.
Proof:
where j < k
ïƒ advertiser j doesnâ€™t want slot i at the current price so j does not want this slot at a higher price
ïƒ this set of bids forms a Nash Equilibrium
Counterexample:
VCG
the worst equilibrium for the search engines
the best equilibrium for the advertisers
Incentive compatible
GSP
Not clear if it maximizes revenue
Has one optimal equilibrium
truth-telling is generally not an equilibrium strategy