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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Lory Al Moakar
Pj = VN-iM – VN-iM-j
Assume i lies and is assigned slot k ≠ j which is the slot i gets if it does not lie.
= optimal valuation – (total valuation when i gets k) ≥ 0
payoff = 28 – 4 = 24 < 30 a1 does not have the incentive to lower its bid
payoff = 60 – 40 = 20 a2 does not have the incentive to lower its bid
the advertiser with the highest valuation per click gets the top slot
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
price per click for slot j : pj* = pj / rj
show that p1* p2* p3* …… pM*
show that pj* pk*
Vk* – pk* Vk* – pj* pj* 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.
where j < k
advertiser j doesn’t want slot i at the current price so j does not want this slot at a higher price
this set of bids forms a Nash Equilibrium
the worst equilibrium for the search engines
the best equilibrium for the advertisers
Not clear if it maximizes revenue
Has one optimal equilibrium
truth-telling is generally not an equilibrium strategyConclusions