5- Keyword auctions

Question 1

What is the measure of success of pay-per-click (PPC) advertising?

Answer 1

Click-through-rate (CTR)

Question 2

What is the formula for click-through-rate (CTR)?

Answer 2

♯users clicking on ad/♯users viewing ad

Question 3

Describe a Generalised Second-Price auction (GSP)

Answer 3

-Each advertiser places a bid
-Bids are ranked by value
-Each bidder pays the next highest bid for each click

Question 4

In a GSP auction, how does the number of bidders relate to the links displayed?

Answer 4

There is always at least 1 more bidder than the number of links awarded. If there are only 3 bidders then only 2 sponsored links are displayed.

Question 5

What is the net payoff for a click?

Answer 5

Valuation for a click - price per click

Question 6

What is the net payoff per hour of a position?

Answer 6

Net payoff per click x clicks per hour

Question 7

What problem did Google identify with the base GSP auction?

Answer 7

Click frequency depends on advertiser, but if click frequency is low then Google’s revenue is low

Question 8

What are the 4 determinants of quality score?

Answer 8

-CTR
-ad relevance
-user experience (UX)
-other things (secret sauce)

Question 9

What is the Final score of a bidder?

Answer 9

Final score = Bid x Quality score

Question 10

How are bidders charged when pricing with quality scores?

Answer 10

Advertisers are ranked according to the final score. Charge each advertiser the lowest price/click p such that final score is greater than next highest

Question 11

What 3 simplifying assumptions do we use to analyse GSP auctions?

Answer 11

-Valuations are commonly known: eventually, advertisers learn all the relevant information.
-Stable bids must form a Nash equilibrium of the
simultaneous-move, one shot game of complete information.
-We use simple strategies

Question 12

Describe a Simple strategy

Answer 12

-Opponent is currently beating your bid
-Player slightly increases bid such that their price and position is the same but opponent must pay more
-Opponent retaliates by bidding slightly lower to swap ranks

Question 13

When will bidders use a Simple strategy?

Answer 13

If the Simple strategy improves their payoff

Question 14

Define Long run equilibrium

Answer 14

An equilibrium of the simultaneous-move game induced by GSP is locally envy-free if a player cannot improve her payoff by exchanging bids with the bidder one position above her

Question 15

What are the 2 conditions for Long run equilibrium?

Answer 15

-Nash equilibrium
-Envy freeness

Question 16

What is the equation/inequality for Long run equilibrium?

Answer 16

αᵢv₉₍ᵢ₎ - pᵢ ≥ αᵢ₋₁ - v₉₍ᵢ₎ - pᵢ₋₁

Question 17

When is an assignment stable?

Answer 17

An assignment (µ) of price p is stable if there’s no advertiser i and a position k such that:
µ(i) ≠ k (k not assigned to i)
αk ×vᵢ > (i’s net payoff under µ) + (k’s net payoff under µ)

Question 18

What is the main difference between equilibrium and stability?

Answer 18

In equilibrium only bidders have to be better off, whereas for stability the seller’s payoff matters too

Question 19

What is the relation between locally envy-free equilibria and stability?

Answer 19

The outcome of any locally envy-free equilibrium in the GSP auction is a stable assignment.

Question 20

Describe a Generalised English auction (GEA)

Answer 20

-Price clock starts at 0 and increases over time
-Advertisers choose price at which to drop out which will be their bid
-Advertisers ranked on bid and pay the bid of bidder just below them

Question 21

What is the perfect Bayesian equilibrium proposition for Generalised English auctions?

Answer 21

There is a unique equilibrium of the generalized
English auction, where an advertiser with valuation v drops out at price p*

Question 22

What is the formula for perfect Bayesian equilibrium price p*?

Answer 22

p* = v - αᵢ/αᵢ₋₁(v-bᵢ₊₁)

Question 23

What is the relationship between GEA equilibrium payoffs and VCG payoffs?

Answer 23

Equilibrium payoffs of GEA = VCG payoffs