Sponsored Search Auctions with Markovian UsersG. Aggarwal & J. Feldman & S. Muthukrishnan & Martin Pal

Brammert Ottens & Florent Garcin

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Sponsored Search• Keyword auctions are used to assign ads to slots• Most commonly used auction is the Generalised

Second Price (GSP) auction- Bidders submit bid- Ads are placed in descending order based on- is the inherent quality of the add

• This model ignores the search engine user!

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Original Model• Every add i has an inherent quality

• Every position j has a probability of being looked at

• Every bidder i makes a bid

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Model Properties• The user:

- The higher an add is placed, the more likely it is clicked on

- The better the add is, the more clicks it gets

• The bidder:- Bidding should be intuitive, i.e. position and click

rate should be monotone in the bid

New Model• Assumptions;

- A users scans from top to bottom- Click probability is dependent on other adds- An add should have two parameters

‣ The probability of clicking

‣ The probability of looking at the next add - and are independent

New Model

New Model

• Value per expression (ecpm)

New Model

• Value per expression (ecpm)

• a-ecpm

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Finding the winnerTheorem 1. In the most efficient assignment, the ads that are placed are sorted in decreasing order of a-ecpm

ExampleBidder

1 $1 0,75 4

2 $2 0,2 2,5

3 $0.85 0,8 4,25

Bidder DominanceTheorem 2. For all bidders in an optimal assignment, if some bidder is not in the assignment, and and , then we may substitute for and the assignment is not worse.

Finding the winnerTheorem 3. Let be some number of positions and let be an arbitrary set of bidders. Then, for all , there is somewhere

Intuitive biddingTheorem 4. As a bidder increases her bid (keeping all other bids fixed):

(a) the probability of her receiving a click in the optimal solution does not decrease, and

(b) her position in the optimal solution does not go down

Overview1. Sponsored Search

2. Original Model

3. New Model

4. Finding the Winner

5. Assignment Algorithms

Assignment Algorithms1. Sort the ads in decreasing order of a-ecpm

2. Solve the following recurrence relation

Assignment Algorithms1. Sort the ads in decreasing order of a-ecpm

2. Construct a solution from a solution by solving

Points for discussion• Independence of and . Realistic or not?• What is near-linear about the Near-linear Time

Algorithm?• How about GSP pricing?• What types of simple bidding strategies are there?