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
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
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