1. Auctions
MS&E 212

2. Outline Auctions, an introduction
Sponsored search and online advertising
Online Advertising Markets By Aranyak Mehta, Google Research
Let me start with some examples. Display or banner advertising is one of the popular models for advertising over Internet. It’s a market for impressions. An impression refers to the display of an ad on a webpage viewed by a users. It is mainly used for creating brand awareness. Therefore, advertisers aim to reach millions of users. They also have complex preferences, that make the allocation problem computationally hard. For example, MANY INTERESTING PROBLEM 2

3. Auctions

4. Auctions A process of selling (or buying) an item by soliciting bids
Rich history: used for selling spoils of war, liquaditing assets of debtors by Romans
Used for selling diamonds, electromagnetic spectrum, ads, flowers, antiques

5. Auctions vs fixed price
Where is appropriate to use auctions?
Pros and cons of auctioning vs fixing the price?

6. English auctions
The bidders keep increasing the price until only the winner(s) are left:
Shotgun bidding,
candle auctions…

7. Dutch auction
price is reduced until a buyer is found.

8. First price (sealed-bid) auctions
All bidders simultaneously submit sealed bids, the item is given to the highest bidder paying the price (s)he submitted. Used in some government auctions, real state

9. Second price (sealed-bid) auctions
All bidders simultaneously submit sealed bids, the item is given to the highest bidder paying the second highest price submitted. Also known as Vickrey auction How is it different from English?

10. All pay auctions
Every bidder must pay regardless of whether they win the prize, which is awarded to the highest bidder as in a conventional auction. Competitions, the x prize

11. Incentive compatibility
In second price auctions, truthfulness is weakly dominant strategy
In first price auctions, that is not the case.

12. A simple auction One item, two bidders.
The utility of each bidder is a random number chosen uniformly at random from
What happens in a second price auction?
How does the equilibrium look like in a first price auction?
What is the expected revenue in each case?

13. The revenue equivalence theorem
Suppose bidders are risk neutral and their values are identically and independently distributed. Then any equilibrium of any auction game in which the bidder with the highest value wins the object, generates the same revenue in expectation. Proof is rather technical. Assumptions are quite important.

14. Is Vickrey the best you can do?
Same setup as before: one item, two bidders, values u.a.r. between 0 and $100. What if you put the reserve prices of $20? What is the optimum reserve price? Myerson’s optimal auction design.

15. Common value auctions
Suppose the auctioned item is of roughly equal value to all bidders, but the bidders don't know the item's market value when they bid. Each player independently estimates the value of the item before bidding.
Example: offshore oil field, spectrum auction, Venture Capital, IPO
The winner’s curse

16. Modern applications of auctions
Ebay
Electromagnetic spectrum
TV broadcast rights
Internet advertising

17. “Here it is – the plain unvarnished truth. Varnish it.”

18. Online advertising Advertisers as bidders
Bid is typically for a click (CPC)

19. Example
Mortgage Refinance IndyMac Bank (Advertiser's Max Bid: $6.00)
Mortgage Refinance - LendingTree.com (Advertiser's Max Bid: $4.57)
Refinance Quotes - LowerMyBills.com (Advertiser's Max Bid: $4.06)
Home Mortgage Refinance Rates (Advertiser's Max Bid: $4.05) ……

20. Online advertising Advertisers as bidders
Bid is typically for a click (CPC)
Which ads to display and in which order? How much to charge?

21. How do you sort the ads?
Sort by bid value: higher bids get higher positions. Higher positions are more visible and have a higher chance of getting a click
What is the problem with the above scheme?

22. How much to charge?
Yahoo’s initial approach was to charge the bid value:
Graph from [Zhang 2006]

23. Generalized Second Price Auction (GSP)
Normalize bids by click probability
The probabilities can be estimated:
Pr[ click ] = Pr[ user sees the ad ] Pr[user clicks| user sees]
Position Normalizer
Click Through Rate (CTR)

24. GSP prices
The ads in one page appear in the order of expected benefit:
bid(1) * ctr(1) ¸ bid(2) * ctr(2) ¸ ..
The advertiser gets charged the next highest bid. More precisely:
charge(i) = bid(i+1) * ctr(i+1) / ctr(i)

25. Is GSP truthful?
Google’s initial marketing message would led you to believe so.
Turns out not so much! Still better than initial models (first price, no CTR) and currently industry standard
An analogue of revenue equivalence theorem (Edelman-Ostrovsky-Schwarz 2005)

26. A very complex market Decision making in real time
Advertisers have complex preferences, users have detailed attributes
Information as well as persuasion
Multiple layers of stakeholders with different incentives and degrees of trustworthiness

27. Budget Optimization Advertiser specifies: bid for each keyword cij
total budget Bi
Search queries arrive
Search engine picks some of the Ads and shows them.
charges the advertiser if user clicked on their Ad

28. Objective: maximize revenue!!
Simple abstraction
N advertisers: with budget B1,B2, …Bn
Queries arrive on-line;
Cij : bid of advertiser i for good j
Allocate the query to one of the advertisers ( revenue = Cij )
Objective: maximize revenue!!

30. Linear program formulation

31. One problem with the LP
is not known…

32. Optimal (LP’s) solution
Bidder 1
Bidder 2
Queries: 100 books then 100 CDS $1
$0.99 $0
Book CD
Revenue: $199
B1 = B2 = $100
Bidder Bidder 2
linear program : all the books to the 2nd bidder
all the cds to the 1st bidder

33. Greedy solution Could be as bad as half of the Optimum!! $1 $0.99 $0
Bidder 1
Bidder 2
Queries: 100 books then 100 CDS $1
$0.99 $0
Book CD
Revenue: $100
B1 = B2 = $100
Bidder Bidder 2
Could be as bad as half of the Optimum!!

34. Is there a way to get something better than ½ of the optimum?

35. Special case: On-line Matching
girls
boys
All budgets = 1
Bids are either 0 or 1
Karp-Vazirani-Vazirani: can get 1-1/e of optimum

36. A simple algorithm
Penalize the bidders that spend their budgets too quickly…
Algorithm: Allocate the query to the bidder with highest value of
Where fi is the fraction of spent budget for bidder i

37. Theorem
Mehta-Saberi-Vazirani-Vazirani: the revenue of the previous algorithm on any input is at least 1 – 1/e of optimal.
This is the best possible ratio in this setting.

38. Implementation in a real setting
What we saw before was just an abstraction of the problem.
In implementing the real problem one has to take into consideration several issues.
I will address some of them here.

39. First problem: objective function
Google is not just interested in short term revenue. More important objectives:
User experience: quality of ads shown
High return of investment (ROI) for the advertisers: Number of conversions per dollar spent.
Fortunately, both of the above can be expressed as linear objective functions

40. Estimating the frequencies
In many cases, we do have good estimates about the frequencies of the keywords.
A good algorithm should take advantage of these estimates without risking too much if the estimates turn out to be incorrect…

41. Changing the LP
The previous design choices can be incorporated into the linear program
The decision variables will not be “which ad to show’’. They will be ``which combination of 8 (or more) ads to show’’. There will be a lot more variables.
Much larger linear program

42. Moral of the story
Optimization is a very important tool in Google’s operation (and in particular online advertising)
As you saw, real life applications are always more complicated than the abstractions studied in textbooks/papers/class
Still, the final solution is built on the basic underlying principles learned from the abstract problems