- Home
- Bengal Math Curriculum
- Statistics Help
- Statistics Consulting
- Popular Services
- *99 Cents for 1 Math Problem
- Statistics Help
- Statistics Solutions
- Statistics Symbols
- Statistics Lecture Notes
- Statistics Class Notes
- Hire Freelancer - xlance Alternative
- Math Olympiad
- Free Accounting Homework Help
- Free Business Math Homework Help
- Free Programming Homework Help
- Free Finance Homework Help
- Free Economics Homework Help
- Free Chemistry Homework Help
- Free Biology Homework Help
- Free Management Homework Help
- Free Engineering Homework Help
- Free Chemical Engineering Homework Help
- Free Mechanical Engineering Homework Help
- Free Computer Science Homework Help
- Free Bioinformatics Homework Help
- Free Calculus Homework Help
- Free College Homework Help
- Get One Month Coaching ($149)
- Math Curriculum(High Expectation)
- 1-On-1 Coaching
- Accounting Solutions
- Bioinformatics Solutions
- Biology Solutions
- Business Math Solutions
- Calculus Solutions
- Chemical Engineering Solutions
- Chemistry Solutions
- Computer Science Solutions
- Economics Solutions
- Engineering Solutions
- Finance Solutions
- Management Solutions
- Mechanical Engineering Solutions
- Programming Solutions
- Donate
- Almost FREE Service
- Chat Core Dump
- WhiteBoard Sessions
- Submit Math Problems
- Checkout Math Solutions
- Sample Math Video
- College Textbooks
- College Courses
- Coursera Courses
- edX Courses
- Give Gift Certificates to Your Loved One
- Get a Scholarship
- Tell a Friend
- *Online Math Help ($16 per Hour)
- Vedic Maths
- Home Schooling
- Community College Math
- Online Degree Program
- Blog
- We are in News
- FAQ
- Contact Us
- Privacy Policy
- Terms & Condition * Restrictions Apply

- Home
- *99 Cents for 1 Math Problem
- Statistics Help
- Statistics Solutions
- Statistics Symbols
- Statistics Lecture Notes
- Statistics Class Notes
- Hire Freelancer - xlance Alternative
- Math Olympiad
- Free Accounting Homework Help
- Free Business Math Homework Help
- Free Programming Homework Help
- Free Finance Homework Help
- Free Economics Homework Help
- Free Chemistry Homework Help
- Free Biology Homework Help
- Free Management Homework Help
- Free Engineering Homework Help
- Free Chemical Engineering Homework Help
- Free Mechanical Engineering Homework Help
- Free Computer Science Homework Help
- Free Bioinformatics Homework Help
- Free Calculus Homework Help
- Free College Homework Help
- Get One Month Coaching ($149)
- Math Curriculum(High Expectation)
- 1-On-1 Coaching
- Accounting Solutions
- Bioinformatics Solutions
- Biology Solutions
- Business Math Solutions
- Calculus Solutions
- Chemical Engineering Solutions
- Chemistry Solutions
- Computer Science Solutions
- Economics Solutions
- Engineering Solutions
- Finance Solutions
- Management Solutions
- Mechanical Engineering Solutions
- Programming Solutions
- Almost FREE Service
- Chat Core Dump
- WhiteBoard Sessions
- Submit Math Problems
- Checkout Math Solutions
- Sample Math Video
- College Textbooks
- College Courses
- Coursera Courses
- edX Courses
- Give Gift Certificates to Your Loved One
- Get a Scholarship
- Tell a Friend
- *Online Math Help ($16 per Hour)
- Vedic Maths
- Home Schooling
- Community College Math
- Online Degree Program
- Blog
- We are in News
- FAQ
- Contact Us
- Privacy Policy
- Terms & Condition * Restrictions Apply

Statistics Help

**Question: **(A challenging question) Suppose that the search engine implements a reserve (i.e., minimum) price of $1 (/click). Find the lowest market-clearing prices when this reserve price is imposed. Edit

**Answer: **among all envy-free Nash equilibria, this particular one is bidderoptimal, in the sense that it results in the lowest possible price for each particular advertiser. Note that in GSP, for a particular bidder, the only position for which envy-freeness is not implied by Nash is the position directly above. It is natural to ask if all these properties also hold true in the presence of position constraints. One of the difficulties in proving this comes from the fact that the VCG allocation no longer preserves the ordering property, as shown by the following simple example. Suppose advertiser A has bottom cutoff (2) and a bid of $2, advertiser B has cutoff (1) and a bid of $1, and we have c1 = 101 and c2 = 100. The VCG allocation gives position 1 to B and position 2 to A, for a total revenue of ≈ $300. The top-down auction will give position 1 to A and position 2 will be unfilled. The revenue is equal to ≈ $200. Despite this, it turns out that there is an equilibrium of the top-down auction where bidders end up in the optimal allocation,

he remainder of this section is devoted to proving this theorem. The bids that satisfy this theorem are in fact quite simple: we set bi = pi−1/ci−1 for all bidders i assigned in Θ. Thus, if we show that b1 > b2 > . . . > bk, we would get that the top-down auction assigns the bidders exactly like Θ and sets the same prices (modulo some technical details). This would prove (a) and (b) above. The chain. Toshow that the bids are indeed decreasing, and to show (c), it turns out that we need to prove some technical lemmas about the difference between Θ and Θ−i for some arbitrary bidder i. In Θ−i , some bidder i 0 takes the place of i (unless i is in the last slot, in which case perhaps no bidder takes this slot). In turn, some bidder i 00 takes the slot vacated by i 0 , etc., until either the vacated slot is the bottom slot k, or some previously unassigned bidder is introduced into the solution. We call this sequence of bidder movements ending at slot i the “chain” of moves of Θ−i . Note that the chain has the property that it begins either with an unassigned bidder, or with the bidder from the last slot.

Edit

**TutorTeddy.com & Boston Predictive Analytics**

[ Email your Statistics or Math problems to **help@teddycan.com** (camera phone photos are OK) ]

Boston Office (Near MIT/Kendall 'T'):

Cambridge Innovation Center,

One Broadway, 14th Floor,

Cambridge, MA 02142,

Phone: 617-395-8864

Dallas Office (Near Galleria):

15950 Dallas Parkway,

Suite 400,

Dallas, TX 75248,

Phone: 866-930-6363