Home
Models for Sponsored Search: What are the right questions? (Panel
Contents
1. Kamal So whatever crude estimates you have we have to normalize certain things if we want them to compete against each other I mean if there s a keyword and there are only four advertisers but one of them is bidding on by acquisition and one of them is bidding on by impression and one of them by click or something then they are not competing against each other Audience I see that there s a scalability problem there if there are a large number of advertisers Kamal There are keywords where the number of advertisers is 4 or 5 Audience Another related issue or direction that the market seems to be moving is to increase the amount of targeting That s definitely increasing the value of the advertisers for the im pressions they are buying but totally fragmenting the market and decreasing the competition on any particular real estate the search engines are selling Kamal But there is a difference that this fragmentation is potentially increasing the value Audience How are the search engines to extract the rent from this increased pie What mecha nisms can be used to price these keywords better Kamal Basically some mechanism of choosing different reserve prices Audience But you have to set the reserve prices Kamal Yes they may not be uniform they may be uniform in certain cases but not uniform per click Audience But this is a question that is going to become a very real issue very soon but I don t see
2. pay per what What s the right way to try to charge for sponsored search In the past it has been pay per click it s been pay per impression and there is talk on pay per acquisition and pay per action through all the spectra of ways to charge are there right ways to think about it What are the trade offs between these ways etc David I think that the answer to pay per what is Yes laughter Essentially you should elicit all of what you are advocating or a subset of what you are advocating Essentially they the advertisers should be able to say this however they want Whatever s important the direct marketers want pay per conversion big branding type companies want pay per impression and they should be able to state in whatever way they want and the search engine can convert it do the optimization to pick which is best in terms of relevance Kamal You could have them in many combinations because I have certain values just for the impression I just want to show my name and certain values when people visit my homepage so in that case I should be able to bid for both I ll pay 2 cents per impression but if you give me a click Pll give you 2 dollars more Audience There could be an issue if the advertiser actually wants impressions but says he wants to pay per click then the search engine will try to show the advertisement as many times as he wants but does not charge him any thing David
3. got it wrong Audience By the way there were several billion dollars of revenue And they still kept it running for a while Michael Also for the record at that time there were no Economists who are involved with Google designing this auction So in defense Economists this was not their fault Audience Just to follow up on the questions Do you know any other auctions using Vickrey that are successful Rakesh Be careful of the criticism of Vickrey auction These objections of Vickrey auction take the following form Under these assumptions Vickrey has these properties Once one as sumption doesn t hold Vickrey doesn t have these properties That s not really criticism of Vickrey auction that s the criticism of the underlying assumptions You could say that because these assumptions don t hold I don t want to use Vickrey But that raise a question what do you want to use On the other hand the English ascending auction you could argue is a particular implementation of Vickrey auction If you actually want the sealed bid second price Vickrey auction it is used for example to sell stamps to collections The earliest recorded version I believe is that Getta sold his manuscript by Vickrey auction And you could argue that eBay is essentially Vickrey auction You could make these argu ments though it s problematic that bidders don t seem to behave according the way Vickrey described 11 Audience In
4. As long as you rank by revenue you can convert everything back into a cost per impression and rank by that because they re not getting any clicks so therefore they re paying for clicks and so they re going to be dropping in their rankings or they can convert back to impression Essentially they won t be getting any impressions after a while I mean this is the same thing as if they paid for conversion and they re actually lying about how many conversions they re getting That s fine too in the long run because they ll just start dropping in rankings or stop appearing So if they want to keep appearing they have to be telling you the truth about conversions Audience Another question is how you rank 18 David You combine all these things you rank by I mean you have some optimizer which is picking the best way to place things in order to get the most money And that s essentially like a revenue ranking It s essentially like converting everything into impression and ranking by that Kamal There is another benefit to let advertisers choose pay per what If advertisers choose whatever they believe is of utility for them then the chances of fraud like click fraud or impression fraud are lower For example in pay per acquisition the fraud is almost zero The only way you can do fraud is actually buying their product Audience But how do advertisers prove the acquisition Kamal That is a technical ques
5. Instead you should bid low and get a smaller slot And still use up your budget Audience That requires automating you can t do it manually Jason I got a question here Audience A primary discussion question for the panel in topic 1 basic issue is about basic model we are using nascent here studying the sponsored search auction for advertising I don t think we have something as formal as common model as an example such as tax model and so on But almost all papers have a common abstract model about what an auction is that there is an inventory of advertisers click through rates and their estimates of click through rates What do you think are the one or two most vulnerable assumptions everyone is making For example one of them I would think might be the click through rate is estimable property We assume the Ad inventory is static over some period time and that general Ad response preview users against click through static ads is going to be estimable at constant rate But if you move to inventory of item level ads that every time someone types in Da Vinci Code one of the Ads pops up with a different used book seller at different price click through rate is varying all the time what might happen So essentially what are the assumptions we are making that might be the most interesting to re examine in the future Jason Anyone want to take that Michael Sure So one assumption that we all sort of universally made which is pr
6. Singapore when you buy a license to drive a car they used multi unit auction which is not a very sophisticated VCG But they do use a Vickrey style auction And I believe Google IPO is like Vickrey We do see examples Audience What about the repeated Vickrey Rakesh There is a tiny literature on repeated auctions Very tiny because repetition means running into Folk theorem So you end up saying that anything could happen anything interesting could happen And that s not particular palatable Audience If I could make one more comment on the VCG issue so another response to why we aren t using VCG is because you know the VCG is not truthful in this setting for all the reasons we discussed because of the dynamics expressiveness and it may be that in practice that for the form that the true preferences take the auctions that they use e g GSP are better I find it a little frustrating the emphasis on the isolated VCG and why we aren t using it it is missing so much of what the real problem is in my opinion David I mean another reason is that the second price auction is much easier for advertisers to understand much easier to communicate much easier to implement So there are other reasons possible Kamal you have to learn other things to run VCG like the relative value of the slots what the CTR will be VCG requires a lot more data and GSP is simpler Audience I have one question regarding the solution conc
7. exact In demand equals supply even if the supply changes a little bit it can reflect big time in pricing So how will you manage demand equals supply if the whole supply is changing Rakesh No no that s it you adjust the prices Kamal You adjust the prices but that is what this auction is doing trying to adjust the prices based on demand and supply People express their demand by mentioning their budgets and it is the price that changes day to day It can t be the same Rakesh I m sorry I am not disagreeing I m just arguing that there s some benefit to the auc tioneer announcing prices and then the bidders saying what they want rather than the other way around which is what we currently have David That pricing will have to be quite complicated because for example prices go up in the evening Rakesh The thing is I think it is easier for Yahoo or Google to bear the computational burden than the bidder Let the mechanism designer take on the computational burden Leave as little as possible for the bidder to worry about Kamal That s what the auction is currently do Just bid and if the auctioneer says that if the prices are below the bid then you will buy it and if the prices are above the bid you will not buy it Anyway the advertisers have to give this number How does it resolve the issue Rakesh I d argue that there is a qualitative difference I have to come up with a number or in the second format I
8. has to be Vickrey and if we want revenue maximization we know it has to be an allocation by virtual values So that leaves us with a puzzle why don t the companies use these mechanisms Why do they use the other ones One possible explanation is that this is a mistake in the same sense that those of you who have taught mathematics to undergrads have seen is something called the freshman binomial theorem that A B AN BN So maybe what s going on here is the freshman Vickrey theorem where the generalization to N goods is simply the price of the person just below you But if you take this one dimensional type model seriously as I ve said it does not explain why we see the mechanisms that we see One explanation that has been offered is that well why not look at budgets Well the problem with budgets is that they are soft The bidders can change their budgets every time So it is not so clear that these budgets are really serious and even if you take budgets seriously you have to be careful how you set up the model Here is a really stupid model with budgets if I leave you parked on a keyword long enough I soak up your budget So in that case why am I not selecting bidders by their budget All the bid per click is saying is the speed at which I use up the budget so if you really take the budget seriously then it would say that the allocation should depend not just on the bid per click but also on the budget In terms of the various wa
9. it s not really the right model in this framework In this framework we have huge amount of statistics basically we have very good estimates of priors essentially so I think the Bayesian type model or expected case analysis is more relevant in current setting Let s see some other specific questions One of the questions was if truthfulness is important To me it seems like truthfulness is not really achievable in practice So to me that as a quality of mechanism design may not be that essential But on the other hand stability is nice The stability is not essential but its nice at least in terms of computational resources of the system So let s see what the current system does right I think in the head terms those that are frequently searched for things work pretty well And this may not be the case in the tail terms those that are infrequently searched for This is partly because of the cost for eliciting bids across all these tail terms and inexact match e g broad match addresses this to some degree It is sort of like an automated way of translating the bids from current terms to some other terms but essentially eliciting the true value across all these terms maybe just not be feasible Along these lines there is a general tradeoff we want to elicit the advertiser s value for everything Right we want to elicit their value for impressions for conversions for clicks for calls for all different terms for different times on
10. mecha nism I heard that in the next stage you may have something like Google telling that OK give me your dollars and your preferences and I m going to give you the maximum compet itive number of clicks per dollar So you delete the middle industries which I think so far have added value They had a role to play in the price going from cents to dollars David Actually Yahoo acquired one of these SEOs and that became the search optimizer product Audience If you want to use that then you should not use an auction You have to use something like what I m proposing number of clicks per dollar Because you are gaming your own system that has more of an incentive issue If you want to use your own bid optimizer you have to change the rules You can t use that auction That also relates to this comment earlier about expressiveness Right now the end user does have expressiveness He can tell the bid optimizer spend thousand dollars for something today He can say different things So the bid optimizer tries to do all those things for him There is expressiveness this way If you put the bid optimizer in the black hole Jason Ahhh huh comments laughter Audience Nobody can do efficient pricing if they don t control the clearing algorithm So the clearing point like Yahoo and Google and MSN can do more than someone who is outside the system Audience True I think right now the efficiency in the system i
11. selling for the current period you don t want to sell it for 2 seconds you want to sell for a day The small advertiser can not afford that slot for the day So how do you want to involve him Michael To pull off from the budget discussion there is actually a lot of academic interest in budgets partly because there are some fascinating theoretical problems associated with the budgets But then there is another question Although budgets are not binding if they are then they don t matter why does an advertiser have budgets Well a simple reason for budget is when you have an attack of fraudulent clicks if you have budget then that couldn t damage you that much And of course the problem is that though you get refund in the fraudulent clicks you may wait for a month for that refund So you have an incentive to set budgets perhaps a non binding budget just to save your self from the attack of fraudulent clicks So then there is a question an empirical question to what extent are those budgets binding What percentage of advertisers that have binding budgets And we know the answer that Google gives to this question The answer is that it is confidential information And we know the answer that Yahoo gives to this question and I am afraid that s very similar to the one that we get from Google And you can also try asking MSN So some folks here work for i prospect and other companies that actually handle advertiser s accounts So th
12. should the bidders be told what the mechanism is I think the other half is do the bidders understand what the mechanism is having been told or do they know what to do how to act having been told what the mechanism is And this seems like a problem This morning just before lunch I thought of these great papers appearing in this workshop on mechanisms for maximizing revenue and so on But the bottom line in each one of those papers as far as I can recall at this point was that the mechanism that maximizes revenue is very intricate Can we use 16 such mechanisms And if we use such mechanisms are the bidders going to understand to do the right thing or do we even have to get them to understand in somehow a deeper way Rakesh And why don t you let software tell that to you Audience I might be able to build the software agent and you want everybody to use the software agent then I don t know David I think a lot of small size advertisers may or may not understand but the big advertisers who are the largest chunk of the revenue if enough money is involved they ll figure it out That means the incentive is there for them to figure out how to do the right thing Audience You don t think that they ll understand it They ll just try it out and eventually would figure out what to do David I mean there s a limit Audience This is a really big question Does Blue Gene understand it
13. take advantage Audience On the acquisition issue all the industry people are you ready to track the entire process and make it part of your mechanism David Yahoo does have a search optimizer product where they track conversions So the mer chant puts a little javascript on their page Yes I think all of them have some kind of tracking and some of them allow bids per action Kamal But some advertisers may not participate David Right 19 Audience And also there s a correlation effect People discover something and they click some of them and then later they go to the advertiser So each of these components has a synergistic effect on the next and has to be taken into account It s a very complex issue It is very difficult to keep an account for acquisitions Audience Mixing different payment mechanisms in the same auction seems to be a big data problem You have all these different data and applying different conversion factors to them seems like a losing proposition to me So what about trying to finesse this by doing the opposite by having a single criterion auction David I think you still need to convert it because essentially the search engine is selling impres sions That s what the search engine has to allocate Audience We have data on impressions we have data on the aggregate income and in fact the query income from the different businesses The individual bidders don t have that
14. the search engine where the search engine has adopted some of the risks rather than selling on a pay per impression basis It seems natural that the search engine would want to rank the advertisers based on relevance and the search engines have been already in the business of determining relevance of web pages anyway they use very complicated formulas So it seems that now they are not looking just at click through rate as a proxy for relevance but using this whole complicated mechanism the search engine already has for determining relevance But now it becomes very important for the search engines to keep the mechanism secret because otherwise they give away the whole game they give away the way that they rank all the web pages not just the ads And I wonder if this is the reason that it s so important that the search engines mechanism must be a secret Kamal CTR at a very vague level is converting a pay per click system into a pay per impression system So in that case pay per click and pay per impression would be the same system Eventually what the search engine s goal is that he is getting inventory in terms of impres sions He wants to make sure that this inventory is sold on an impression basis And that s what s really happening in some sense You are trying to optimize the placement of ads for each impression for each ad slot Jason Comment Audience It seems to me that only half of question number 3 is
15. Just do find and replace and you get a pricing mechanism laughter Kamal Doing find and replace is not answering a mechanism design question it is answering a legal question Michael I just made a prediction 21 Rakesh In the find and replace you can say replace the word auction by pricing or you can say replace the word auction by dynamic pricing Currently we have the bidders bid and they accept the price but you can imagine the auctioneer sets the price and the bidders accept what they want at that price The auctioneer can vary the price depending on how many people want the top slot or the second slot One advantage to that is that if there is enough stability then at the going rate for that slot bidders may be much happier with that because then there is no need to optimize for the advertiser over how much to bid That s the going rate for the top slot Audience Isn t that variable reserve pricing Rakesh There may be many different phrases to describe the same thing Auctions can be run when you have the bidders tell you what the price is and you decide what they get or you can have the auctioneer announce the prices and the bidders say what they want right They are two sides of the same coin The advantage of the second is that if there is stability then there are going prices for everything Kamal I d say there won t be any stability because the number of searches no matter how well you estimate is not
16. Models for Sponsored Search What are the right questions Panel Discussion Panelists Kamal Jain David Pennock Michael Schwarz and Rakesh Vohra Moderator Jason Hartline Transcript Maria Florina Balcan Jianqing Chen Nikhil Devanur and Anuj Kumar Panel Jule 11 2006 Transcript September 27 2006 The Second Workshop on Sponsored Search Auctions was held in conjunction with the Sixth ACM Conference on Electronic Commerce in Ann Arbor Michigan on June 11 2006 The workshop closed with a panel discussion on the subject Models for Sponsored Search what are the right questions This panel was proposed by Lance Fortnow and Rakesh Vohra The panelists were Kamal Jain from Microsoft Research David Pennock from Yahoo Research Michael Schwarz from Yahoo Research and U C Berkeley and Rakesh Vohra from The Kellogg School at Northwestern U The panel was moderated by Jason Hartline and transcribed from a noisy recording by Maria Florina Balcan Jianqing Chen Nikhil Devanur and Anuj Kumar The transcript is as accurate as possible given the nature of the recording and is meant solely as a research aid for those doing research in the area of sponsored search Thanks are in order to all who participated in the panel and to those who made this transcript possible 1 Opening Statements Jason I m delighted to introduce our panelists Kamal Jain Rakesh Vohra Michael Schwarz and David Pennock The topic of this panel is on models for
17. a satisfying answer 20 6 Other Mechanisms Jason All right it may be time to move on to our last topic Maybe we should do it rather quickly since it has gotten pretty late So the last topic is other mechanisms and this is considering maybe not running auctions and instead doing negotiations or running different mechanisms for different kinds of things instead of a single rule to sell different kinds of keywords e g the frequent keywords the infrequent keywords the tail etc Maybe dealing with big players who have these budgets like HP and dealing with the small mom and pop shops maybe there should be different mechanisms for different kinds of people So that s the last topic Kamal One thing it should provide is let s ask people to take the risk In that case the search engines can distinguish between big advertisers and small advertisers If there is a mechanism in which they can take a risk maybe big advertisers want to take the risk because they can absorb the risk whereas small mom and pop advertisers may want to pay a premium to be risk free Rakesh you pretty much said it Jain On the less frequently used key words you could imagine an auction and letting people choose that would give them the competition You could imagine posted prices for the static market where the customers would be willing to pay a premium to guarantee its position over a certain period There is no reason why the sam
18. ability as there should be no incentive to deviate in a simple way and do better I say that as a first cut I guess I m sort of skeptical because you could simply hire someone to write code to deviate in a complicated way so maybe we end up having to worry about equilibrium anyway but perhaps if the situation is complicated enough we only need something milder which is the mechanism has the property that certain deviations will not be seen and we believe that these deviations are in some sense the more salient ones Audience As a corollary do you guys believe that truth actually exists Small advertisers might not necessarily know what their value per click would be and that is the bulk of the market 13 Rakesh Um so one answer is that we care about these things so that you can make predictions about whether we prefer one mechanism over another Since we are only after stylized pre dictions it is not so important that in reality they don t actually know what their values are For the earlier question is there such a thing as truth the answer is yes because I can simply define something and say it s true Audience There are about 75 academics in this room so that s about 75 factorial definitions of truth Kamal It is a stochastic problem that advertisers don t know what to bid at least for small advertisers They don t know that their probability of acquisition will be so at least to get that number t
19. and all search engines do com ply with this advice Certainly FCC feels that way and I have no argument Kamal I think that one of the things we want is that the average advertiser should feel that he had justice with the system There are currently let s say about six million small businesses and about 250 000 are advertising online And there are potentially a huge number of advertisers who could be there but they are not as smart as let s say HP people are They need to be told like very simple things And if you tell them very simple things then it means you should be implementing only simple things Maybe you want to have some freedom to make sure that you can optimize on top of that 17 David Yes you could tell them very simple things You are a direct marketer type advertiser You could say I want a pay per conversion and I d like the search engine to optimize for me and you know what keywords to buy and everything and that s a very simple state but yes the mechanism becomes very complicated Audience I have a question maybe not to the panel but to the search engine optimizers Do they get these small users do they actually use search engine optimizers that we have to worry about them Kamal You get users that spend a few hundred dollars 5 Pay per what Jason I think we should move on to the next topic We seem to be having a very long panel discussion So the next topic is
20. and we manage differently We are able to predict how much you are going to spend to a very close approximation but even then the customers are very particular about their positions they want 5limit It is true that in some businesses for example lead generation where you lead them to a form for a home application they say ok get us any number of forms per dollar There are also other kind of constraints that come in to play For example a call center they are not able to take more than 500 calls a day there are inventory problems We may say that get me any number of forms but there are finite number of offices employees etc so there is this resource constraint too There are also website constraints where your website can not handle more than certain number of visitors So budget is made a proxy for all these other kind of things If you have any interesting research problems you can contact me we ll provide you data to research more David I was just curious how do you manage certain unexpected jumps in volume like Janet Jackson episode etc Audience That s a very interesting question I think it happens once in a while maybe some news event happens though news event are less likely it is more like Yahoo changes it s front page Say it put a few baby related things So all your baby related products are going to sell like crazy So we constraint it because we have a totally automated software platform looking at i
21. auction mechanism has to be exactly as complicated as it has to be to fully express advertisers preference but no more complicated And I don t quite know how exactly to nail it but that s what you re shooting for Solution Concepts Jason If don t go to topic 2 we are going to be here for another hour on topic 1 So the next topic is on solution concepts And I think for me the thing I want to highlight about this question is that we learned that something was important when we switched from the first price payment rule to the second price rule That wasn t necessarily truthfulness We didn t switch to Vickrey No one does that So I am kind of curious of what is important in a solution concept for designing new mechanism in this area What property is it that we need to make sure that our mechanisms satisfy Jason So Yahoo just switched their mechanism a month ago from something to something else laughter In the switch there was an opportunity to adopt Vickrey Maybe they didn t Maybe I don t know did they laughter David One feature that second price has that is useful is more stability than first price There is no pure strategy equilibrium in first price And certainly with first prices advertisers will 10 be constantly switching And now they can still constantly switch even with second price But I guess it is a little bit less burden on recording things and logging all that stuff And it is pro
22. avid Maybe they should get an email saying you should improve your quality score or you should bid higher Michael I m sure you would get both of those emails every day Kamal It s easier to just tell the users what their ad status is what the fudge factors are not just whether they should be improved He maybe thinking bidding higher will cost this much or improving quality score will cost this much and he needs to know how to spend his investment David You have the model where the search engine and the advertiser have the same goals that they are trying to optimize The search engine and the advertiser have almost the opposite goals It is not clear that they should be providing all this information to the advertiser Kamal There goals are to use the advertising space effectively and in some sense those goals are aligned Audience So I think that posting the bids is different from posting the rules of the mechanism Kamal They are posting the rules they just aren t posting the CRT or fudge factor The rules are its your bid times some fudge factor Audience Posting the rules is one thing but I think it is not very common to post the bids in an auction For example in sealed bid auctions in Economics you don t typically open all the envelopes after the fact Maybe because the companies think this information very is private Yahoo posts the bids and Google does not 15 Kamal It is the GSP
23. bably not that important but that is one feature that second price has but first price doesn t Kamal Even the GSP has such features Allocation depends on bids but price does not The price could be a continuous parameter allocation is a discrete parameter If you increase or decrease your bid by one that doesn t really affect you But in first price you can get immediate profit So I would say for any auction it is a good thing to have that the allocation is a function of the bid but the price you pay is not Audience Vickrey and truthful auction leads to academic journals in business Audience I have a hard time believing Google didn t know GSP wasn t VCG Michael I would make a claim I claim that there is witness in this room who can testify that Google when they actually introduced GSP at that time they actually had no idea whether it was a truthful mechanism Does the witness want to speak out Audience I was the first one to tell Google that their mechanism was not VCG Rakesh We shouldn t single Google out Twenty years ago there was a debate on how to run treasury auction whether they should move from discriminatory price auction to uniform price auction In uniform price auction the last winning bid would pay the smallest winning bid Milton Friedman came out to support the uniform price auction because he said that that s the Vickrey auction Milton Friedman had the noble prize in Economics and even he
24. but there are lots of other parameters when you want to post the auction rules you have to know the definition of those parameters and those parameters are software code They have to say this is the software we are using to learn CTR and this is the software we are computing the quality score from Jason But that software might be dependent on their hoards of data Kamal Yeah so they ll have to post the data in that case What I m saying is that the rules have been posted but these parameters allow them to do anything they want to Audience The first thing a judge is going to do when they look at a dispute is look at the contract If they find an ambiguity in the contract it is going to be used against the entity that writes the contract So there is a possibility that if you don t write the rules then the judge can make the rules There is a possibility that regulation can come into the industry So from a legal perspective on not defining the rules I think it is a big problem in the industry For example one of my friends is working for a credit card company They have to be able to explain why a person didn t get a credit card So on the same lines Google must be able to explain why an advertiser didn t get shown Audience I have a suspicion about this I was wondering what people s reaction to it are There s been a lot of talk about how this pay per click model is a risk sharing mechanism between ad vertising and
25. d like to make the users able to read the rules and know what is going on but at the same time they shouldn t have to read them to figure out what s going on just like your VCR you ve got the user s manual but if it is a well designed VCR you don t have to use it David This religious belief is only true if there is no one who goes and screws with the environment all the time So in Google or other search engines so you tinkered with it for two months and you figured it out and well guess what they ve changed the rules They do it all the time there is actually no reason to believe so you can either avoid the question or you can rephrase the question should Google keep changing the mechanism and not telling anyone Then advertisers never figure it out or take a long time to figure it out or not Kamal They should be telling each advertiser what their statistical parameters are They don t even tell the advertisers what their quality score or click through rates are for different key words Maybe if the advertisers knew what these parameters they could optimize better maybe he would know that one keyword is not good or something These things can have impact if they are known to the public like in Yahoo s auction Yahoo shows all the bids publicly and an advertiser can see how they would need to bid to chance the outcome So at the individual level should they be providing this information the fudge factors D
26. e mechanism should be used for everyone Michael I will make a prediction it ll probably not come true but i will make it anyway laugh ter I think they will move away from auctions And I think we will move towards pricing mechanism advertisers will get prices Why will people move away from auctions Because once you call something an auction you are on the hook legally to respect the laws that govern how you conduct an auction and what you could and couldn t do there are laws about bidding But anything could be interpreted as bidding But nobody tells Walmart how to do the pricing Well they could respond to the demand But once you rename something as a pricing mechanism you pretty much rule out about half of the law suits that could be filed against you And on the strength of this reasoning I d think they ll move away from an auction I d argue that in some sense Google already moved away from an auction because in my mind it is not an auction when the bidders don t know the rule That is what makes the difference between an auction and a pricing mechanism is that you tell the bidders the rule that is what makes it an auction Michael It is very simple to do You just do find and replace you just replace the word auction mechanism every where with pricing mechanism Say currently on their webpage a particular keyword is running for 11 cents That is the current going price That becomes the pricing mechanism
27. ement is everywhere It s crouching We heard this morning that the yield from advertisement in different media is dropping as there is more and more advertisement coming in So one thing that we perhaps should be thinking about is what are the main competitors to those Google sponsored search links and there is one thing I know for sure it s not radio city spectacular Christmas products So then what is the main competitor to Google sponsored search links and you may say that it s Yahoo And actually it is not It isn t at all What is the main competitor for them is Google organic search results So in fact if Google was a monopoly if there was no Yahoo if there was no MSN imagine if Google were to dramatically decrease the quality of the organic search results Well you would think that advertisements would become more competitive and a user would click more often on the sponsored search links Well how do I know that for example in the days when Overture was an independent stand alone company and it wasn t owned by Yahoo pretty much every user who went to Overture website would click on one of the ads What a miracle and in the absence of organic search results that would happen The same thing would happen to sponsored search results if organic search results were not there So of course there aren t many people who are willing to go to the site but don t want to click So when you think about it and you realize that for Google spon
28. ept basically the organic search is to make the user a k a the searcher happy sponsored search is to make the advertiser happy But I think in the long term you really want to make the user happy To make the user happy you really want to make the advertisements relevant to the user How can we make the user of sponsored search more happy Kamal I think long term that what s really happening Lets say you are delivering a web site users want to see a web site and at the top but you are anyway bidding on it To measure the quality of the overall page the user doesn t see what the targetted bidder bid the user sees the whole page You paid and you are showing up so sooner or later for the quality of the user your rank in the organic search would have to go down In the long term what s the natural equilibria All the commercial sites are there and all the informational sites are there on the right hand side Not a single advertiser although those that are not bidding you do you show for free but no advertiser would be able to do that because if he doesn t bid he is not shown and all the competitors are out bidding him In the long term the equilibrium is the overall quality of the page remains high the users are happy but a certain set of advertisers have to pay to be on the page So it does take care of the user happiness If the ad is not relevant no matter what you want to pay it is not shown David one po
29. ey could share their experience on how constraining binding budgets are But I think one interesting question is it something that s actually important out there Kamal One thing which Google says is that if you have budget limit we will try to uniformly spend your budget over time and only to give you that much You can see that when you reload some of the ads disappear And you can see at least from the perspective of the advertisers that the budget is a constraint Michael Right So the question is is it something which is empirically relevant It happens 1don t know Kamal You can notice ads disappearing if you keep pressing reload button Michael Well part of what that might be that if it s a rare keyword you may want to experiment with different ads to get clicks Kamal I think the counter fraud attack argument for budget is not correct because it would be same for all the advertisers David Well it can also be sort of an estimating procedure of expected click through rate If you just saw a bunch of ads and then reload the page You already didn t click on those ads Kamal If you keep reloading the ad goes away and then reappears So the most plausible explanation is that they are trying to uniformly distribute the ads Michael So that seems like a nice methodology for figuring out the answer to this question with out relying on Google David So you can ask Yahoo We do have mechanisms for smooth spendi
30. have to look at a number and agree Kamal But you don t because this number changes every second You don t you have to pre decide automatically what the level would be So that s essentially call a bid 22 Audience You don t want a situation where everybody wants to buy the second slot nobody wants the first Audience more important thing is they are perishable products Compare it with airlines they are priced there are mechanisms to price and there is a pricing problem It s very hard dynamic pricing is hard Rakesh So the airlines have that pricing Audience But the airlines are going bankrupt laughter Rakesh But that s not the reason Kamal You go there you are not buying a hundred thousand tickets You just go there and then they decide whether your true value is above the price or below it but you decide it after looking at the price which is essentially the bid If you are buying hundred thousand tickets you can t look at the price and then decide what your true value is whether you should buy it or not You have to tell your software upfront that if the ticket price is this much then buy it if the ticket price is that much then don t buy it OK And that s essentially you are giving your bid to your software Audience I have a comment It s about search engine getting into bid optimization Today they the search engines are trying to design a bid optimization to game their own
31. hey have to do this analysis long enough Audience I want to go back to the business model where users should get paid and the other side where content providers get paid I go to Google not necessarily to read something Google is paid for I go there because I believe the listings that come up will be high quality There are some people who are not comfortable with that large content providers newspapers people who have syndicated content Do you think in the future that there will be an issue with content providers saying that they want to get paid David There is a search engine that is trying to do this If you have some content and you go to the search engine and you prove you own it by changing something on the HTML then they actually are paying the content providers I can t comment on what Yahoo is doing But this company indexes the entire web they still are a regular search engine but they allow content providers to go in and say i own that page and i want to get paid and then they get a share of the ad revenue 4 Should bidders understand the mechanism Jason So i guess we can move on to topic three which is should bidders understand the mech anism This topic is being posted because a lot of the details of the rules of current im plementations of sponsored search auctions aren t precisely specified There are little fudge factors that Google has and I couldn t say about the other search engines Yet clas
32. ht to MSN thats a huge Kamal That s one way to bring value competition Search engines have to pay to have their search box in the browser For example Google pays Dell to be the default search engine and now the PC market is inherently more competitive and that value eventually gets trans fered to the user If you buy a computer and promise never to change the default search engine then you should get the computer for cheaper Jason Are there any more questions on solution concepts Or are there any questions on this topic we ended up on Audience I have one more question Most people think truthfulness is important How far is GSP from being truthful Rakesh So let s start with why does anyone even care about truthfulness I think the usual answer is that if bidding truthfully is an equilibrium maybe that s an argument for why amongst all the many equilibria of the game that s the one that we will pick But notice that there is nothing in that argument that says that a mechanism has to be dominant strategy incentive compatible There is nothing sacrosanct about that Maybe we want something fuzzier like truthiness So here I would build on what David said which is maybe what really matters is that we want to argue that the mechanism is stable in some sense So we want some notion of what the stable outcomes of the dynamic process would be when using this mechanism So as a first cut you could define st
33. is playing against Kas parov laughter Audience The computer scientists have the answer You build a software agent and you don t care whether they understand or not laughter Audience Why don t you build a software agent they ll understand Audience Question 3 taken literally implies that through the answer it might actually be hap pening in practice If you re going out to the field and asking advertisers what they want what they think they need some of that has to do with perception Another question is that should the users the ad readers and so on of these search engines understand the mecha nism Because there is a very mild default understanding that for organic search results the good sites make it to the top for some mysterious reason For prime time TV ads it might be a good one or it might be a bad one but it s not an illegal one It s not something pretending to be on TV Is it important the mechanism we use if we re talking about the average person when they re told an analogy they ll understand it a they advertise this yeah these are ads and b yeah people would pay to be up there it s not something like they climb up there So isn t it important that the mechanism be transparent to people who use search engines too Michael According to FCC the answer s unambiguous Yes They have an advice that strongly encourages search engines to clearly designate advertisements
34. le exchange files where you give as many packets to others as you receive The BitTorrent system is much better than any other peer to peer system These systems are a starting point There may be many other systems like that where we use the power of the computer to optimize and price at an atomic level What it is lacking in sponsored search auctions i think is that it excludes the user a k a searcher from the game It has two parties the advertiser and the search engine and the searcher is not in any bargaining position right now We should bring the searcher in to the picture since the search engine business is a competitive field Yahoo MSR and Google each has capacity to serve all the searches in the world it is a good amount of supply but the competition between the search engines does not get transferred into competition on the pricing model There is no reason for Yahoo Google or MSN to change their pricing to increase their market share in terms of volume of searchers because these two are completely independent Rakesh Im Rakesh Vohra from the Kellogg school I have a list of things to talk about that roughly match what s up here The first is complaints One has to do with the fact that a lot of work has been devoted to a special static model where the private info is one dimensional This is odd because in this model because when the private value is one dimensional we know what the answer is If we want efficiency we know it
35. ll other auctions in this sense that expressiveness would make market more efficient and also you can control the revenue estimate We heard an early comment that MSN is giving more expressiveness than Yahoo and Google and Yahoo and Google have different types of expressiveness as you can see at their sites But those are all what we call local expressiveness So they can take a little thing and translate that to price They are not allocation level of expressiveness And there are a lot of things at the allocation level inherently and then you cannot use the current mechanisms that requires a completely different architecture You got to have something that optimizes at the allocation level and in these other markets what we have seen is that at the allocation level you need to solve NP hard optimization problems for determining the winner for example That s not a problem you can absolutely solve NP hard stationary problems Then the question is can we do it in real time And the answer is no You cannot do it You need do this Ad auction in a dynamic sense Our proposed solution that David and I presented in this workshop a year ago is that you optimize and parameterize a dispatcher that doesn t use optimization Then run the dispatcher in real time and the optimizer every so often A related problem is there is a long term market and a spot market Spot market is in real time and long term market is optimized I think the current model
36. ly just part of model So there are a lot of things you can think in terms of standard model But one has also to be honest to say the alternatives are very analytically intractable So it s not clear what one could say Perhaps there is a way out by looking at the keywords which are extremely popular in the sense of having a large number of bidders Then you may be able to make asymptotic arguments because the number of bidders is much larger than the number of the slots available Perhaps one can say something about very popular keywords but be silent about the keywords that are clicked on very rarely David What assumption that almost all the auction analyses make is that the auction is in isolation sort of monopoly type of situation So in that case you know you maybe do Myerson to optimize the revenue or something like that In fact this world is competitive landscape You may not want to optimally squeeze as much as possible out of So essentially what the search engine do is that they add value to advertisers and take some amount of that for themselves And so you may not want to optimally squeeze as much as possible out of pie because this is a competitive landscape You know that advertisers and end users can defect very easily Rakesh Actually this is not so easy to do The defection is not so obvious right which is you could say as Pennock said why cannot Microsoft lower the price you have to pay to advertise But the p
37. ng over time Audience But why do you do that Is it because of the budgets or because of some other reasons or it s just that the advertisers want that Kamal You know value of clicks are different over the day If you are letting them bid for the day and not for the hour no advertisers gets a bad set of users That should also motivate the desirability of smoothing out the spending Jason The questions was about the existence of this mechanism at all Audience It s an advertiser s preference Audience I can answer part of the question I am not from iProspect I am from their competitors I have seen every kind of advertiser from 1 million dollars to a few 100 Dollars I would say budget pretty much drives what they are spending per day for several reasons One is that they want to spend it throughout the month and not just one day Let s say you are running a business you want to see customers coming in throughout the month not just 5 days of action and then 25 days of silence The second is risk You want to limit your risk Also most of them do operate with many other constraints For example maybe they have a cash flow problem or something In some cases in our product we have a statistical model which predicts how much they are going to spend and how many clicks they are going to get So we ask out customers to remove and not to set the budget constraints at the search engine level because Yahoo behaves differently
38. obably or not always true is the assumption that advertisers don t really care who are the other advertisers on the page or if there are other advertisers on the page Somehow I would imagine that if I were HP and it seems that HP is a canonical advertiser today and I was bidding on the word cartridge If I was there only ad for cartridges I would imagine that I would get more clicks than I could get otherwise I would also imagine that I would in fact get a lot more conversions than I would get otherwise I would even eventually perhaps choose to charge a higher price on my web page than I would otherwise because really people who came there don t have much other choice So this seems like that something that could be potentially quite important and relatively easy to address and yet so far we sort of conspire to ignore it Probably we shouldn t I think I could also mention another three thing that are equally important Rakesh So you can say that click through rate is changing The problem is that in static model you cannot really address this issue And so if you want to address this issue you ve got to start thinking about dynamic model where the keyword arrives over time and the bidders arrive over time You saw some papers already talking about this They were talking about the competition between two bidders and perhaps trying to drive the price down or up there are lots of other things that could happen which are frank
39. ol of bidders that you are going to attract The last issue is ambiguity A couple of the search pages have auctions whose rules are ambiguous in certain respects One question is as to whether this is necessarily a good idea Apparently two arguments for ambiguity are 1 is prevents free riding on the part of your competitors and 2 it would allow you to change your mechanisms without having to deal with complaints on the part of your bidders On the other hand the empirical evidence suggests that ambiguity would make bidders more risk averse and so that could potentially lower revenues Michael Hi I am Michael Schwarz and I am from UC Berkeley and I would be joining Yahoo Research labs in couple of months First I would like to thanks the workshop organizers specially Jason and Asdemir I think this is wonderful conference and it s great that people from academia and from industry come here and talk to each other I think it makes a difference for all of us So let me start with a question that has one very very important advantage Nobody mentioned this question today So maybe if it s not THE most important question which it isn t at least perhaps it is controversial and entertaining enough to grab your attention for next 100 or so seconds So on the plane to Detroit I was reading a newspaper article and here is what I learned for the first time in 73 year history the radio city Christmas spectacular will use product placing So advertis
40. roblem is that is not enough you also care about the number of viewers you are going to get at MSN pages So it is not clear that I can necessarily defect if I don t like the mechanism because I also care about the number of viewers that your page attracts David Right If you get essentially no profit at all in one engine you just put more money in the engines where you get defect problem Jason Eh yes Audience One thing drawn from my experience from about 300 markets is that the story is always the same in all of these which is you want to increase the expressiveness of the bidding language and you want to customize to the applications and that would make market better And in that sense I see all of these Ad auctions as extremely simplistic And this is really most related to what have been mentioned by David and by Rakesh And you know is the budget constraints really hard There are a number of other things we should be expressing in different ways Let me just mention a couple of things I am not an expert on that auction so these might not be the most important things If I get exclusive Ford cars for the next month you don t show Ads at all in the next few weeks I will pay you just for not showing them regardless of whether you show me I might say that I want to get 40 000 clicks in the next week And things like these that you cannot see in current markets And I suspect that Ad auctions wouldn t be different from a
41. s are pretty naive in their approaches they are limited inherently in that no one can support allocation and expressiveness Michael So first I am very much in an agreement with you You really need an auction mech 3 anism to allow advertisers to express their preference because if they couldn t fully express their preference then there is no efficient outcome in optimizing the total pie So this being said I think there is another side of story And the other side of the story definitely doesn t want a mechanism that allows advertisers to express preferences that they don t have Let me elaborate what I mean For example suppose you create a mechanism where you can express preference I want to be number 3 on the page for a keyword Ann Arbor for the next 30 days So this is a well defined preference Should we allow advertisers to express it I think they should not because there is no advertiser who truly has this preference Because being in slot number 3 is not that similar or different from being in slot number 4 or slot number 2 So once you allow it you can make preferences infinitely complex The question is how many advertisers have this kind of preference So if you make a mechanism more complicated than it has to be in order to express all possible real economic preferences so what you are doing is simply piling on advertiser increasing his communicative burden without in fact increasing efficiency So I think an ideal
42. s being determined by the bid optimizers and not by the auction Audience The thing I really want to say is that you don t want to segment the market completely because every time you split the market into submarkets you take a heap off the efficiency available 23 Jason All right I think it is time to bring the thing to a close so I was planning on taking questions that didn t fit in this model but instead we should take dinner Laughter So let s thank our panelists Applause and apologize to our scribes for talking for so long Laughter And hope that at some point we manage to get some notes published 24
43. sically in mechanism design a paramount assumption is that bidders know the game they are playing in So this is at odds and the question is what is the right way to approach this issue Michael Ill give you an economical answer According to economic religion there are two major truths about bidders in auctions First bidders are infinitely wise and they basically instantly figure out the equilibria even if it s not computable Second to do that trick bidders really don t have to know the rules because they just evolve to them This is just a religious belief So the question is how do you view that religious belief Do I subscribe to it Actually since I am an economist I do subscribe to it I think it is actually pretty reasonable that people would tinker with things learn the outcomes and figure out reasonable ways to bid It is also reasonable to think that when they are tinkering they don t have to read the manual In fact you ve probably done it many times with your VCR without having to reading the manual So you can think of the manual as the rules of the auction So I think a good mechanism is one where bidders can relatively easily tinker their way to a good outcome for themselves 14 I think there is a good argument to be made that you want the system to be transparent because if anything it should help the users to lower the cost to figure out the mechanism So I think there is a good argument to be made that we woul
44. sored search links the main competitor is Google organic search and for Google organic search the main competitor is Yahoo So that necessitates keeping the organic search results there So the question is and I think there are many questions here first how do we think about competition in this market And I know that I am picking something that is somewhat relevant because completely without prior communications with Kamal I think this question echos his comments and the other question is first what is the future of the Industry How does that competition play out To what extent will we see product placement in the organic search results in the future just like Radio City Christmas spectacular is experiencing and if that would ever happen contrary to FCC s best advice how would it be priced How would competition play out So I think it s both an interesting question and perhaps a plug for my future work David Hello I am David Pennock and I am research scientist at Yahoo Research and myself and 2 my group work on a variety of market mechanisms that are important to Yahoo and of course sponsored search is one of the most important to Yahoo It s one with the biggest leverage we have in terms of revenue And one of the short and medium term targets that we can work on In terms of models what s the right model So I think in this framework the sort of worst case analysis or adversarial type analysis is of some interest but
45. sponsored search what are the right questions The way that we are going to run this panel is that first our panelists are going to have a moment to make a brief statement about this topic in general and then we are going to proceed through a number of broad topics We are going to give the panelists a chance to respond to the topics and then we d like to encourage questions from the audience on these specific topics Then after proceeding through these specific topics if you have questions that don t logically fit under these categories then we encourage you to ask those at the end Also Pm delighted to announce that a number of students have volunteered their time to take very careful notes during this presentation and including the fact that we are recording this discussion so that we can make sure not to miss and gems that are said laughter uh gems or otherwise that are said during the course of the panel So we should definitely be appreciative of their efforts as well as the efforts of the panelists So let s start with Kamal with his brief commends Kamal Thanks my name is Kamal Jain and I m from Microsoft research the first thing I would say about sponsored search is that it tries to price everything at a very atomic level and individual auctions are run very often That allows a higher optimization There is another place where the same thing happens It s called the BitTorrent system It is a peer to peer system where peop
46. ssible way to make users happy directly is to attach a coupon to the link so if they click through they get cash back or something So you could directly compensate people and that makes them happy but there are other ways too Kamal One think you want to do is bring the user into the bargaining process we expect search advertising to be more efficient than other forms of advertising because the user expresses 12 what they are interested in This increased efficiency should not be kept by the search engine because it is a competitive market It should be some how given back to the economy One way is to make the user happier to use this money There are currently no practical ways to give the money back to the user Audience Build a better search engine That s how the money gets spent often in providing some free service like free email Kamal If you have three different search engines then you have three different qualities If you don t let companies compete on value just on quality then whoever has the best quality whether it is Google or Yahoo or MSR will start taking all the business and there won t be any competition left In other markets people compete by value Cars are a good example not everyone buys Lexus People by Toyota too because they get better value from Toyota David Also people are inherently lazy so they use whatever is most convenient If InternetEx plorer had a search box that went straig
47. t every hour So when something goes above the limit we shut it down Kamal So any information about clicks and impressions do you get real time information Audience As real time as it can be Yahoo guarantees to publish this information say every morning so there are some other limitations But we are trying to be as real time as it can be So there are also quarter end effects Somebody wants to optimize revenue towards the end of the quarter of the fiscal year Or somebody says I don t want more revenue I want more profit So the budget becomes a proxy for all this Rakesh So this raises the issue that whether budget constraint is necessarily the best way to address this Right Audience There is no alternative to this Rakesh I guess I wouldn t be prepared to go that far unless 50 people thought hard about it and come back and say that there is no alternative Then I might be persuaded Audience So why not have budget constraints on number of clicks rather than money Audience it s just like financial market click is currency and budget on number of shares is same as on cash Audience I just want to make a quick comment Following the previous comments that in my experience that in this you can choose how much you are getting though the bidding price instead of controlling though the budget because if you have high bids but have small budget actually you are paying more for the traffic you are getting
48. the day for different demographics their value for having guaranteed click bundle vs just spot markets All these things we want and that would maximize certain social welfare and maximize value but of course we can not ask all these things So what we need to do is essentially figure out the ones that would add the most value with the least complexity for advertisers the least amount of things that we need to elicit from the advertisers So that s all Pll say for now I just want to say one other thing I just want to encourage people I just want to point out while I have the microphone at the main conference on Tuesday there is some more Sponsored Search activity So I encourage you all to check it out There is a session on Sponsored Search on Tuesday at the main conference and also Hal Varian would be giving a keynote address on Wednesday related to Sponsored Search Models for Sponsored Search Auctions Jason Thanks you so we proceed to our first topic which is the current models for the sponsored search and again focusing on what these models get right and maybe what they are missing and how we need to proceed to get models that are appropriate We want to consider things like reputation multiple keywords and a number of other aspects that are missing in the models that are considered so far So are there any questions Audience Rakesh you had some comments about the budgets So we don t use virtual valuations and yo
49. tion laughter If they are reporting a lower rate of acquisition then their bid per impression goes down Audience This argument about self supporting acquisition is very weak What you re saying is that there s an optimal number for them to report and there s the number they re actually getting It will only happen by luck that those two numbers coincide Kamal There are ways to verify acquisition data but unfortunately I can t share it laughter David Actually the search engine doesn t really they care if they tell the truth or not They can report whatever they want all they care about is revenue Audience Then you basically converge to pay per impression and all those other things are a waste of expression David Well presumably the advertisers find it easier to figure out their value for conversions and so it s just a convenience for the advertisers but the search engine doesn t really care I mean assuming their estimates this is the biggest assumption that they can estimate things very well Jason It s also risk mitigating too You paid for acquisitions paid for money you got a lot less risky for advertisers Audience It s a little bit of a big jump from pay per click to pay per acquisition I think because click impression is controlled by search engines and acquisition by customers There s a big gap there David There is a short term window when they could
50. u don t use VCG and they are saying that in the community one reason for this is budget But you don t believe this reason because budgets are in some sense soft and if you really care about the budget you should use that information in the ranking mechanism So what about using it in the ranking mechanism Do you advocate that or do you think it s completely I mean these things exist in the market and they have existed for a long time so you can t just say they re Rakesh Right I guess so I have asked various people why we have budgets I have asked advertisers and the sense I get is that they like the budgets because it allows them to do something else Which is to minimize risk I want to control my exposure So that s the real reason that they like the budgets I don t think that the budgets necessarily reflect the hard constraints So if you take what they said seriously then it says that there is a preference for something that the bidders have that they are not able to express directly in the current mechanism Which is that I like to pay but I want to make sure that I don t pay too much over a two month period So one could imagine a mechanism that would say well fine I would guarantee you a certain slot for a certain defined period And whatever you make from that you are allowed to keep but then pay me upfront You could imagine doing something like that then you wouldn t have that problem Then the bidder would kno
51. w that well this is all I am in for so the budget constraint is not so important Now the other thing is that if you do take the budget constraint seriously there are arguments that say it should be taken seriously because the advertising department of large companies are given budgets that determine their expenditure over a year then if that s the case then why aren t you selling advertising upfront because if I can capture a larger portion of your budget there is less and less budget to go around for my competitors But I don t see that happening in sponsored search In advanced markets or serious advanced markets So again I come back to the point which is that I am in two minds about this I can see the arguments for it to be serious but if you take it seriously then I don t understand the current mechanisms Audience So what mechanism would you advocate Paying upfront involves some sort of nego tiation and presents a barrier of entry to mom amp pop shops The nice thing about auctions is that they are very transparent and low cost automated pricing mechanism Rakesh So the general proposal was a system where you offer a slot for a defined period of time Kamal So the issue would be that there are two type of advertiserz 1 the big advertisers 2 the small advertisers And we don t have two different set of tools For small advertisers which may form a long tail the main preference is small budget If you are
52. ys of paying for example pay per click pay per conversion this deserves more discussion because this says something about how risk is being shared between the search engine and the advertisers The nice thing about bid per click is that the search engine is taking on more risk that otherwise the advertiser would have done Other arrangements result in more risk sharing One question is which risks are the advertisers better able to take care of because they are diversified over many keywords Another issue has to do with the fact that you ve got competing search engines so if they use different mechanisms that could induce a selection bias in terms of the kinds of advertisers that would be attracted to a particular search engine So something very simple minded if one was using Yahoo s discontinued mechanisms one would have thought that maybe it would have attracted the kinds of bidders that who generate a high expected value given a click but generate very few clicks They would have preferred the auction where bids are not normalized by the click through rate They would have preferred the first price auction to the second price auction This would have resulted to a different distribution of bidders at the web site So in thinking about whether you switch from one mechanism to another it is not enough to look at the mechanism in isolation in the usual classical framework but you also have to think about how that is going to affect the po
Download Pdf Manuals
Related Search
Related Contents
Novembre 2013 November 2013 SucheBiete Kleinanzeigenzeitung Birnbach Samsung Galaxy S4 mini User Manual ACASI User Manual ELF User Manual MODULO HI-TECH RIALTO HI-TECH AMALFI HI-TECH Copyright © All rights reserved.
Failed to retrieve file