 the major application domains of these mechanisms with money is that in the context of internet advertising. So internet advertising is a broad umbrella term used for advertising on on search pages or on social networking pages and several other parts of the internet. And this is one of the major sources of revenue for this platform. So there are various reasons why internet advertising is very successful over the traditional form of advertising. The first reason is the user data. The advertiser can gather a lot of data from the user to design very targeted products, so targeted advertisements. So that is not possible in the traditional form of advertisement. One can also take measurable actions. So once it can characterize the put the bias into certain categories, then the advertisers can measure the interest and then take appropriate actions. So maybe if someone is watching a specific kind of a product page multiple times or specific kinds of YouTube videos or Facebook pages, then one may target that kind of an users because of their actions that they have taken. And also it has a very low latency. So one can actually do this bidding on the real time, the bidding could be automated and decisions certain decisions that can be made on the on the fly. So all these things happen at a very short period of time and that is something which is very much appreciated in the context of internet advertising. So what kind of types of ads that are that are prevalent on the internet? So the first type is that of sponsor search ads. So advertisers bid on the keywords that are entered by the users during search. So if you are searching certain things on the Google or Bing, there are advertisers who are actually bidding on those keywords and they and their ads being shown up in the corresponding products that you are using. So similarly, you can see certain contextual ads. So depending on the content of that page, so maybe if that is a page on cars, then you will be shown certain ads which are related to related to cars. So this could be from the web page, it can be from the post that you are making on a social media platform or could be your email message. So these days, even if if you are using some free email services, then they use your data in order to show you ads. That's how they are. And the not so used form of internet advertising is that of display ads. This is the traditional mode of advertisement. So if you are just showing certain ads on the newspapers, websites, or some similar websites, based on just the display they are being charged, those kinds of advertisements are not very popular in the context of internet, because it has very little information that you can gather. You cannot really target your users, you cannot see the context at which these ads are shown and similar other aspects. Now advertisements, modern day advertisements on the internet is very complex. So just to give you a feel of how it works in practice, they are generally handled via something which is known as the ad exchange. So what is an ad exchange? Think this is as an analog of telephone exchange in the traditional form of telephone. There is some exchange sitting at some place, some centralized location. And if you are making the call to someone else, that you are the client who is making the request to that exchange, telephone exchange. And then this exchange will connect your call to the other side of its network, which will be the destination, the intended person whom you wanted to call. Now a very similar thing happens in this context, here the destination is the publisher, we will publish your ad. So maybe this is the webpage where your ads might be shown. And on the other extreme, you are the client who has a specific advertisement to show. This is the advertiser's site and it has certain requirements. For instance, it might want to target a certain section of the population or maybe show ads for only certain kind of keywords. All those requirements in certain form will be placed on the ad exchange. So ad exchange is a mediator between these two parties. And based on the requirements of the advertiser, it will place the bids, automated bids on the publisher's side. So publisher also can give its requirements, which kind of ads it wants to show. The ad exchange does the computation and all the decision making of which ad should be shown at which position in the publisher's site and that will be given back to the publisher. So the publisher and the client do not have to do a lot of computation. The ad exchange actually takes care of all this computation and that significantly reduces the latency, the complexity at each of these places. So this is typically used by small businesses who cannot really customize ads on their own, but they can customize their ads via these exchanges. Now let us look at the position options. Options where the objective is to sell multiple ad positions on a page. So let us assume that there are n set of advertisers. These are the set of players that we will be talking about. And there are m slots in the advertisement. So in that web page, there are m slots starting from 1 to m. And there are n advertisers who wants to show their ads in one of these positions. And we are going to assume that there are sufficient number of slots. So you never run out of slots. The number of advertisers generally less than that. And as usual, the position one is the best possible position and m is the worst position. So everybody wants to show their ads at a higher level. So these position options have also evolved over the time. So the very early position options were ordering these ads via some bid per impression. So they were just charging these agents or the advertisers based on the bids that they can place for each of these impressions. So just to show that ad at that position, there will be charges fixed amount of money. And you can relate it to something similar to newspaper ads. So newspaper ads which are on the first page has a higher value, higher cost than something which is in the internal pages. And what it does is it puts all the risk onto the advertiser, whether they will be able to, whether they will be paying this money without knowing whether that ad will ever be seen or will be clicked or whatever. Now when the bids became online, it brought the advent of paper click models. So now the advertiser and the publisher are sharing this risk of when the ad will actually be seen. And click is a very explicit way of measuring that this ad has been seen. So in that situation, what is how the ranking is changed is that it now instead of charging each of these advertisers on the impression alone, it is going to charge on the click. So which means that the publisher will not ask the advertiser to pay anything if the ad is never clicked. But if it is clicked, then they will have to pay their bid. And they will also, so the earlier versions of this paper click auctions also ranked them by bid per click. But the problem there is that some of these advertisers can actually bid a very high value to a situation to certain pages where it is not actually relevant. So it is showing some irrelevant ads. And it is it can be certain that it has a very low probability of getting a click. But it still reaches to some of this population without even any payment. So the publisher in that case earns nothing because those ads are never clicked. So this is a loss on the publisher side. So to alleviate that problem that the modern approach is that they rank advertisers based on the product of the probability of click and their bid value. So not just by their bid value. So this probability of getting a click is what is known as the click through rate CTR for short. So this is why so you can think of this when you take the probability of a click and the bid value, then this is the expected revenue that you are going to get because you are when the agent is getting getting that click it is getting it is paying the publisher that amount of bid value. So that is that is giving it the expected revenue when you are multiplying the probability of that click with the bid value. So the CTR with the bid value. So we will make a few assumptions on the advertisers valuation. So the first assumption is that this clicks generate value to the advertisers. Of course when someone is clicking and going to their website it is certainly getting some amount of value but all clicks are going to be valued equally. So no matter so from the advertisers side it does not really matter whether the click came from the first slot or came for the last slot. So this is the position only affects the chance of getting a click it does not change the value. So these are the two assumptions that we can that we make our analysis a little simpler. So this actually helps us decouple the value effect and the position effect. So once you get a click then the user is actually going to the website the website of the advertiser and it gets the same value whether the click came from the first slot or the last slot. But there is a probability of getting a click which is actually giving the chance of whether this valuation will get realized or not and that has a position effect. So in some sense the VIJ the valuation of agent I when its ad is shown on the jth slot can be written as the VI. So notice that this VI is the value of the click which is not dependent on the position at all. The click through rate is essentially dependent on both the agent's identity and also the position. So there could be so why is it depending on the agents because if that agent if that particular advertiser who is the agent here has a very relevant ad then the quality component or the context component is very significant. So and of course the position of that ad is also important to estimate the probability of getting that click. So the quality component so this CTRIJ can be actually decomposed into two components. The first one is the quality component and the second one is the position component. So therefore this can be decomposed into these two parts. So notice that this is the user effect or the advertiser effect and the second one is just the position effect. So the expected value so VIJ as we said is going to be the this quantity the PJ which is a position times the rho Y which is the user effect times VI. So now within this parenthesis we have isolated only those part which is the advertiser dependent and outside it it's PJ which is the position dependent part. And we are going to always assume that the position effect is always going to be decreasing with the position. So if you are if the position is J then it has a higher probability of getting a click than if the position is J plus 1 and so on. Now VI is the only private information of the advertiser that is what we are going to assume in this context and we can see that both the PJ and the rho I are actually measurable quantities. So we can actually measure or estimate the this rho Ys let's say it is estimated as rho I hat and this is something that the search engines always do. They try to find out for every advertiser what are their rho Y components and what are their position components. I mean position component is common for all the agents but the rho Y component is specific to a specific advertiser. Now what bidders do bidders bid their VI's and ads are ranked in the decreasing order not just by their bids but the product of this rho I hat which is the estimate of their probability of getting a click the user component of the probability of that click times their bids that they are making. So we will see that what properties it satisfies in the next module.