 So this is all from my side, so Martin, the floor is yours, 40 minutes. Thank you, Özlem, for the introduction. I will talk about a particular type of bias recommendations, which we call inflated recommendations. That's a situation when a product is recommended too often or is recommended to too many consumers. As mentioned by Özlem, this is joint work with my colleague here in Mannheim, Anton Sobolev. So what I want to say is this is an issue of policy relevance, but I don't think that there's anything which should bias me in a major way. And that's what the slide is supposed to tell us. Now, we have a model of bias recommendation. You can think about a firm, say an intermediary who recommends, has to decide whether to recommend a new product to consumers. And there are different types of consumers. And the important ingredient in our model is that there is some extant heterogeneity among consumers. There will be some consumers who can be pleased all of the time, but others cannot be pleased all of the time. And that's one way of reading this phrase, which I've put up here. So a key ingredient of our model is that you can't please all of the people all of the time. Recommendations play an important role in many markets, in particular in the digital economy. We have recommender systems. So these are then algorithmic solutions which tell consumers which kind of products they may want to look at. They may want to buy an important and that's an important ingredient. What we have been seeing in the digital economy is that many of those recommendations are personalized. So they're conditioned on some characteristics of consumers. The kind of recommendations we're looking at here are recommendations for a new product which will be an experience good. So that means consumers are initially, or at least some consumers are initially uncertain about the value, the consumption value they will obtain. And the recommendation becomes biased if consumers end up buying products which are not in their best interest to buy. And clearly in an experience good setting that can be a product which delivers a valuation which is less than the price. I mentioned that there are some policy interest in bias recommendations. We see this in particular in the case of first party content or first party products and to the issue of self-preferencing, but it applies more generally. Also two cases where only third party products are offered, but for example they generate different commissions or they generate different conversion rates. What we aim to do in this paper is not to have a general theory, but a very specific model which allows us to look at a particular type of bias recommendations. And as I mentioned already, the key element here will be some extant heterogeneity. In particular, and this is the basic idea of the model, there will be two types of consumers, some consumers we call flexible consumers. They like this new product, there's some positive valuation they get which is above the cost or above the opportunity cost of providing that product. And this gain, if you think there's some base product out there, this gain is above what the base product can offer. And then there are the picky consumers and for them it depends. So it might be that they very much like the product, but it might be that they have somewhat lower consumption value compared to the flexible consumers. These are then the consumers who can benefit from advice, who can benefit from a recommendation such that they are recommended the product only in case where this new product delivers a good consumption experience. To place this in an e-commerce setting, we are allowing for two distribution channels. There will be a direct distribution channel and an indirect channel, the indirect one. That's when the consumers buy through an intermediary. This intermediary offers is different from selling from the direct purchase in two ways. First, consumers, all consumers obtain a higher benefit using this indirect channel, maybe superior logistics. And the consumers who rely on recommendations, they may benefit from the recommendations provided in the indirect channel. So it's the intermediary who can provide those recommendations. Those recommendations are not available on the direct channel. And in this setting, the intermediary may maximize its profits by inflating recommendations. The inflating recommendations here means that picky consumers receive a recommendation not only when their consumption experience will be good, but also with positive probability when the consumption experience will be not so good. And the reason the intermediary wants to do this, it has to deal with this eccentric heterogeneity of consumers and what it is doing. It is reducing the heterogeneity of the expected consumer valuations for those consumers who buy. And this allows for a better surplus extraction on the consumer side. Intermediary may pick this inflated recommendation outcome. So it means recommending it to some of the picky consumers who dislike the product and all consumers who buy will buy through the indirect channel. So in the sense of thinking about is it efficient where consumers buy. Yes, it is efficient because indirect channel provides the additional consumption benefit over the direct channel. But the inefficiency here is that some of the picky consumers buy who actually dislike the product and that reduces surplus. The other possible outcome is one which we call inefficient bypass. Here the recommendation is not biased and it will be only the picky consumers who actually like the new product will buy the product from the intermediary. The price will be such that the flexible consumers will not buy through the intermediary. They will buy on the direct channel and therefore the inefficiency from a total surplus perspective is that some consumers buy through the less efficient distribution channel. There is a question Martin from Jacques Kramer. So he's asking whether the indirect channel you meant here is for instance buying a game or an app or subscription through the app store rather than directly from through the publisher, for instance, would that also apply to that context. To the extent that these recommendations also matter on the app store. Yes, that is also applicable so you can think it in the in the app store context. I think when I will phrase it I will more I will put it more in an e-commerce setting that you have sellers. For example, a hotel you can book directly on the hotel or you can do it through a hotel booking portal. Okay, so here's a very simple model. We have an experience good, which is introduced in the market. They are picky and flexible consumers. The fraction is exogenous fraction alpha is picky. The picky consumers have high or low valuation here for simplicity just suppose that the probability is one half one half. And then they're the flexible consumers and for this presentation they have some value they derive some consumption value vm and that is greater than the marginal cost of production. Consumers know their type so they know where they're picky or flexible. However, the picky consumers do not know upfront whether the realization will be VH or VL. We're assuming here that the the flexible consumers have a higher expected valuation. And then these valuations are the valuations buying in the direct channel. There's the convenience benefit of buying through the indirect channel B which comes on top and that applies to all consumers. And in addition, what the intermediary does it is providing a recommendation. It's easy to see that the intermediary will always recommend a good match. So the probability of recommending a good match is one and therefore the only parameter the only variable we need here is the variable beta, which is the probability that a bad match is recommended. So when a picky consumer actually has VL which the picky consumer doesn't know but the intermediary knows and the intermediary then can decide to recommend the product to this picky consumer even though the intermediary knows that the valuation is VL and can do so with any positive probability between 0 and 1. So here I put another parameter restriction in there, but I don't think that this is important, but we have to the full analysis depends a little bit on where we are in the parameter space. So here we have the marginal cost being above the expected valuation of a picky consumer buying through the indirect channel. So let me illustrate what that means in terms of willingness to pay. So consider first the case that the intermediate that the recommendation is fully informative. This is beta is equal to zero beta equal to zero means that none of the picky consumers with a bad match receives a recommendation. Okay, so that means then we have these this black demand curve. They are those consumers who are picky and have a high valuation so they are willing to pay VH plus B. Next come the flexible consumers with a valuation VM plus B. And finally the picky consumers with a bad match with valuation VL plus B. The opposite case would be to have a fully uninformative recommendation say recommend the product to all picky consumers in that case. Picky consumers cannot update their belief and what we have is the the valuation of VM the willingness to pay VM plus B for the flexible consumers and VL plus VH over to plus B for the picky consumers. Okay, and what we see under the assumption that actually this marginal cost is above VL plus VH over to plus B, two prices can be profit maximizing it's either VH plus B, or it is VM plus B. And what we can see then if we want to sell at VM plus B, we can actually do better than having this fully uninformative recommendation policy. We can pick some interior beta so as to equate to equalize the willingness to pay off the flexible consumers with the expected willingness to pay of all picky consumers who receive a recommendation. Okay, and you can see that's of course better than running beta equal to one. Therefore we have two possible outcomes one with inflated recommendation the other one where only the picky consumers with a good match will buy they will then have to pay VH plus B. And the the flexible consumers will be served outside the intermediaries channel outside the indirect channel. Okay, so let me look first at what is the vertically integrated firm so it's one firm which is both selling and doing a recommendation. The recommendation policy as I said is then just this beta the probability of recommending a product to a picky consumer with a bad match and the firm will set prices on the indirect and the direct channel. Consumers observe that type and they decide whether to go to the direct or the indirect channel and if they go to the indirect channel, they receive a recommendation. Important are only the recommendations here for the picky consumers and this recommendation is then used by the consumers to update their beliefs. What I spell out on this page and I think I can rather go through this quickly because I already gave the intuition of what is happening that to potentially optimal strategies inflated recommendation or inefficient bypass. The inefficient bypass outcome is straightforward. So here the price on the indirect channel is the VH plus B as we saw on the in the drawing and the figure. And the price in the direct channel was again is now the full surplus extraction of the flexible consumers and their willingness to pay for the direct channel is the end. Here there's no recommendation bias and we can write down what are the profits of the firm using this strategy. Alternatively, the firm can use the inflated recommendation strategy in which case it will extract the surplus from the flexible consumers and the indirect channel. That's the M plus B everybody who buys will buy in the indirect channel and beta is just picked such that the conditional expected willingness to pay of the picky consumers or those who receive a recommendation is just equal to what's the consumers. What the flexible consumers are willing to pay and there's a typo that should be VM plus B. And then there's a cut off alpha. So it depends on the fraction of picky versus flexible consumers where there is inflated recommendation or there is inefficient bypass. So if this fraction of picky consumers is efficiently small, there will be inflated recommendations and otherwise there will be inefficient bypass. It should be clear if they're just there's a very large fraction of picky consumers, then you don't want to give up on the surplus of those picky consumers and want to extract as the as the firm V H plus B, and therefore there will be an efficient bypass. Whereas if that fraction is small, well then you're rather want to enjoy the the price VM plus B instead of VM you can get from the flexible consumers and then do the best to extract surplus from the picky consumers and this is by introducing inflated recommendations. So we can then embed this into the setting where now the intermediary and the seller are not identical. We have now the intermediary formulating a recommendation policy. So this beta is now conditioned on the retail prices. And I believe that that makes a lot of sense recommend a recommender systems recommendations do depend on the prices which are set by sellers. And here we are looking at the intermediary who commits to such a recommendation policy and asked for a share of the profit in the in the indirect channel for from this seller. Second, then given the intermediaries recommendation policy and the price or the profit share it asked from the seller. The seller sets the retail prices on the indirect channel and the direct channel and then the game continues as we have seen before. Consumers learn their types make a choice between the two channels and if they are in the indirect channel they receive a personalized recommendation. What will happen in this model well will exactly the same thing as in the vertical integrated models or the solution will be in a way decentralized. And why that is the case it's easy to see that the sellers outside option is always to sell to flexible consumers in the direct channel so it can sell at VM incur the unit cost see and sell to the fraction one minus alpha consumers. So that's what the seller can make for sure. But the seller cannot make anything on top of that the recommendation policy beta can be formulated such that all the additional surplus which can be extracted from consumers then goes to the intermediary. And this is done by adjusting in the inflated recommendation outcome the lambda in a way that the seller is indifferent as to whether to sell through the indirect channel or whether to pick the outside option. And since we have the same outcome it means we obtain exactly the same critical alpha which separates the case where we have inflated recommendations from the one this inefficient bypass. And this is stated in this proposition here. So again, we have this critical threshold alpha bar. And what the intermediary is doing to implement the inflated recommendation outcome is to have a recommendation policy such that when the seller sets the price in the indirect channel equal to VM plus B. And sets a sufficiently high price in the direct channel it will use inflated recommendations according to beta star. And otherwise it will be completely uninformative. And this is one way of implementing implementing inflated recommendations. The associated welfare in our solution is the blue straight the solid blue line. And clearly here we have an inefficiency and this inefficiency is due to the ex ante heterogeneity of consumers and the borderline cases where there are only picky consumers are only flexible consumers. We obtain the first best outcome but they are welfare losses whenever there is a mix of flexible and picky consumers. So this was my claim that this model really relies on ex ante heterogeneity and the welfare loss is depends on whether we're under inflated recommendations or inefficient bypass the inefficient bypass case. There the welfare loss is due to the fact that some consumers by so the inefficient channel which is the direct channel and the the welfare loss and the inefficient. In the inflated recommendation outcome is that some picky consumers with a bad match by now you may find the model. Particularly in some ways special. The message I want to convey is that this kind of inflated recommendation appears to us a very robust phenomenon relying here on ex ante consumer heterogeneity. So here we have the specific setting just of two types. One type there's this uncertainty it's V H or V L the other one there's no uncertainty so there's a change. There's a difference both in the expected valuation and in the variance. Now you can keep the variance the same and just change the expected valuation. This model becomes somewhat richer. That's why we focused on this one here that different types of inflated recommendation outcomes which can then obtain but the general message that recommendations will be inflated is preserved and this we can also then write down with a continuous type model. Another alternative is to actually work with heterogeneous consumer and ex ante heterogeneous consumer information instead of working on the preferences and also that's the way how we can generate bias recommendation. So in that sense I think we have a the outcome of bias recommendation is not specific to one particular type of modeling ex ante heterogeneity. But ex ante heterogeneity in general is a reason why recommendations will be biased. Let me make a comment on the related literature. I only put up here one reference for each bullet point and I understand that the audience is an expert audience. And there are some other contributions so we do cite a few more papers in the references in the paper but of course if you think that for some strange reason we have overlooked you shout out and we're happy to to improve our exposition on the related literature so quite clearly we are contributing to the literature on recommendation biases. A different way at looking at what we do is call this targeted advertising when you think about advertising a product and as the advertiser or the intermediary deciding on which adds to put. You may have information on consumer characteristics and if you use that information then you can go for targeted advertising what we show here inflated recommendation means that you're not fully targeting you could be provide a better targeting but you decide not to and the reason is that this allows you to sell more units at the general level. This is just an particular instance of Bayesian persuasion what we're doing here looking at the direct and the indirect sales channel is a contribution to analyzing the dual mode and looking at what firms possibly also partially vertically integrated firms optimally do. I was showing you the distribution of the willingness to pay and the derived demand curve depending on the recommendation policy in a way you can see this as a kind of demand rotation or at least yeah you'll just stretch and rotate demand in the sense of Johnson and Myatt and this also relates to paper by Rhodes and Wilson on false advertising where here you can call the recommendation of a bad match as a false advertising if you want. And what we have is that this is an equilibrium phenomenon without any punishments by outsiders for false advertising. Here you want to use this kind of false advertising inflated recommendations because of Exante heterogeneity among consumers and so that's the new our new ingredient. Now if you think about these picky consumers who can have a high valuation or low valuation this you can think about two different states of the world. Then if you recommend the product only in case the valuation is high then you sell the product independently or you can recommend it both if it's VH and VL in which case you're essentially selling the bundle. And what inflated recommendations then is is a mix between selling the product in separately and selling the pure bundle because we're you're selling the product with a good match with probability one and the product with a bad match with some strictly positive probability probability is strictly less than one. In terms of the outcome we have recall that by using these inflated recommendations, the picky consumers will buy the product with strictly positive probability when they experience then a bad match. Now think instead of a refund contract a refund contract is when you sell a product and give the option to consumers after purchase to return it if they didn't like it. Now if we introduce a refund contract where you have only a probabilistic return right then this the outcome is essentially the same as what we have here because then consumers with a bad match will try to use this option to return the product. They only can do so with positive probability and this is then the same thing as those consumers not receiving the recommendation to buy the product and therefore they don't buy it in the first place. So that's our my quick relationship to the literature. What we then do in this paper is to look at a number of regulatory policies where the the regulator imposes restrictions on the recommendation policy. First, suppose that the regulator can fully condition this recommendation beta on the retail prices on PI and PD. And then we move to a much more restrictive recommendation policy, namely one where the intermediary is not allowed to recommend the product to picky consumers with a bad match. And then we introduce a recommendation cap where the interpretation is well this is the regulator is more lenient and allows for up to a certain level it allows for these this inflation to take place. And well, so I think these are the the ones I want to want to mention in this presentation. Now if the the regulator can fully control the recommendation policy without controlling any price or neither the lambda that's the price or the profit share extracted by the intermediary nor the retail prices itself. It is actually able to implement the first best so that means when only when the regulator is more limited in its instruments will we get something which is different from the first best. Now clearly, if the if the regulator imposes a very strict rule, namely that inflation inflated recommendations are not allowed, then we obtain a deviation we obtain a result which is different from the first best. What will happen now if the fraction of picky consumers is sufficiently small, then this policy improves on the laissez-faire, because in the laissez-faire the intermediary would introduce some level of inflated recommendation now this is ruled out. But then the intermediary still prefers to sell to everybody on to choose a policy such that everybody who buys will buy through the indirect channel. However, for some intermediate range alpha, the trade off between selling everything on the indirect channel or having some sales on the direct channel and another fraction on the indirect channel this trade off is different. Now for a smaller critical alpha, do I want to move as the intermediary to the outcome, which is then inefficient bypass and therefore this regulatory policy can backfire and deliver an outcome which is worse than the laissez-faire. And if alpha is then sufficiently large, this policy is neutral, we will get the inefficient bypass outcome in any case. If we allow for recommendation caps which are here conditioning on the alpha, then we can show that this policy weekly improves on the laissez-faire. And here what we get is an intermediate range where the policy allows for some inflation so as to make sure that all trades still happens on the intermediary. And this is then this line which lies above the laissez-faire outcome. What is important for our result to hold is that while prices here depend on the distribution channel, they do not depend on the consumers in the sense that there is no personalized pricing. Clearly if there was a possibility of using personalized pricing, then there wouldn't be any reason to keep consumers outside the indirect channel and this benefit B would materialize. So therefore there wouldn't be also then any reason to inflate recommendations because inflating recommendations reduces total surplus and since personalized pricing allows for surplus extraction in any case, this can't be the optimal thing to do for the intermediary and the seller. And also I think it's important to see what our model does is assuming that there is this new product out there and it can really deliver bad experiences. If there's a large set of products out there such that consumers can always make a good experience, then there is no reason to make a recommendation favor towards a product delivering a bad experience compared to one with a good experience. So that means what we are essentially implicitly assuming is that we don't have a variety of products out there such that all consumers can obtain a high valuation. The intermediate price instruments do not matter here and price parity clauses here are not beneficial for the intermediary. So that means our results do not really rely on this. Now one variation you may think is perhaps more realistic is that the recommendation policy should apply for all alpha. So that means there's a different product categories out there and this with different with the composition of consumers is different and the recommendation policy should they not condition alpha. This means this would imply that inflating recommendation becomes somewhat less attractive, but it will still be an equilibrium outcome. So the critical alpha will be above zero, but less than the critical alpha we have determined here. Perhaps one last thing I want to mention given time is that we also look at platform leakage. Platform leakage is then the situation where consumers can first go to the indirect channel, obtain a recommendation and then still decide to go to the direct channel afterwards. If that applies to a fraction of consumers or not to everybody, but to a fraction of consumers, then what we will actually get is more inflated recommendations. So it's not only that inflated recommendations remain robust on top of that these inflated recommendations hold for a larger set of circumstances. I think I used up the pre-assigned 40 minutes. There's much more one can do and there are quite a number of things we do in the paper. And if you're interested, well, the paper is publicly available. Excellent. Thank you very much, Martin. You are very good on time. Thank you. So Hesky, please floor is yours for five minutes of discussion. So thanks to the organizers for giving me the opportunity to read the paper. I read some of it. It's 90 pages with the appendices. So when Martin said there's plenty more to chew over in the paper, this was not just for effect. There's plenty here. I want to sort of step back from the details for a second and then I'll talk you through my perspective on the paper from the literature that I know. So I was very happy that in the related literature section, Martin put Chemnitz and Genska, which in the version of the paper that I have, there's no reference to, but to some extent, I think that's the closest reference. So, I mean, I think the big picture overview is one that's familiar to this group and has some novel economics, which is the importance of these gatekeepers in managing what retail competition looks like in managing what consumers know. And I think there's been a focus in the last few years on this gatekeeper role in part due to reports like Jacques, if he's still online and others. And this recognition that through their, through, in large part, the information that they provide through consumers, whether that's rankings in positions or information directly is, or opportunity to acquire information is stuff that Fithenton Guillermo and I were thinking about a while back. That has the capacity to influence what demand looks like what prices look like what the nature of competition looks like. And I think these are important questions and finding nice tractable models, where in particular we can think about the effects of policy which is what some of these 90 pages are about a good chunk of that is geared up to try to think about some plausible policies I think is important and is very valuable. Anybody who knows me in these seminars know that I like to start from thinking at specific applications. So that was something that I was missing a little bit in the paper. Are we thinking about Amazon are we thinking about her. What are we thinking about a little bit delicate because consumers have the choice of whether to go to this indirect or direct channel first. And then once they've gone to one channel or another, having observed prices in these channels that that's it that they're done. So that was a little bit hard for me to think about I appreciate the extensions. Much easier for me to think about is what what Martin calls the vertically integrated case. I think actually another interpretation of the vertically integrated case that's a bit more natural to me. It's just to assume away the direct channel. So when I go to Amazon, it never even occurs to me that a lot of the stuff I could buy, I could go and find somewhere else. So in the model, you know, that is just the vertically integrated channel, or you could think of setting be up to infinity or thinking about some comparative statics with be would be relatively easy to implement. But that's a much easier application for me to think about. And I think it brings it a lot closer to existing literature, like whether that literature is cabinet and chance cow or I'm realizing now that I'm very old I still think in terms of Lewis and Savington, you know, who had these models of providing information that was a very specific form of information provision that we then saw evolve with Justin and David's work and there's a very nice version of Lewis and Savington that the, you know, even before cabinet and chance cow that deals with an unstructured format that's an economics letters paper by Alex back, and I can provide translator that just says you know for a monopoly. If I could choose price and if I could choose information, all I'd want to tell you is, is the evaluation above marginal cost or not and then I can extract the full consumer surplus. So, what we have here, I think kind of builds on on those intuitions that, you know, if I'm targeting a price I'm just going to lead you to have an average valuation equal to that price and here what gets me to target specific prices potentially is the presence of this heterogeneity, which I think is very interesting so for me it's like easier to come at it from that way and then introduce the indirect channel. I mean, for a lot of the results for this inflation you don't need the indirect channel at all. And so I think kind of being sorry the direct channel at all and the bypass associated with the with the direct channel. There's these two forms of this inefficiency. So the paper is titled inflated recommendations, but then this other form of inefficiency is buying this stuff directly and paying this higher penalty from not having the convenience of Amazon or whatever it is. And I think if you want to have that second form of inefficiency you have to justify it a lot more discuss what it's relevance it's importance and explore it to a greater extent than than you do. I've probably gone over time already. So I hope that was of some use again the kind of big picture I very much appreciate and in terms of the paper. I think I would start with just ignoring the direct channel. I'll move closer to some existing literature. So Camelich and Jen scowl and stuff like that for me should be the first reference and then move from there, but great stuff.