 Good morning, good afternoon, and good evening, everyone. Welcome to the third seminar of our series on the economics of platforms. And today we'll have Renato present a paper on regulating platform fees under price parity. Just a reminder, this is the session is being recorded and we'll go officially for one hour. So depending on where you are, it's either 8am to 9am or 2 to 3pm or whatever it is. And after one, so the official seminar is over after one hour, but people can stay after one hour if they want to ask questions, you know, for more clarifications. And I think we'll stop the recording after now. And also a reminder, Renato will speak for about 40 minutes and he'll pause to take any clarification questions and we prefer to keep the more substantive Q&A for the last 20 minutes. But that's Renato, all yours. Okay, so thank you so much for having me. I'm very happy to take part in this initiative. So this is joined to work with Andrea Mantovani from Bologna. So the topic of this paper is how to regulate information or matching platforms, which I'm sure everybody agrees on that with me, are increasingly important, right, in today's economy. So I'm thinking about marketplaces such as Amazons or OTAs, online travel agencies or Uber or, you know, open table if you want to reserve restaurants, such as NANIs if you need a NANI and your name. Okay, so in these platforms, the agency model is often employed, and that means that platforms got to cut out of each transaction that happens in the platform, right? So this, of course, leaves room to a lot of opportunistic behavior, right? So, you know, for instance, buyers and sellers, they might meet inside the platform. And then engage in subsequent interactions outside of the platform, therefore bypassing the fee, right? Depending on the context, this is not a concern, for instance, in Uber, the matches are transactional. If you want to reserve a restaurant, perhaps the only way to do it is through open table that the restaurant doesn't take reservations directly. But in other cases, it's a concern. If you think about Airbnb or the student NANI is whatever, right? Another important concern is what I call showrooming, what I call it, the literature called showrooming, which means that people gather information inside the platform. So the information provided by the platform is a public good, so people can just go there, learn what they have to learn, and then they transact outside also by passing the platform fees, right? So price party clauses, they aim at preventing the latter kind of opportunism. And these clauses, they stipulate that prices cannot be lower, cannot be lower elsewhere, right? And that also applies to availability, conditions that cannot be better elsewhere, and so on and so forth. So that basically makes sure that consumers have no incentive to bypass the platform. Of course, there are opposing views on price priorities, right? So platforms would like to claim that price party is essential for the business, precisely to prevent this kind of opportunism. But competition authorities, they see it differently. They see it as a source or a reinforcer of platforms market power, right? So the commentary of harm in this context is that a price party clause reduces competition between platforms, because if you think of a Maverick platform, an entrant that wants to enter the market by setting a lower fee, under a price party clause, hotels won't be able to set lower prices in that platform if they still join the dominant platform, which makes it entry and which makes competition in commissions something not very possible, right? So basically retail prices are not very elastic to platform commissions, which also leads to a barrier to entry, because entrant platforms have a hard time to undercut commissions and to generate an impact on consumer behavior, on consumer choices. And all of this also leads to a common selling agent effect in that price, in that platforms can raise prices in a coordinated manner downstream, right? So by setting high commissions, they can uniformly raise the price set by sellers and lead to much higher prices, potential low elf and so on. So these concerns, they led to a lot of scrutiny by especially EU competition authorities, right? So in this table, I summarized some of the recent developments. So starting in April 2015, the French, the Italian and the Swedish competition authorities, they made booking that come commit to switch from a wide price party clause where prices cannot be lower anywhere, right? In comparison to the platform, to a narrow one where prices could be lower in other platforms, but not in the direct sales channel, right? So this commitment came into effect in July 2015, but one month later in August, the French promulgated the Macron law, which prohibited PPCs altogether, right? And the Italians, the Germans, the Austrians, they went on a similar path just after the Italians as well in August 2017 and so on. So that pertains to OTAs, right? To online travel agencies. When it comes to marketplaces, I think about the Amazon's marketplace, price party has been banned in the UK and it has been very recently, this year in fact, removed voluntarily in the US. So price party has been, how can I say, deemed illegal or have been voluntarily removed so they are no longer part of most cases of the legal ladder that binds sellers on the platform. But it's not very clear that these measures produce tangible results, right? For one, sellers might still practice the price party to be in good terms with the platform, right? For fear of being downlisted. So it's a conduct thing, okay? Even if price party is not in the contract, you don't want to be seen by the platform as someone that is sabotaging the business because you're going to be downlisted, okay? There are also loopholes. So in France, the Macaulay stipulates that price parties cannot be imposed, but they can be voluntarily accepted. So in this respect, there has been a lot of, let's call it preferred partner programs whereby a hotel accepts voluntarily to practice price parity. And in exchange, it stops listed, it becomes kind of a prime deal, you know, your name. It's also a concern that many of the hotel's passengers, especially the known chain ones, they are quite unsophisticated in the pricing. So they have a scarce propensity to price differentiate and many of them have limited awareness of these policy changes. And there's plenty of evidence that I think are explained by all these factors. So the European Commission Network in 2017 documented only minor changes in the commission fees following major decisions that were still very high. So in the case of FOTAs, they are close to, on average, 20%. Honored and co-authors, they found evidence of the downlisting, they call it dimming, whereby the OTA scandalized hotels that charge lower prices with worse rankings. Mantovani and co-authors, they also find a limited price effect on the short and medium run after the elimination of OTAs. They conduct a study comparing Corsica with Sicily and some Spanish islands where they managed to control for changes in legislation, keeping constant, let's say, the environment, right? Because these places are, one can argue, they are somewhat similar. Ennis and co-authors also find a limited price reduction on the direct sales channel following the removal of these price parties. So in a sense that our take might be controversial, but our take is that the policy on academic debate has been centred on whether one should uphold reform, for instance, moving from a wide to a narrow price party, or band price party altogether, and yet little consensus has emerged, both in terms of the effects of these policies, as well as in terms of whether this is theoretically desirable. You know, whether when you do the economic theory, you do the step back, whether this is something that we actually want to do. I'll talk about it in the next slide. So in this paper, we make kind of a first observation, which is somewhat obvious. In there, we see the parallel with the payment industry where there is a price party clause, which is called the no-soul charge rule, which prevents merchants from price discriminating according to the payment method. So if you are a merchant and you're making a sale, if you accept a max, you cannot press discriminate. You cannot charge more for the guy that's buying with an American Express, even if the merchant commission is 3%, even if it's super high. So that's the no-soul charge rule. And also in the payment industry, there are claims that no-soul charge rules, they give too much market power to the card networks. And countries adopted different strategies to deal with that. So the UK, the Netherlands, New Zealand, Australia for almost 20 years, they lifted the no-soul charge rule, allowing merchants to price discriminate according to the payment method. Whereas other jurisdictions, such as the US or in Europe, the European Commission, they regulate the interchange fee. The interchange fee, you should think about it as something very close to the merchant commission. So it's very close to regulating the merchant commission, let me say. So in fact, in a policy briefing in 2013, the European Commission suggested that allowing surcharging for cards, which is not subject to regulation, should be okay. So there is the implicit idea that the competition policy alternative, which is banning this clause and the regulation alternative, which is regulating commissions that destroy substitutes. You can do one or the other. So in a sense, we kind of leverage on this parallel to develop a theory of how one should regulate platform fees under prosperity. So we're kind of taking the stance that in light of the empirical evidence, banning prosperity can be done legally, but not de facto. De facto is an ambitious thing to do. The effects of banning prosperity is small. So let's consider a world where prosperity is still there or it's de facto difficult to ban. And let's think about how to regulate commissions directly. So we develop a theory in this direction. We derive an optimal cap that is a formula on how to regulate, on how to cap these commissions. And in particular, we relate this optimal cap regulation to competition policy alternatives, meaning relaxing or banning a price product. So I'm not going to go for details now because that's just the introduction, but we articulate a theory of harm that's based on the contractual externalities that joining a platform generates to non-joining firms. We propose a simple test to assess the platform contribution to producing consumer surplus. And we also compare the optimal regulation with, for instance, banning price parties. That was de facto possible. And we show that banning price parties, that was de facto possible is akin to capping the platform fee at an efficiently low level. So that's one of the takeaways from the analysis. So there's a lot of related literature on this topic. So Edamon and Wright in 2015, they argued that platforms typically over invest in the provision of non-pecinary benefits, which leads to higher prices, lower welfare, and so intermediation is well for decreasing somehow under conditions of course. Boic and Cortes and Johnson, they are the first to articulate the tier of harm that I mentioned before, in that price parity leads to higher commissions, prevent entry, and increase final prices. One can write, they argued that the narrow version of price parity in fact improves upon the wild one, especially when platforms are not viable in the absence of price parity. So that would be a good compromise. A dissenting view is offered by Johansson and Verge, who argued that price parity makes firms more prone to the listing, which tightens the participation constraint and in fact decrease commissions. So as I said, even from a theoretical standpoint, it's not entirely obvious that banning price parity is a good idea. And empirically, the effects are also kind of not very present. So that's why we explore the regulatory avenue. So these are my bold claims. I'll substantiate my claims and what follows, but I should stop here to see if there are any questions about my bold claims. So there are no questions in the chat. What I suggest if people have clarification questions as we go along, it's a good idea, either raise your hand or maybe write the question in the chat and then we can ask him to run out as he stops at regular intervals. But I think there are no questions up to now as far as I can tell so you can go ahead. Okay. So yeah, so feel free to ask them. But let me describe the model. The model is quite simple. So they're in firms, which I indexed by J. And there is a unit mass of consumers that have single unit demands. So if you think about the hotel application, consumers only need one hotel, of course. So the consumers gross utility from J's product is the sum of two terms. Okay, one is a vertical component, which is like the number of stars in a hotel. Okay, a level of quality. And there is a match specific component. Okay, so you should think of this match specific component as having to do with the location of the hotel, the facilities, whatever you know that that's specific to the consumer. And each consumer has preferences described by a profile of match values, which we call Z and this is drawn from some symmetric distribution G. Okay. So this is idea across consumers, but the match values can be correlated for a given consumer. Okay. So each firm faces a constant marginal cost CJ and sets a price PJ. So this is the standard the script choice model. So the key idea that we explore here has to do with consumer information with the impact of platforms on consumer information. So we say that the firm J belongs to the consideration set of a consumer. If this consumer observes the pair of gross utility and price. Okay, and consumers can only transact with firms they are aware of that is that belong to their consideration sets. Okay, so if a consumer doesn't buy from any form it gets zero. Okay, but it has to choose something from from from from the consideration set that he knows. So and crucially consumers are heterogeneous on this consideration sets. Okay. So think about coming to to lose. Okay. So I believe that many of you know the Hotel de Brienne. You might know Albert Renier and they, you know, well, the bees who know. So people are, you know, some people know this hotel's others that come to visit their buzz might know others. I know others and so on and so forth. Okay, so consumers have heterogeneous information about what's in the market. Okay. And the way that we formally describe visit originator of information is for a new friend that recall a consideration profile, which is something that maps a subset of firms to a subset of consumers that knows precisely that set of firms. That's a consideration profile. Okay, so that's this this friend here. And this allows us to express a concept that's crucial for the analysis and I'm going to come back to it quite often, which is what I call the firm's potential demand. So that's the set of all consumers that know that firm under that consideration profile. So it's the union of false subsets of consumers that have that firm in their consideration set. Okay, so that that describes the potential demand of a firm. So in most cases, we want to have a tractable model. So we're going to assume that this consideration profiles are symmetric in the sense that all consumers process consideration sets of the same size and all firms have equally sized potential demands. So so so information is symmetrically distributed in a way to make things to make things simple. So this implies that the potential demands, they are precisely the, the, the, the size of consumers for station sets divided by the total number of firms. This should be intuitive if consumers know 20% of firms, and if the consideration profile is symmetric firms have a 20% potential demand. That's right. So what's the role of a platform in this world. Okay, so the, the, the obvious observation that we make is that platforms, they, they expand consumers information. Okay, so in the, in the baseline model, there is a monopolistic platform. And before consulting the platform, think about a consumer that needs a hotel room to lose and this guy hasn't gone to booking.com yet. Okay. So the information that this guy has is described by some consideration profile, Sigma lower bar. Okay, that's what he knows absent booking.com before visiting book.com. So this captures all the information that can be obtained for advertising, travel shopping guides, friends recommendations, you know, previous experiences, whatever. So, so the way that we model the platform's contribution to information, we do it in a very stark and simple manner. So we assume that all firms listed in the platform are added to the consideration sets of every consumer. Okay, so there is an implicit assumption that visiting the platform is costless and that wants to visit the platform you seamlessly learn everybody that is there. Okay, so I mean the idea is that platforms, they have quite efficient search tools, you can sort hotels that you want, you have many ways to search. So, so kind of the implicit assumptions that consumers they learn everything they have to learn very fast. And if all firms joined the platform, that means that consumers, they seamlessly learn everything that's available in the market. And that's described by this information, this consideration profile, Sigma upper bar. So which has the highest reach. So that is all consumers know everything. So, so in this way of modeling makes it makes it makes something evident that I would like to emphasize here, which is, which is the fact that firms that joined the platform. They expose non joining firms to an externality. So that's an externality of non participants. Okay. So, so to, to, to understand this idea, suppose that all firms joined the platform, except for some firm J. Okay. So what's going to be the consideration profile that describes information in this economy. It's going to be something that I call Sigma minus J. And, and it has two features. One is that all consumers that considered from J. Now they consider all other firms. But those consumers who did not consider from J. Now they consider all firms other than J because they learned everything that's in the platform. So what this means is the following. Suppose that I'm the firm that doesn't join. Okay. So if I don't join, I'm going to enjoy the same potential demand that I had before. Everybody that knew me, they still know me. But the point is that now they know many other firms. So my potential demand if I don't join is the same that I had absent the platform. But those guys that that populate my potential demand, they have much more information. So my potential demand is much more contestable. So the fact that firms joined the platform impose an externality of non participating firms by means of the fact that the potential demands are much more contestable. There's much more competition for my potential. Okay. So I'm going to come back to this idea in a second. So let me just finish the description of the model by describing contracting. So price party is in place. And the platform is going to offer each firm J privately a fee FJ. The private contract is not essential. Our results they hold with public contracting as well just being private contracting because somehow I found it simple. The platform is profit maximizing. And we assume that if all firms join, if a firm join all of its sales happen through the platform because it's somehow more convenient. And a firm enjoys a convenience benefit B if the transaction happens within the platform because the firm doesn't need to process the transaction process the payment and so on. So there is a convenience benefit that has nothing to do with the informational benefits just convenience. And so to summarize what I just said the timing is as follows the platform privately offers each each firm a fee FJ firm simultaneously set prices and decide whether to join the platform and then consumers are going to buy from some firm. They are aware of of course there's a function of who joined the platform. So the solution concept is the usual one perfect vision equilibrium with passive beliefs for short equilibrium. And in order to get some tractability I'm going to impose some symmetry assumption that basically means that the gains from trade are constant across firms. So this means that the Delta which I define as the gains from trade VJ minus CJ is invariant in J meaning that hotels with more stars are more expensive in a commensurate manner. Just one quick question here. Sorry. When you say firm set prices is are there two prices for each firm one off the platform and on the platform only one price. No no we are assuming that there is price parity in the baseline model so there is a single price. And then you have a question from Jacques do consumers have to make a choice of joining the platform. No they don't. We assume that if booking.com is there everybody goes to booking.com is our first decision. Okay. Okay. Thank you. So these are the these are the main elements of the model. I give some some small preliminaries here. So of course we proceed by backward induction. I'm going to be fast on this. So the first thing we need to think about is how consumers choose among what they know from their consideration set. Okay. So if a consumer knows a consideration set S is going to look at all firms K that the long that consideration set is going to pick the best one. The best one is the one maximized the difference between the gross utility and the price. Okay. So this is just this quick choice. There's nothing special here. And you can write the sales of each firm as a function of the distribution of match values right just like in any discrete choice model. So here in this assumption don't pay much attention to it. We may we find a way to describe demands in a very natural manner and we impose an assumption hazard rates that assures quasi-concavity. So all that I want you to retain is that quasi-concavity is good. Let's move on. So let me describe the price equilibrium in the last stage. Okay. So I said that the price equilibrium is symmetric if firms have constant markups. Okay. So in a symmetric equilibrium prices increase one-to-one with the vertical quality of the firm. So markups are constant. This is for tractability. So basically if you take a construction profile sigma which is symmetric with reach n then the symmetric price equilibrium will be such that prices are marginal cost plus a markup term which you call lambda n. And that's a function of the reach of the consideration set that describes consumer information. So this lemma is important because it syntactically describes price equilibrium in a different number of settings. For instance, if all firms join the platform and they face a symmetric phi f then the symmetric phi f is understood as a marginal cost. And the equilibrium phi is Cj plus f plus lambda of n big n because all consumers they know the whole thing. Okay. So that's just a, let's say, convenient way of describing price. And the special case of this model include logit or the spokes model. It's a generalization of hotline, among others. Notice that this markup does not need to be decreasing in n. Okay. Competition can increase markups. You know, Chen and Reardon have noticed that sometime ago. So these are just preliminaries just to make the pricing clear. A few feet to interrupt me. If something's not unclear, it's not here. But that's just about the pricing. So if everybody is happy, I can go to SFR. Which means what fees would prevail if there was no regulation whatsoever. So that's the content. I think there is a question popping up. Andre, is there a question? There is indeed. So is n a real number or an integer? It's an integer. Big n is an integer. It's an astronaut. Right. Big n, I think it says small n. Is there a small n? There is a small n. The small n is basically, before consumers visit the platform, what do they know? So it's also an actual number. Consumers know an average five firms. If they join the platform, they know 20 firms. You know? That's right. Okay. So now I'm under SFR. There's no regulation. The platform is free to do whatever it does. And price part is in place. So the claim of the proposition is that there exists a symmetric equilibrium where all firms join. And the equilibrium fee is the following. So the equilibrium fee makes firms indifferent between joining the platform or not joining the platform. So in the left-hand side, this friend here is the profit that firms obtain when they join the platform. So it's the markup when all consumers know all the firms divided by the sales share, which is one over n, because the model is symmetric. So that's the left-hand side. What's in the right-hand side? The right-hand side is what the firm gains if it does not join. Everybody else is joining. I'm the one that doesn't join. So what happens to me? I have my potential demand, my pre-visit potential demand. The folks that know me, if I'm out of the platform, times the maximum profit per sale that I can make in this world. This profit per sale is potentially higher than the one if I join the platform. Why is that? Because I'm facing lower marginal costs. I'm avoiding the commission. To adjust my price by a friend that I call Delta P to maximize this profit per sale. So the equilibrium fee makes firms indifferent between the listing, which reduces the potential demand because I only have the guys that knew me before, but I'm competing with lower marginal costs. The other alternative is to remain in the platform and enjoy a super large potential demand, but I'm competing with no marginal cost advantage whatsoever. So just a small observation. This equilibrium is also an equilibrium if the platform is choosing a public fee, uniform fee, uniform public fee. But yeah. So let us look a little bit more into the pricing of a firm that delists. So the optimal price adjustment satisfies this first order condition. There is nothing special here. And the key is that the optimal price adjustment will be a discount if the net fee, which is f star minus the convenience benefit, is positive. So the platform has always room to charge more than its convenience benefit because if you charge precisely the convenience benefit, the optimal price adjustment is zero and all firms have a dominant strategy to join because the profit inside the platform will be larger than the profit outside of the platform. That's what's written just here. So the one small observation is that the platform will always set a price higher than the convenience benefit. In a sense, the major concern is that the platform will set a commission that will be much higher than even the informational benefit generates to the other market participants, which are consumers and firms. And the way to see this in a simple manner is that the platform will always set a price higher than the convenience benefit. In a sense, the major concern is to think about how equilibrium fees change. As we change, the size of consumers' consideration sets before they visit the platform. So the information that consumers organically know. So in this corollary, we show that the size of potential demand is a sufficient statistic to do comparative statistics. So if the pre-visit consideration profile has a smaller potential demands, then the equilibrium flow will be larger. That's precisely the content of the lemma. So firms will accept higher fees, the smaller the pre-visit potential demands are. And in particular, if you make the potential demands very small, you can make the equilibrium fee grow unbounded. So all of this to say that if potential demands are small, the platform fee might well exceed the convenience and informational benefits that it generates to consumers so it's the familiar insight that intermediation can be well for decreasing. So what's the source of market power for the platform? The source should be familiar. It's a contractual externality in the parlance of SIGO. So it's the external non-participants that I described a moment ago. So listed firms, they render the potential demands of non-listed ones more contestable because the consumers that belong to SIGO demand, they know much more now. So there is a reduction in the outside option which leads to high fees. And that can actually lead to a reduction in welfare. So in a sense that the problem that we're going to define is that the platform appropriates too much of its informational benefits. It appropriates more than the informational benefits if it's not subject to regulation. And something that I'll come back to in a second is that by the end is that banning prosperity in fact prevents, if you could de facto ban prosperity, it would basically prevent the platform from appropriating any of the informational benefits that it generates. So we have two extremes. If you de facto ban prosperity, the platform won't appropriate any informational benefits. As I'm going to argue later, it's akin to capping the commission at the convenience benefit. If you let the platform do less effort, no regulation whatsoever, it might appropriate much more than the informational benefits it generates. So the middle ground is what's achieved by capping commissions. So which is what I want to talk about now. Renato, just one quick question. If you can go back to the previous slide. So actually one more slide. So did you say that F star, so the optimal fee can grow outbounded? That seems, I mean, I can understand why the platform can set a much higher fee than the informational value, but how is it possible that it grows unbounded? Yeah, I'm being precise here because we have to, I mean, we're always assuming that the market's fully covered. So it cannot really go unbounded because I have to change that at the same time. So unbounded is an exaggeration, but it can go large and we can cook up examples where it grows very large. Okay, yeah, it just goes beyond the informational value, but not exactly. That's the point, yeah, I'm being precise. Okay, so let me talk about cap regulation. So in order to, yeah, there is a question there, I think. So you have, as long as all firms join the platform, the welfare is constant. Is that true? As long as all firms join the platform, let me talk about welfare. I'm going to talk about welfare in a second. That's just the baseline. So if all the firms join the platform, is welfare the same, no matter what? It would be, yeah, yeah, especially if you are utilitarian, if prices cancel. And then USC has a follow-up, I guess on my question, why does the optimal fee go above the informational value? Maybe you can clarify that a bit. That's precisely because of the externality among participants. Basically because when firms join, they are generating an externality on those that do not join, because the potential demand of those do not join, it becomes smaller because their potential demand is much more contestable. So the outside option goes very much down. Right? And that's what, this externality is what provides platforms market power. So that's why the platform can charge more than the informational benefit generates computed from the perspective where the platform is not there. So that's what generates market power. Okay. So Jacques actually had the follow-up on the previous question. So it says welfare must increase as there are more participants on the platform as there's better matching of consumers to firms. No, that precisely occurs, yeah. I understood the previous question. The welfare is not constant. So you can have, no, so, okay, so, right, fair enough. Okay. But if you have all the firms on the platforms, then welfare is the same. Yes, yes. Okay. So let me now talk about cap regulation. So in order to talk about regulation, we have to introduce an extensive margin that describes the platform's decision to operate. Okay. So this operational cost, we describe it as K, it's private information off the platform, has some distribution, doesn't really matter. Okay. Okay. And this operational cost, it involves monitoring costs, making sure that hotels are respecting price parity, advertising, for instance, OTAs are the main clients of Google sponsored links, you know. So there's a lot of these platforms they engage in a lot of advertising and there are a lot of expenses related to advertising. Okay. So if the platform wants to operating to lose, it has to spend a lot of money. Okay. So, for instance, to being Google, so the regulation that we consider here is a cap regulation. Okay. So it's putting a max on the platform's commission. Okay. This cap is unconsequential if it's greater than the equilibrium under less effort. But this cap is going to bind. It's less than the less effort platform's fee. In each case, because we are looking at an equilibrium where all firms join as a unit mass of consumers, the platform's revenue is going to be precisely this FR, which is the minimum between the less effort and the cap. Okay. When the cap binds, of course. Renato, sorry, I just realized something. Just a quick reminder. So we're supposed to be, you're supposed to present for about 40 minutes. It's about 839. So I see, again, like counting questions. I was hoping can we go to like 845 after you think you can make it? Yeah, 47. 47. Okay. Just a heads up. Okay. Yeah. Thank you. So our offer measure combines two terms, right? So in the paper, we do things more generally, but here we are doing utilitarian welfare. So we count consumer producer and platform's profit similarly. And in order to express welfare, we need to, I mean, anticipating what Jacques was asking about, we need to talk about the match benefits that the platform is generating. So I have to introduce this notation, which is another statistic, the one out of N, okay? Because the distribution g is symmetric, it doesn't matter which coordinates you pick. So the platform's objective is then it consists of two terms. When the fee allows the platform to operate, the welfare consists of the gains from trade plus the expected match benefit plus the convenience benefit minus the operational costs. But there is a chance that the cap is too tight, the platform does not operate, in which case you just get the trade gains and the smaller match benefit because consumers will be picking the best firm out of N hat as opposed to out of N. Okay. Okay. Okay. So when I describe consumers' information in the absence of a platform, here I'm making a counterfactual statement, okay? Because if booking.com was not there, consumers might go back to the travel guides or might just look at Google, perhaps which is simple, okay? So if the specialized platform does not operate in a market, then consumers will probably search more because they don't have booking.com to go to. Right? So the consideration profile that would prevail in this counterfactual is what I call Sigma hat and that's where the N hat appears. So there is an implicit assumption that the time searching by consumers is similar with or without the platform but that the platform, because it's a specialized search engine, it's actually improving market information relative to general purpose alternatives, okay? So what's the optimal cap? The optimal cap is the sum of the convenience benefit and the informational benefit that the platform generates. So here's the convenience benefit and here is the informational benefit generated by the platform, okay? So this formula should be familiar because it's in fact an expected externality rule. It's basically saying that the platform commission cannot be higher than the expected externality that's imposed on other market participants, okay? So it's very much in the spirit of the pivot mechanism and it's also similar to the tourist test except that there is the tourist test from payment cards except that there is an informational benefit on top, okay? So this is all nice and beautiful, okay? I mean this formula should not be very controversial except that it's not useful at all, right? Basically because we cannot express these formulas in terms of distribution of consumer taste. Who knows? So in a sense the idea that we do here is to employ approximation techniques based on extreme value theory to talk about the expansion informational benefits to express this expansion informational benefits in terms of stuff that's easier to observe, okay? So you should think of what we're doing here as an econometrician that has to do a hypothesis testing. He has a sample, he doesn't know the probability properties of his statistic in a small sample but he knows that, you know, if the sample is large, he has an asymptotically normal distribution and then he's going to make hypothesis testing hoping, praying to God that his small sample is close to the asymptotics, okay? So we're going to be doing a similar thing here. It's an approximation, has no economic content. It's just an asymptotic approximation. So what we're going to do is that we're going to let the market grow large. We're going to make what consumers no grow large and we're going to approximate the optimal cat formula in terms of observance, okay? And this is potentially helpful because things are measurable. They're going to be profits and markups and convenience benefits are measurable for surveys for instance, consideration sets and so on. But the main statement since I'm running out of time I'm not going to spend too much time on it but the main statement is that under regularity conditions that are easily satisfied by most distributions that people use and applied work. This left-hand side which is the expansion in consumers information, information benefit, right? Divided by firms markup with us in Manhattan and grow large while satisfying this formula. 20% but the market's large. So this 20% is 20 million divided by 100 million, okay? So I'm just making the market grow large to get an approximation. So the ratio between informational benefits and markups equals the expansion that the platform generates in consumers consideration sets times a constant, okay? So that's where we're using extreme value. Extreme value tier. And for most distributions of interest so we can approximate the optimal cap as being the convenience benefit plus the expansion in consumers consideration sets produced by the platform times the markup, okay? So that's an arguably easier to use formula, okay? This is an approximation it has a good performance in small samples. For instance, if the distribution of match values is extreme value, okay? So here's just an illustration with OTAs, okay? So with online travel agencies. So most empirical sources they estimate that hotel markups are in the range between 20 and 30%, okay? So the convenience benefit we're going to assume that it's commensurate to rates of online payment gateways like the Spade Paul, 2%, okay? So if you just apply this formula you'll get this graph here where in the x-axis you have the potential demands of consumers when the platform is not there and in the y-axis you'll have the fee as a proportion of the retail price, okay? So if the potential demands of consumers are very small the cap is irrelevant, okay? So the cap is not going to bind it's a consequential. If on the other hand in the other extreme the informational benefits then the cap is just a convenience benefit, 2%. The cap is going to be 20% for instance if consumers the counterfactual in the counterfactual profile consumers the firm's potential demands are basically 50% of the market. In this case if the platform doubles the consideration sets of consumers then in this scenario that I just described the optimal cap is 20% okay? So the claim here is that the average fee of booking.com is well for neutral if booking.com at least exactly doubles the consideration sets of consumers relative to its easiest alternative which would be Google for instance, okay? So if booking.com less than doubles the consumers consideration sets then regulation would bind the optimal cap would be less than 20%. Okay? So that's the kind of illustration that we can make this just just illustrative, right? There is a there is a challenge of actually measuring by how much these platforms expand consideration sets relative to the best alternative and that's what gives the optimal cap that we can plug in the formula we just described. So I'm out of time so I mentioned one thing if you could de facto de facto then price parity that would be outcome equivalent to capping the platform's commission at the convenience benefit that the platform generates the reason is that consumers would always go to the to the channel offering lower retail prices and if hotels can discriminate according to the retail channel then the platform won't make any sales and it will charge more than the convenience benefit generates because that would pass through to consumers. So banning price party is akin to capping commissions at B but the optimal cap is B plus the informational benefits. So all in all if you ban price party de facto you are stripping the platform of the possibility of appropriating any informational benefits. In general the platforms would be more than the informational benefits. Optimal regulation finds exactly the right middle ground and in this paper we try to to make it operational by using this extreme value approximation which works so the challenge of course is still to measure the expansion on platform's consideration sets and that's something that I think can be done with service or experiments but then it's out of my turf. I'm sorry for screwing up. No worries. Thank you Renato. So we'll open it up for questions. I guess from here on people can instead of writing the questions in the chat people can raise their hand and I'll unmute them. So I will unmute Oslem. Go ahead. Thank you. Thank you very much Renato for this very clear presentation. So I wanted to ask this very important and crucial for the impact of this policy recommendations but at the beginning you also motivated your work by saying that when you you know band prosperity closes those platforms react by delisting some of their hotels or putting them on the second page is the same as kind of delisting them so nobody checks those hotels so in a sense consideration sets are in practice endogenous as far as I understood you said that if I visit the platform I see everybody. Right. Have you thought about this also because this is kind of very crucial for your recommendations the recipes of regulatory interventions. Absolutely I completely agree kind of my take is that there's some some people have don't corroborate in that way is that is that price party the fact to applies so so so in equilibrium or in reality as we see it firms are firms are not delisted you know there might be some phase of experimentation where they you know they tried to to price discriminate and then they were downlisted and then OK they behave not to be not to sabotage the business model again or they joined the position that we take is that in equilibrium price parties respected and that and that firms are not discriminated in equilibrium and that consumers they seamlessly can use the search tools of this specialized platform to learn whatever they have to learn. That's not the question I think I think the question is in the model when I go and I looked on the platform I see everything and consumers cognitively can't do that so they are going to look on the first page and if the platform has sorted exactly according to their preferences then they will see the max on the first page but this is not in the control of the consumer so it seems like it's another element of that's not in your model. Yeah the way I think of that is that I mean when I talk about this I think of you're not going to use the specialized search engine which might be booking.com you're going to use a general purpose one so you're going to have less of an easy time to find what you have to find right because the search tools are not that precise. I would guess booking.com or OTAs in general they have a more precise search tools which allow to actually find the best that they can actually find and if that's not the case I mean qualitatively I don't think it would be if there's no discrimination inside booking.com because underpriced party there's no reason to discriminate then consumers would have larger consideration sets perhaps that doesn't include all the firms that exist but they would certainly get larger consideration sets because booking.com is not operating in a given market and that's what actually matters for the cap. Cool we have a question so Hanna has a question Hanna I'm going to actually go ahead. Yeah I unmuted myself so I really like the results I like the results about how are we getting how the platform is actually getting the market power and the results are in your analysis so I'm trying to figure out what is the crucial assumption that is getting us this difference in modeling that is getting us this result here and I'm thinking that in most a lot of platform competition or platforms models we assume that outside of the platform there's just no matching there is if we do not participate in the platform we're not going to get any information that there is some information and some this demand set outside of the platform and therefore when when the platform shows up there are those two forces that you also kind of identified that on one hand you can benefit from joining the platform but you can lose you're not joining the platform and others are joining the platform so is this the so would we get your results if we assume that outside of the platform either there is no platform or we do not join the platform our demand set is zero because then I don't think we're going to get the result that the platform is going to price more than the informational value because then everything is informational value that the platform provides what's about the cup deficiency of cup regulation well if when firms don't join the platform they get they get zero then basically the platform can extract everything that firms would be would be opinion right so I mean so I have a difficulty to think about to think about welfare right somehow right so that's a bit of my difficulty so I think it's natural to assume that firms have a potential demand in the absence of the platform right well I mean this would be driving a lot of arguments would be like they wouldn't get this demand if it wouldn't be for the platform so it's justified no I understand the rest so you're saying that the platform expands the market demand right a lot of consumers that would not be on the market to the market right so firms have a demand expansion because of the platform that's something that we have in the paper and you derive the optimal regulation when the platform is greatly expanding demand so that can be addressed I didn't talk about because I already screwed up not talking about it so if I were to talk about it I would take more but we can address a platform expansion I completely agree with you that the externality on participant relies on the idea that firms have a potential demand that becomes more contestable because of the platform so this assumption is crucial in general other authors that were working on similar topics for example in Julian Wright's paper for instance the firms they have are captive consumers and the demand for captive so that's why the showroom is limited because you still want to milk your captive consumers so there are many different ways of modeling what's going on but the point that I wanted to take home is that in general there's no reason to expect that a ban in prosperity or upholding prosperity is going to lead to a well for maximizing outcome either because if you introduce market power on captive consumers the platform will have even a higher leeway to set high commissions if there's no market power whatsoever ban in prosperity will set a much lower cap so we see room for regulation precisely because there's no reason to expect either less affair or ban in prosperity so we need to directly address informational benefits and try to cap commissions this way I'm speaking of Julian Wright I think you have a question from Julian so I'll go ahead Julian yeah just agree with the last point certainly we also got externalities to the outside outside the platform I think they're basically coming from the price parity you know the factor fees will be higher and that that the alternative that sort of raises the cost of using the alternative and that can come about in different models in different ways the point I wanted to make was I think in sort of going back to the original motivation alternative to regulating the commissions which is obviously to ban price parity clauses but then you say well any price parity causes doesn't really work probably the main reason the platforms have control to steer consumers away from those sellers that are encouraging consumers to show room so that suggests an alternative to regulating commissions is to ban price parity clauses and to stop the staring I think that's certainly a regulation that authorities are looking at now which is going beyond just that they're using to steer consumers away from sellers that are undercutting you know on cheaper channels so I think that's possibly alternatively you need to at least sort of acknowledge or address I see I see yeah yeah that's a great point if you can ban price parity and actually make sure that there is no discrimination going on then yeah this regulation might be more effective but in this case the platforms will be capped by the convenience benefit or whatever other benefits they're generating but not the informational ones so that's the not to say it's the optimal thing to do but it's definitely another instrument absolutely kind of our claim here is that perhaps capping commissions is a more direct way and yeah if you compute things right you're going to get close to what you want to get whereas if you defacto ban price parity you might overshoot I was alluding to your paper just to say that under different modeling assumptions I think you still have you still have you still have exonauts across firms of course exactly but there's no reason to expect that you're going to get to the right outcome by banning them yeah alright so we're out of time I'm going to stop the recording here so this marks the end of the official talk of course people that want to stay and ask more questions we can still stay for another 10-15 minutes but I'll stop the recording here so for anyone that needs to leave thanks for your attention thank you you're welcome