 Alex, you have about 40 minutes. The floor is yours. OK, thank you, Junje. And thank you all for being here. Thanks for the organizer. Thanks to the organizer for the opportunity to present. So thanks to Chengzi for agreeing to discuss the paper. So this is joint work with Andrea Montovani, who I saw is in the room, and Shiva Shekhar from Tilburg University. Third-degree price discrimination in two-sided markets. So what are we talking about? So we're talking about price discrimination by platforms, which is a practice which is quite common. So let me give you a few examples. For instance, if you consider the Amazon Marketplace, you will see that Amazon charges different transaction fees depending on the category of products that is sold. So here you have a table. So you see that it goes from 8% for appliances to something like 45% for the accessories to Amazon devices. And other platforms also charge different fees depending on the sellers or developers' characteristics. So for instance, Apple or Google's app stores charge different commissions depending on the revenue of the seller. So it used to be only 30%. But since last year, they've changed, and now Apple and Google charge 15% commission if the revenue per year is less than 1 million, 30% if it's above. You have other examples in the video game industries. For instance, Microsoft is going to charge different fees depending on whether what you sell is a game or not. In other industries as well, credit cards also charge different fees depending on what kind of merchants we're talking about. So the very basic questions that we ask are what are the effects on welfare of such practices of price discrimination by a platform? And what we find interesting is to actually contrast these results with the traditional price discrimination, so in markets which are one-sided, so without network effects. So just to make it clear what we are looking at. So here's the standard setup of third-degree price discrimination. So in third-degree price discrimination, you would have a firm that faces a group of consumers when it cannot discriminate. So it has to charge the same price to everyone. So here we call it FU. You're going to see why we use F because later on it will be the developers that pay a fee. But so you have this market. So under uniform pricing, you charge a single price to everyone. And you contrast that with a price discrimination where you can actually distinguish between the strong market and the weak market and you can charge different fees where usually the fee or the price in the strong market would be higher than in the weak market. So what we do instead is we add another side to the story. So we're going to add the consumer side. So there's going to be a population of sellers, we're going to call them sellers and buyers on the right. And so when the platform cannot price discriminate, it's going to charge the same price for every seller and the same price to every buyer. And then there's going to be network effects across the groups, right? So the buyers like that sellers, the more sellers they are, the happier the buyers are. And we're going to contrast that with the situation where the platform can actually distinguish the sellers based on a characteristic. And so separate them into a strong market and a weak market, charge different prices. We're going to maintain the assumption that buyers pay the same price for now but it's not very important but it makes our life easier, right? And so you're going to have network effects as well. Okay, so before I state what our main results are, I think it's interesting to go back to what we know from the classic results in the early literature on third degree price discrimination. So the first papers go back to the early 20th century, the first half of the century with the Pigu or Robinson who had the first important results. And in particular, so there are two cases to consider. So first, there is a case where absent price discrimination, the weak market would not be served. So in that case, price discrimination allows to serve a new market. And so it's going to lead to an improvement in terms of welfare and also parietal improvement, a weak parietal improvement in the sense that the consumers in the strong market, the price that they pay will not change but the weak markets, they can be served under price discrimination. So something to keep in mind, this is not what I have on the slides. What I have on the slides is the other interesting case where under uniform pricing, both markets would be served. So in that case, there's an important result which is that when you have linear demands, then price discrimination is going to lead to the same quantity overall. So the aggregate quantity is going to say the same and that means that welfare goes down because there's a misallocation. So some consumers in the weak market are going to buy even though their willingness to pay is lower than some consumers in the strong market who are priced out. The welfare goes down. Later on, this kind of work has been extended to more general demand functions. So I think the latest paper, the more general approach is by Aguirre, Cohen and Vickers who provide conditions on convexity of the demand for the quantity or the welfare to go up or down. Okay, so what we're going to do for tractability, we're going to focus on the case with linear demands because what we do is we add network effects so it makes things quickly intractable. But I'm going to discuss, of course, the robustness to how general the results are, but this will be quite informal. And later on, there's a big literature also on price discrimination and platforms. Maybe I'll come back to that later on. Actually, I should have put this slide first. The main results, what we find is that when demand is linear on both sides, so that is both on the buyer and the seller side, we find that price discrimination is going to lead to increased participation on both sides. So we're going to have more buyers and more sellers in equilibrium. And this also going to lead to an increased welfare, right? And kind of a striking result is that price discrimination may also result in strict Pareto improvement. I emphasize the strict because we know that price discrimination can result in weak Pareto improvement. I described the story when the weak market was not served. But here, what we find is that even though some consumers may end up or some sellers in this case may end up having to pay a higher fee, they may be strictly better off under price discrimination than under uniform pricing. And we also discussed the optimal pricing strategy of the platform. So without further ado, unless there are questions, but I think I'm going to stop describing the model. So we have a monopolist platform that matches, that helps interactions between buyers and sellers. Okay, we call them buyers and sellers, but actually we're not going to model the inter, we're not going to open the black box of the interaction between the buyer and the seller. So we're going to use a reduced form way to model how buyers and sellers interact. And the platform charges participation fees on each side. Okay, so I will discuss later on why we don't do Advaloem fees, which are quite common, but I would say the main reason is for tractability. So it's easier to explain things with membership fees. Okay, so the fees are going to be P for the buyers, the price and the fee F for the sellers. So on the seller side, we have two groups, L and H, and there's a unit mass of each group. A seller of type H gets a profit per interaction with a buyer of theta H, which is going to be larger than the profit that a low type seller gets for each buyer. Okay, and both are strictly positive. There is no competition among the sellers. So you have a unit mass of sellers that sell independent goods, right? So there's no congestion or things like that. And sellers are also heterogeneous with respect to their participation costs. So the cost of signing up to the platform on top of the membership fee, which we assume is uniformly distributed on zero one and independent of the type. So that means that the profit of a seller of type J is gonna be theta J times the number of buyers minus the fee that this type has to pay to the platform minus the participation cost. On the other side of the market, we have buyers, a unit mass of buyers who have a standalone value V for the platform. Okay, so think of the iPhone. So even if there are no apps on the iPhone, you can still use it to browse the web or to make phone calls. And then buyers also enjoy interacting with sellers. And we assume that buyers get a benefit B per seller, which in the baseline model, we're going to assume that this is independent of the seller's type. And later on, we relax this assumption when we look at maybe the more plausible case in which buyers prefer to interact with high type sellers than with low type sellers, which is I think a natural thing to look at. But for clarity, I think it's better to start with the case where buyers are indifferent about the type of the sellers. And the buyers also have an outside option, which is also uniformly distributed on zero one. So that the utility of a buyer is the standalone utility plus the network benefit times the number of sellers minus the price paid to the platform minus the participation cost. Okay, so in terms of pricing, we distinguish two regimes. So under price discrimination, the platform can set a different fee depending on the type of the seller. So it can observe the type of the seller and set FL potentially different from FH, but buyers, they pay a same price PD versus the uniform pricing. You've got the constraint that the platform has to set the same fee for sellers, FU and the buyers pay the same price. All buyers pay uniform price, PU. And we're going to assume that the parameters are such that we always have interior solutions, right? So we're gonna avoid dealing with the corner solutions. So we discussed that in the paper. And also importantly, we're gonna focus on the region where even under uniform pricing, you would have some L type sellers who would be active in the market, right? So we're gonna kind of assume away the scenario where price discrimination allows the platform to serve a new market, to serve the low types, right? So we're gonna assume that they can be served. Some of them can be served even under uniform pricing. Okay, so if there are no questions on the setup, I guess it's fairly standard. Let me discuss how we compute the demand. So because we have uniform distribution of a participation cost, means that the number of buyers that are active on the platform given price, given a price PU and a number of seller NS, this is V plus BNS minus PU. And the total number of sellers is going to be equal to the number of high type sellers plus the number of low type sellers, which is this expression, right? So here, one could do, you know, you just write the profit as a function of the prices given those demands and you saw the rational expectation equilibrium, that would be fine, that would give us the result. But instead we find it more illuminating to use actually inverse demand. And hopefully I will convince you that using inverse demand is useful to understand the intuition of what's going on. So instead we're going to assume that the platform chooses directly the participation levels. So it's going to choose how many sellers it wants to attract and how many buyers it wants to attract. And then the prices, so this is in the uniform pricing case, the pricing will adjust such that given those prices, these are the realized participations. Okay, so we simply invert the system and get these inverse demand functions. Now the platform's profit is then the price of the price to the buyers times number of buyers plus price to the sellers times number of sellers. And the first order condition is the following. So for the number of buyers, we have the standard marginal revenue, traditional marginal revenue. And then we have an extra term that captures the network externality, so that every time you add a new buyer to the platform that increases sellers willingness to pay so that the price is going to increase. And you multiply that by the number of sellers that are active on the platform to get the gain to the platform. And a similar expression for the first order condition with respect to the number of sellers. Okay, so graphically we have two increasing curves. So on the X axis, I have the number of buyers, on the Y axis, I have the number of sellers. And so here I plot as a function of the number of buyers, how many sellers does the platform want to attract? So this is the blue line and here is how many buyers you want to attract as a function of the number of sellers that are on the platform. And a remark is that, and that's gonna play a role, is that both of these curves have to be increasing, right? So the number of buyers and the number of sellers are complementary. The intuition is fairly straightforward. So an extra buyer is gonna be more valuable if you have many sellers on the platform because then you can increase the price and it's gonna be multiplied by a larger number. Okay, so now what happens under price discrimination? So under price discrimination, given again the uniform distribution, we have a demand participation level for buyers as a function of the number of low type sellers and high type sellers that are on the platform. And you also have a participation of the low type and participation of the high type as a function of the fees that they have to pay. Again, we're gonna invert the system and get the inverse demands so that this is going to be the price for the buyers. And now there's gonna be a price for the low type seller and a price for the high type sellers. So the difference between the two cases is that under price discrimination, basically the platform not only chooses how many sellers in total it attracts but it can choose the composition of the seller pool. So that's gonna play a role. And the platform's profit is price times to the buyers times number of buyers plus the fees times the number of sellers of each type. And here is the first order condition. And this is the one I will discuss that plays a role. The first order condition with respect to the number of buyers. So again, we have this traditional marginal revenue. And then you have this effect which is how much value does one extra buyer create on the other side and this value will be extracted by the platform, right? So basically an extra buyer, it allows to increase the price for the low type sellers multiplied by the number of low type sellers plus the same for the high type sellers. The first order condition for the sellers does not change compared to the case with the uniform pricing. So now what I want you to do is I want you to look at these two expressions. So this is the first order condition under price discrimination. And this is the first order condition under uniform pricing. You see that the first term is the same as traditional marginal revenue but the second term is different. So the red expression is how much value the platform can extract under price discrimination for each new buyer that it attracts. And so basically the point, a very simple point of the observation that we make and that's gonna generate results basically is that the platform is better able to extract the value of an extra buyer on the seller side, right? Because now it will extract the full value. So if you attract one extra buyer, you can extract the full value to the low types plus the full value to the high types. Whereas under uniform pricing, basically if one extra buyer comes on the platform, there's gonna be an increase in the price which is gonna be such that the total number of sellers remains the same but there's gonna be more high type sellers and fewer low type sellers and the difference will be, I mean the sum of the two will be equal to zero but surplus extraction is imperfect in that case. So what does that mean? So first actually, and this is going back to the traditional results from Pigu or Robinson. If we fix the number of buyers and we compare the level of participation under uniform pricing and under discrimination, if we compare the participation by sellers, then we have the classic result that the total quantity remains the same, right? So under uniform pricing, the total quantity of sellers is this, it's gonna be equal to the total quantity of sellers under price discrimination. So what that means is that, so the continuous lines are the previous one, so this is the solution in the case of uniform pricing but now the dashed line is the optimal strategy under price discrimination. So it means that for a given number of buyers, the platform wants to attract the same total number of sellers. So the curve is located exactly in the same place. Now the second step is using our previous remark on the fact that you can better extract surplus under discrimination, it means that there's gonna be a stronger incentive to attract buyers because each new buyer can generate more revenue for the platform. So this means that for a given number of sellers on the platform, the platform wants to attract more buyers when it can discriminate. And so graphically, this means that the red line shifts to the right. So for a given number of sellers, you want to attract more buyers, which means that the optimal solution is necessarily going to be greater, both participation of buyers and participation of sellers is necessarily going to be above the case of uniform pricing. This is our first proposition is that under price discrimination, participation increase in both sides. Now here, I think it's useful to pause and to, well, first, if you have any question, don't hesitate, but if not, let me take a moment to discuss how robust this insight is because here we're using the fact that demands are linear to use the fact that basically the total quantity doesn't change, the fact that the blue line doesn't change, it comes directly from the assumption of linear demands. Now, when we have non-linear demands, we no longer have this result that the total quantity is the same. So the first step of the reasoning no longer works. And so basically what we say is that provided that price discrimination does not lead to too large a drop in the desired participation of sellers, then the proposition will hold. So the proposition would hold if the dash blue line was slightly below the continuous blue line, right? But of course, if the dash blue line is too much below then we no longer have this result that participation on both sides increases. And so there we can directly apply the result by Aguirre, Cowan and Vickers because they give conditions on the convexity of demand for price discrimination to increase output. And so if output increases, then it means that the dash blue line is gonna be above the continuous blue line and so that would work. What we require is that it doesn't decrease too much. But in any case, I think a more general point is that participation is less likely, overall participation is less likely to decrease with price discrimination compared to a traditional markets without network effects. So if you want to take really what is the robust insight is this one. Now in terms of welfare, we can show that well, the platform is gonna be better off. Of course, that's by reveal preference. The buyers that's also are gonna be better off because the participation increases so they must be better off. And the low value sellers are also always better off with price discrimination. But what we find striking is that total welfare always increases under price discrimination with linear demand. So this is a big contrast with the traditional markets. Well, remember, so quantity remains the same and welfare always goes down. So here quantity increases and welfare goes up. So this is quite a stark contrast. Now another striking result that we have is that provided that the network effects precisely how much the high type sellers value each buyer and how much the buyers value sellers provided these two parameters are large enough, then the high type sellers are gonna be better off under a price discrimination. So this means that in that case we'd have a strict Pareto improvement. And this generally doesn't happen in a standard model third degree price discrimination. In general, consumers in the strong market they end up paying a higher price. And so they are either worse off or when price doesn't change, they are indifferent. As a few, actually we became aware of these papers recently but there's a couple of exceptions in the literature. So this paper by Natha Ostajewski and Sahu in 1990 where basically they have the profit functions that are not single peaked. And so in that case they can show that you sometimes have a strict Pareto improvement. And another which is more related to what we do a paper by Osman and Macky Mason in 1988, they use the model of market with economies of scale. In that case, they show that you can have a strict Pareto improvement. So of course, network effects, economies of scale it's related. Actually the mechanism is a bit different because in their story, basically once you can price discriminate you're gonna lower the price to the weak market. So that means that you're gonna serve more consumers there. And because you serve more consumers it means that the marginal cost is gonna go down. And so this gives you, if it goes down enough it gives you an incentive to also lower the price on the strong market. This is a different mechanism but of course it's related. Am I doing on time again? In terms of pricing, we identify several regimes so several situations. The typical one, I put quote unquote typical because it's so, when we plot the parameters this is the largest one. And this is also the more intuitive one is such that the low type sellers are gonna pay a lower fee on the price discrimination than under uniform pricing. And the high type sellers are gonna pay a higher price. So in that case, what about consumers? Well, they're going to pay a higher price when the network effects are large enough but when the network effects are smaller then basically they have to, I mean the platform finds it optimal to lower the price. So think of maybe that case first the case where B is small so that there's not much of a network effect on the buyer side. So remember that the platform finds it optimal to increase participation on both sides. So if the buyers don't care much about sellers if you want to attract more buyers you have to lower their price. On the other hand, if buyers value sellers a lot then actually you don't necessarily have to lower the price to attract more buyers because they are gonna be attracted by the fact that you have more sellers. So there's gonna be feedback effects that allow the platform to attract more buyers even though the price to buyers goes up because of the increased participation by sellers. A second regime which was more surprising to us is one where actually all fees increase on the price discrimination. So this happened when theta L is intermediate and B is large enough so when this happens we find that buyers are subsidized both under uniform pricing or price discrimination. And so in that case discrimination is gonna lead the platform to increase the subsidy to buyers. And notice that an interesting result is that all sellers pay a higher price and yet they are better off, right? Because of the increased participation result. Finally, there's also anything can happen. So there's also almost anything because actually in this model FL is always going to be below FH but it could be the case that both types end up paying a lower fee under discrimination than under uniform price. When this happens, we find that the sellers are subsidized so that means I should have added this inequality so FU is also negative. And in this case, the platform wants to increase the price to buyers when it can be priced for me. So that's it for the baseline results. And so in the remaining five minutes or so that I have unless there are questions on this I will discuss some extensions. I think there's a question in the chair room. Do you want it? Yeah. I think Luis wanted to ask probably the compare static results whether this traditional results is the case when some of the parameter is zero, right? So, and then you have a strict Pareto. Yeah. Yeah, let me take that after if that's okay. So, okay. In terms of robustness and extensions we look at three main extensions and our results are mostly robust to this. So the first extension that we look at is one with heterogeneity in how much consumers value different types of sellers, right? So we're going to allow consumers to prefer to interact with high type sellers. Then there's going to be, we look also at add value and fees. And third extension that we look at is one sided pricing. That is what happens when the platform cannot charge a price to consumers. So, the assumption that B is the same that consumers are indifferent about which buyer they interact with. Of course, it's not very natural. It can be microfounded. We provide some microfoundation but it's probably more plausible to assume that the buyers would prefer to interact with the high type sellers, right? So it's easier to find. So if you think of the high type as having either a high quality or a lower cost and you endogenize the price. So in equilibrium, you would find that buyers prefer to interact with the high type sellers. And so we have a lemma that says that basically the platform charges. So in the baseline model, the platform always charges a higher price to the high types. This may be actually counterfactual. I mean, in some markets what we observe is that actually the popular app developers are charged a lower commission or things like that. So when you allow B to be different depending on the type, then you can find this result because actually what matters is the difference between how much a developer benefits or a seller benefits from interacting with a buyer and how much the buyer would like this, interacting with this seller. And so basically the more value you generate either for you or for the other side, the lower the fee that you, no, sorry. So if you generate a high revenue or if you don't generate a lot of value for the buyer, then you're gonna pay a higher fee. And so this is consistent, for instance, with examples such as this team that actually charges more for the less popular games. And we have a result that actually the results from participation with the graphical analysis. So you have to change a bit the proof, but it goes through. So participation is gonna increase. Now the result on welfare is not going to hold so that there is a region where welfare goes down, but actually what we find, and this is a numerical exercise, but is that in general when welfare goes down, it goes down by very little. So it's usually less than 1% for whatever that figure means, but given the parameters that we use it's less than 1%, whereas when it goes up, it can go up by a lot. So more than, sometimes more than a hundred percent. So we feel like this broadly confirms our results. The second extension that I want to discuss with you is AdValor and fees. Because in all the examples that I've used, actually in practice, the platforms use AdValor and fees. And in our model, we have membership fees. So I would say that there are three reasons, three main reasons why we do that. The first one is attractability. So it's easier to disanalysis and transparency. I think the analysis with membership fees is very easy to understand. Now there's also an interesting paper by Drew Wong and Wright who show that AdValor and fees, they already represent some kind of price discrimination. So that if we really want to understand the effects of price discrimination starting from a situation where there is even uniform AdValor and fees, it would still be some kind of price discrimination because of course, the more you sell, the more you pay. It's proportional to how much you sell. And finally, it is optimal in our setup to not use AdValor and fees, to use membership fees. I mean, if price discrimination is possible, you have to try to do membership fees. But still, these reasons, if you put aside these reasons, what we show is that our results in terms of welfare and participation are going to go through even if the platform charges AdValor and fees to sellers. But the thing also, maybe I should have added it, is that with AdValor and fees, you introduce also consider distortions in terms of pricing. Of course, if the marginal cost is not zero, you're gonna have some double marginalization and this makes things a bit more messy. Finally, in the case where the platform cannot charge consumers, then we find that the total participation goes up. Now welfare doesn't always go up, right? So the network effects have to be large enough. I mean, basically you have one fewer instruments so you're not gonna be able to do as well, but we still have the possibility of a strict Pareto improvement. So to wrap up, what we do in this paper we present what we think is a very simple model of price discrimination by a two-sided platform. We show that with linear demand, price discrimination increases welfare and can even lead to a strict Pareto improvement. And one kind of counter-intuitive result is that even when consumers pay a higher price, they may be better off because of the increased participation by sellers. Thank you for your attention. And I'm looking forward to change this discussion. Thank you very much for giving me the opportunity to discuss Alex's paper. I really enjoyed reading the paper. I think this is similar to a lot of Alex's work, identifies very important question and provide some interesting trade-off that's very relevant answers to the practice. So I just have a few comments. So I think first, when we talk about dominant platforms which holds different sides of small users, probably the total user surplus would be a better measure, a welfare measure than consumer surplus or the total welfare. And actually in this model, the results obtained is actually stronger than that the total user surplus can be increased on the price discrimination because actually on the price discrimination, the authors find that both sides participation will increase. So that actually means both sides are better off. So that would be stronger than just the increase of total user surplus. So this could be something highlighted in the paper. And we know that this total user surplus is actually more difficult than the total welfare because the platform would be always better off. Otherwise it will not use the price discrimination in equilibrium. I think that's just something interesting. Also another benefit of focusing on total user surplus it might have some implications for extending sort of generalizing the model beyond the linear demand because here if you only focus on the total user surplus then it seems that what happened to the buyers and the low type sellers are quite robust. So the only problem is what happens to the high type sellers. But that could be probably you borrow some techniques from the Agia, Kowan and Wickers. But then because your current result is stronger than the total user surplus. So if you can't get that result with certain conditions but that condition could be actually sufficient for getting improved total user surplus. So I think that might be a way to generalize the insight. The third point is that... So I find one result is particularly strong is that the seller participation always increase on the price discrimination which is independent of NH and NL which is the size of high type sellers and the low type sellers. I'm just wondering whether... So let me imagine a scenario where NL is almost the one and NL is almost zero. So basically almost all sellers are high type. Do we still get that the seller participation will always increase? So I'm just wondering whether this scenario is actually covered by the assumption one or actually also covered in the discussion of corner solutions. And finally, given this is a two-sided market model so I'm wondering whether the platform have any incentive to offer a negative price to any of the groups because here you have actually three groups like the buyers, the high type sellers and the low type sellers. So it might be quite interesting to consider this kind of thing especially in a competing environment when an entrant is in the market and an entrant probably can use a subsidy to overcome certain disadvantages as an entrant but then the issue is which group should the low price or the negative price to be used to target. So I think that will be a quite relevant question for platform business. That's all I have. Thank you.