 We were interested in trying to understand the issue of market power, how it relates to data or information in the context of large internet platforms. So I think for this group, I don't need to motivate this. There's no arguing that these large platforms have changed the way many market participants interact. There's also it's also obvious. In fact, it's stated from the inception of, say, Amazon, that data gathering was front and center in the business model. And so we're interested in what are the effects of this data collection on market participants, but that's a bit broad. And so we are going to focus on like a subset of issues. So specifically, how does data gathering affect the buyers and sellers? Is there a role for regulation of the amount of data collected? And why are these new platforms different from traditional retail stores? So the first thing about the data. So of course, you could have many different models of data. So just to be clear, we are not going to have anything to say about privacy or it's purely about efficiency and market power. So we think of data as a way to improve the quality of matches that is offering the right product to the right people. And that's the plus side. And the downside is going to be the market power of the platform vis-à-vis the sellers. It could be buyers and sellers, but I think most of the talk we're going to be in the case where one side of the market pays nothing and the other side pays everything. So the sellers, in fact, pay the fees. So that's all the trade off with respect to data. So people don't care about privacy. They don't value the risk of leakage of information or private information, none of that. So it's a subset of the potential data issues. And then for regulation, it's the same thing. We just ask, is there a point where the regulator thinks that the amount of information collected on the platform increases the market power of the platform relative to the sellers too much to the point where it would be efficient to limit the collection of data or the market power is feasible. And in terms of the welfare effect here, essentially all that happens in our model happens via the entry of sellers. So you could imagine other ways where welfare would be affected, but in our model is going to be purely like an entry model. So all that happens is at some point, if the platform has too much power, it's going to increase the fees that it charges to the sellers. And that's going to reduce their expected profit. That's going to reduce the entry of new sellers. And the consumer are going to be negatively affected because they're going to have fewer sellers to transfer. Again, I'm not saying that you could definitely imagine other ways in which welfare would move, but in our model it's just that. And then the last question, what do we have to say about these new platforms that you hold on? In our model, there's nothing qualitatively different between, say, Amazon and a large retail store, but the model is non-monotonic. So it happens that when information gathering capacity is small, then improvement in this processing capacity tends to improve welfare because the efficiency gains from better matching is much larger than the potential market power issue. But if you keep increasing information processing capacity, at some point, the gains in matching efficiency become small relative to, I should say, maybe it depends on the parameters, but it may become small relative to the market power of the platform. So I think that may not be a very bad description of reality because if you look in details of what did Amazon versus a standard retail store, it's not clear that there's anything Amazon does that hasn't been done before by retail stores. Having your own brand, looking at what your consumers buy, using consumer information to put your product on the shelf in the right place, all of that has happened for 200 years. So in the model, it's true as well. And the only thing that happens is it's really the size and efficiency of Amazon that can get you in the parameter space where further improvement of data gathering could potentially reduce welfare. So it's more like a good quantitative difference. Compared to the existing, well, so I guess maybe in 40 minutes, I'm going to be quick here because I also want to have that discussion with you guys at the end, try to figure out what's the best way to compare what to do with what has been done. Of course, we know the classic from Katschapiro to Rocher Tirol. So I think one way to think about the difference is we come from a more macro perspective. And so in macro models, the benchmark for search and matching is constant return to scale. And so in a standard model, we think about people matching randomly or directed. And once you have a constant return to scale matching function, you have network effects, but you have congestion effects. And they tend to balance on average so that it's not obvious that the outcome is inefficient. While many of the papers we've seen in the literature, they tend to have this super strong accusing return to scale where essentially there is no congestion effect. So like the welfare of the buyer is proportional to the welfare to the number of sellers with no impact of having another million buyers. And then of course in that world, things are typically inefficient to start with. So we're going to do the opposite. We're going to start in a world where things are typically efficient and then try to understand how the market power could bias the results. But on the other hand, I don't want to claim that this is like the best model or this is just, I think it depends on the application. On the retail platform, it still seems to me that constant return seems like a pretty reasonable approximation. But in the matching function, of course, in the setting of the platform, you could have fixed costs obviously, but if you think about credit cards, maybe it's less obvious. So I think it depends a bit on the platform you're modeling. But that's going to be important, I think, for the results. It does, yeah. But I think in the interest of time, it's better if we have that discussion at the end. Okay, so the model is quite simple. You have buyers and sellers, and then we're going to have a place where they meet. And so we want to think about the platform, the new platform competing with the old, say, brick and mortar retailer. So let's describe first the world pre-Amazon, and then we describe the world with Amazon. So pre-Amazon, there are buyers and sellers, so these guys are not going to change. And then there's a place where they can meet. We're going to call it the outside market that's going to remain there. And in the outside market, there's also some data that buyers and sellers can exchange to figure out what kind of goods people want to buy. So the data for us is, well, that's exactly straight from Shota's paper. So we're going to discuss that. So we literally lifted that from his ER paper. So people have different tastes. There is a capital I number of goods they could buy from. They don't know which one is good. And then you get a signal that tells you something about the one that's likely to be the right one for you. So the signal has a realization sigma and a precision delta. So that information is going to improve the matching. The matching itself, it's a standard competitive search framework. So if we just to make it formally, there is a mass and bar B of buyer. So notice here, and I think for most of the talk, we're going to take the number of buyers that's given. It is actually an assumption. I think something could change if we change that. So in the right now, we're working on bringing buyers entry. But right now, I think there's a pool of buyer that's fixed. So there's a mass of people who want to buy stuff. And they don't know their tastes. So they have a test UI across a bunch of varieties of the same good. This big I is the number. And the best one out of this pool gives them utility you and all the other ones give them zero. So the name of the game is to figure out the what right to buy. To do that, there's a signal. Sigma realized on the same space. Okay. And the precision. So the probability that the signals give you the right outcome is Delta. So the priority that the signal Sigma points towards good high conditional, the fact that good high is indeed the one that is good for you. That's Delta. And we start with uniform distributions. So the your priors across all these guys is uniform. So Delta is also going to be the, you know, expose probability of making the right choice. So Delta could be anything. So between, so of course, one of our high that would be uninformative and then some upper bound Delta bar. So we have two versions of the model, one in which people can choose Delta at some cost. So that could be, you know, either. So in the old days, you would be filling in the forms that people asked about your taste or some feedback today would be like accepting cookies. And that means that there's a cost for you of doing that. And then there is a technological upper bound Delta bar. So that's the maximum amount of data or maximum precision of the signal. I think for most of the talk, we're going to forget about the private costs and just have the technological upper bound. And we can discuss what it changes later. It doesn't change much. Okay. So the sellers on the other side to remember like start the buyers. So the buyers, they're uncertain about their taste, but they can disclose information to the buyers. So formally, they disclose information to the buyers to guide so that the buyer can offer them the right good. Then so to the seller, so that the sellers can offer them the right good. The sellers, they are pretty simple. They sell one unit of good in the outside market. They have an entry cost Kappa. And then they get the consumer data. They see the disclosure choice and the signal. Then condition of the signal, of course, they're going to choose to offer the good that is the one corresponding to the signal. And then the probability that this is the right good is Delta. That's because we start from we start from a uniform. So therefore, if Delta is the conditional that way, then bad base low is also the condition of the other way. So Delta turns out to be also the probability to make the correct that your choice is correct from the signal. And then we have competitive search. So I mean, maybe it's, yeah, okay. So in the outside market, we're going to have a mass end bar of legacy sellers who are always there. This doesn't matter here. It will become convenient after when we have the platform as well. So there's always some buyers. So in other words, this entry cost is for the new sellers who might decide to enter. But there is some legacy sellers who are on the outside market always. And the matching technology is controlled to scale with power gamma one minus gamma on sellers on buyers and sellers. So as usual, in this case, the matching can be summarized with attention in the market. So the ratio of seller to buyers. So little n is the ratio of sellers to buyers. It's like, I can see to an employment ratio in the search model. So n is the number of sellers relative to the number of buyers. So then the probability that the buyer meets a seller is depends on the matching efficiency alpha bar. So that's just a technology parameter and O for the outside market. And to the one minus gamma where n is the tension. So n goes up, there are more buyers per seller than each seller is more likely to meet a buyer. All right. So then I think we are ready to solve for the first equilibrium. So you have, so it's like the standard competitive search really. So the value for seller is what? Well, there is the probability of getting a buyer. And then there is a priority of getting the right product and then the price that the buyer would pay for the buyer. It's the same thing. You have the priority of meeting a seller. And then you have the priority of the right product. And then you have the UTT conditional on trade, which is U, the UTT of getting the right good, minus P, which is the price that you pay. Okay. So if you solve that equilibrium, then you get the standard solution. So because we assume cup-do-glass matching function, so constant elasticity, the price is going to be just a sharing rule gamma, one minus gamma. So one minus gamma times U. Okay. So the buyers, if the sellers get one minus gamma of the surplus and the buyers get the rest. Of course, in general, this would be the elasticity. So it doesn't have to be constant, but with cup-do-glass, it's constant. Then the number, then to solve, so that gives you the price. Once you have the price, you can get the value functions as a function of N, which is the tension in the market. The last thing you need to do is to solve for N. So that comes from free entry. Remember on the buyer side, it's very, it's, it's simplified. So I don't have free entry of buyer. So this guy, the number of buyers is just a fixed number. So N is the ratio. So all I have to figure out is the numerator and S number of sellers. And it's going to be the exogenous part plus the number of entrants. And if, and if the number of entrants is positive, then the free entry condition has to be satisfied. That just says that the value of the seller has to be equal to the entry cost. Then for that, you can solve for, for the tension N. Finally, you can, you can go back to, so that now that's the equilibrium conditional on a particular information gathering, information sharing choice. Then you can go one step before and say, given that the buyers know they're going to enter this market, what would be their choice of sharing information? Since here we assume no personal cost, they will go to the corner and choose the maximum because each value function, you can just, you can see it right there. The value function of the buyer is trivially increasing in Delta. So they will go to the corner. If you wanted to introduce the interior solution, you would have to introduce a private cost of increasing Delta and then you get an interior solution. But that's not critical for what we do. So let's go, let's let them go to the corner, Delta bar zero. Okay, so then final argument, this actually is efficient, like all direct search with constant return to scale. And then the market tightness increases in Delta. So Delta is good. Of course, it improves the quality of the match. It's going to bring in, therefore, these better matches more value for sellers. So more sellers are going to come in. Now the sellers, since they break even, they don't really matter for welfare. But of course, the buyers are very happy because they see more and more sellers. So that increases both their priority of matches and their welfare. So that's the advantage of Delta. So now we're going to bring a platform that's going to compete with the outside market. So buyers are going to have the choice to go trade on the outside market just like before, or go to the platform. So the only difference you see from the outside market is the technology is the same, but out of the buyers, there is a mass N bar B of buyers. Of course, in the, in what we've described so far by by definition, all of them have to go to the outside market because that's the only thing now they're going to have to split between the platform and the outside market. So there's going to be an indifference condition that says they have to be indifferent to go on the platform on the outside market. And on the seller side, I still have my legacy seller stuck in there. So that thing is not going to disappear. Okay, that's where the legacy sellers are useful. If you don't have that, you need to bring in some kind of division return somewhere. So the outside market is still going to have some of the legacy sellers, but the new sellers, just like the buyer, they're going to choose, do I want to trade here or do I want to trade here? So for the platform, for the outside market equilibrium, it's the same as before, except that now the number of buyers and seller is going to be reduced and it's going to be sold in equilibrium. So the buyers decide where to search. And they have the same technology with the platform as they had with the outside market. So they can share the information. The key difference is we're going to assume, and that's the big assumption. In fact, that's the definition of the platform. We're going to assume that the amount of disclosure or the quality of the signals that can flow through the platform is higher than on the outside market. So if you remember on the outside market, we had this technological upper bound here, where we're going to assume that this upper bound on the platform is higher or potentially much higher than on the outside market. And the sellers, same thing, they're going to be in different, the new sellers entering, they're going to go where they prefer. As it turns out, the equilibrium is going to be such that the buyers in different conditions is going to hold, so buyers are going to choose where to go. And the sellers, if the platform is active, all the new sellers are going to go to the platform and the outside market is going to be only the legacy sellers. Okay, so on the seller side, the same technology as before, so they can sell their unit of goods on the platform or on the outside market. They still have an entry cost cap up. They still get consumer data. The difference is on the platform, they can get better data, but they have to pay for it. So there's a price M, which is the markup or the margin of the platform. And that's going to be determined by bargaining between the seller and the platform. And I'll talk about that in one slide. In the outside market, they get the data directly from the buyers. And then the rest is the same. So for instance, on the platform, they're going to get a signal delta. And then they're going to produce the correct variety with priority delta on the outside market just as before with delta bar O. And the buyer and the sellers interacting competitive search markets, the platform and the outside markets are formally the same in that sense. So everything that's on the platform is indexed without the O. So for instance, let's look at the priority that the buyer meets the seller with alpha and the one minus gamma. It's the same as before. I just don't put the O index for the, when the platform is alpha bar in the outside market with alpha bar O and something with delta. So delta bar now is the technological limit for the platform. Okay. So the first question is, when is the platform active? And that actually is very simple and bang bang. And that's because everything here is pure conservative to scale. So either the platform is more efficient or it's not. And that determines whether it's active or not. So alpha bar is the matching efficiency of the platform and delta bar is the information. What matters is the product alpha delta. So if alpha delta of the platform is better than the outside market, the platform is active, otherwise it's not. If the platform is active, then the buyers have to be indifferent between the two places to buy their stuff. But all the new sellers are going to enter on the platform. And okay, so then we solve with the, yeah. Yes, regarding the previous slide. So you rule out the case where the platform is better for buyers so that all the buyers go to the platform? No, I don't rule out. It's just, it's not an equilibrium because there is always some legacy sellers here. And so if you're the only buyer in a market who is a non-zero mass of seller, the tension in that market is infinitely in your favor, it's still going to go. It's still going to go. It could be that, the thing that's, if you prefer it's continuous. So what happens if the platform gets better is the number of buyers going there is going to get smaller and smaller and smaller. But it's not technically zero. It would be, but again, to get that, I assume that there is a number, a finite number of legacy sellers in brick and mortar who are stuck there. So these guys value function is not going to look pretty like they're going to lose because they are fewer buyers and they wouldn't enter if they had no, but they are stuck. Okay, sorry. Oh yeah. So then to solve this pretty straightforward, you do the usual backward induction. So remember we have competitive search conditional on all information technology. We have competitive search between buyers and sellers on the platform and on the outside market. We have the indifference condition of the buyers. Then we can solve for the tightness and the equilibrium. Then we can compute the value functions. And then we can look at the key decision for us, key decisions for us. And these decisions are the entry decisions of the sellers. And that's going to depend on how much the platform is going to charge. So it's jointly the entry of the sellers and the bargaining between the seller and the platform on how much the platform is going to charge. The other decisions is the disclosure choice, which again here I'm just going to assume away all the private costs. So they're going to the consumers, self privately consumers privately consumers always going to go for the higher possible delta. Okay, so I guess to the value functions, then not surprisingly, once you know the tightness of a market, it's fully characterized. So conditional on tightness. So that's a number of sellers or two buyers on the particular platform. Then you can solve for the value function. Same cup to glass. Therefore, same constant price. So in particular, in this model, by the way, the price of the good is the same on them on both platforms. It's always one minus gamma times you. So that the relative price is not going to change. It's not like the platform gets more efficient. And then you buy you get the goods for more expensive or whatever that's not the price of the goods is if you looked at the data in this model, the price of the good would be exactly the same. The only thing that would change is the is the tightness of the market. That's from cup to glass. Otherwise, you would otherwise it would be a potential change. Okay, so then you get the value function, a function of tightness. And it has the bargaining, the competitive search bargaining. So the gamma one minus gamma, he has the information efficiency delta, and you see delta and alpha. So information efficiency and matching efficiency, they always matter as a product. Because the product of meeting somebody and offering the right good. So it's always they come together, which is why all the results for say entry of the platform depends on delta alpha multiplied together. And you is the that's the gains from trade. So all the standard stuff. So it's gains from trade, weighted by elasticity and tension in both cases. All right. So now we have the value function for the seller. That's what they get. Okay. But to get that on the platform, they need to access the platform and there's a price M for that. Now we in the paper, we look at two cases, we look at the platform as a as a as a monopoly, maximizing the total revenue. And we look at bargaining one by one platform with sellers. I think the prime the right model depends on the application. So here I'm just going to show you the Nash. The monopoly has it's very similar with one extra term. So if you do the manage bargaining, then you have the value for the platform, which is how much they get right to the outside option. So this is if they don't agree with that particular seller. And then the seller pays the fee to a platform. And of course, all the action in the model comes from this, which is the outside option of the seller is to go to the outside market. You always have the option if you don't want to sell on the platform, just say fine, and then you go sell to the buyers on the outside market. So this outside option is critical, because that's the one that affects the the fact that it's like affecting the bargaining outcome for the for the seller. The other option for the platform, we consider two cases, either we kill it, the platform either the only thing you can do is just is to be a platform. If you want to to use the technology to create your own brand, then you can let the platform copycat the goods produced by the sellers. And if the sellers doesn't accept the terms or form of the platform, the platform is so fine, I'll just I'll just do a copy of your good and say it myself. And so that we call that the copycat technology. And the platform is not as efficient ex ante as the seller are doing it, but it can. So it become a in this money, we could become a good threat point for the platform. So given the other option, you get the Nash bargaining solution, which determine the fee. And of course, the key thing here is, if the outside option of the seller is lousy, the price is going to be higher. So the outside option of the platform, so that's just describing the copycat technology. So just saying that they can create the same good, but they have a they have a cost C. So it would not be efficient for the platform to do that. But they can as a threat. Okay. And then the second one is the seller and that we've seen that's the key one. The seller is the value function if the seller goes on the outside market. And the key thing that happens in the model is that this is typically decreasing in Delta. It is decreasing in Delta because if when the platform gets more efficient, more and more buyers go to the platform, the value of being on the outside market goes down and down and down. That's the main effect. If Delta is if the Delta is high, all the buyers are going to flock to the platform. That's going to depress the value of everything else. And that value is the outside option of the seller. So that's going to depress the value of the seller. And for lack of a better name, we call that the gatekeeper effect, which is if the platform is strong enough that it attracts most of the buyers, then they aren't there to, they aren't enough buyers left outside the platform to make trading outside attractive. That depresses the outside option, the option of the seller and then allows the platform to charge a high price. So then, yeah. Let's ask another question. So I may not understand the bargaining. So here it seems like you're assuming that the platform is bargaining with all the sellers at once. Is that right? No, no, no, not. That's the way that that's the part I don't like about Nash. This Nash is assuming that they're buying in with one seller. But then in that case, shouldn't the platforms outside option be its profit if one, if it has one fewer seller on it? Yes. That's what this VM is because it's like you would you would you wrote again is equal to zero or or something. So yeah. So if that seller doesn't come to your platform, you could you could steal the idea and become a seller yourself. That's what we write as your sort of plan. So but I would have I would have assumed that if one seller doesn't come, then you just out you are left with n minus one seller. Suppose you cannot. Yes, yes, I agree. No, no, yes. That's another way of writing it. Okay, then it would be but that would be independent of what you of the deal you strike with that seller. If the number of seller is good. So the key thing though, we can get rid of that outside option. The thing that is important though is written like that is the what I don't like about this is the platform is talking to one seller and then you solve for that thing as one seller. And you don't it's you don't take into account the fact that if you change your term, you might attract a bigger mass of buyer or bigger mass of seller. And therefore, you know, you might have a few men try not to price too high because you want a high volume on your a high number of sellers because that's going to attract buyers and more and more buyers. It's easier to attract the next seller. And that we solve as the pure monopoly where the platform maximizes total revenues m times n s. And then it takes all of that into account as as two polar cases. We just wanted to have the two polar cases. And I think I mean, this one is slightly simpler to write. There's one fewer term. Everything I'm going to show you is there is just in the in the monopoly case, there's one extra term. Maybe I can point it out when we get there. Yeah, so now if you think about the impact of Delta on on the seller's value on the platform vs minus m, which is the thing that's going to determine the entry condition, you have the usual term which is Delta is higher, there's more efficiency. So that's much efficiency gains from trade, standard stuff, that's going to capture, that's going to be captured by this. It's weighted by one mistake because not the part of the gains is captured by the platform. And then here you have the market power effect, which is the impact of Delta on the outside option, either of the platform or of the seller. And this is the part that can create the negative welfare effect. So better higher Delta higher much efficiency. That's great. That's going to not only is going to make the existing matches more efficient, it's going to increase seller entry. But it's going to increase the market power of the platform right to the sellers. Okay, so then to solve maybe, yeah, I should try to go a bit fast. I think we've seen all the conditions. So the free entry condition as before, except that now you net out the fee. And then the the consumer in different conditions says that the consumer can always go to the outside market or the platform, they're going to be different in equilibrium, that's going to pin down the market tightness. I don't think I need to show you who can find sufficient condition for necessary condition for the negative effect to dominate. But maybe I can just show you, I think, the figure is going to be easier. Yeah, five minutes. Yeah, that's why I think the figure is nicer. I think for to plot the figure, I'm just there's one more thing I need to it's more like a, that's not for them, but it's just it makes it easier to describe the figure. So we're going to think about, because now we're going to think about, you know, in which space are we. And so I think at least for me, the simple way to think about it is based on underlying technological progress in society, which has to do with computer and it and stuff like that. So let's call that X. Okay. And think of that as exogenous productivity growth in technology. And then there is the extent to which existing retailers or platforms can use that technology. And that's the upper bound delta. So that's the quality of information that you can extract. And so on the outside market, all we do is this delta or delta bar that used to be some exogenous number. Now we're going to think of it as a function of X and same thing for the platform. And when we said that the platform is better at using IT, formally what we mean is it's steeper delta of X is steeper than delta O of X. So there is, there is a point at which the, when technology keeps improving, it has a bigger impact on the platform than on the outside market. So that's I think is that's the key definition, right? Like Amazon could have been created in the 1980s, but relatively speaking, you would have not given the technology at the time pre-internet, it would not have been more efficient at gathering information than Walmart. But post-internet, it reversed. And so that's, that's what we're writing here. Now you could, you could renormalize and write one delta as a function of the other delta. And that's fine. It just, I think that way is the most intuitive. So think of it as, because now we're going to do some kind of comparative statistics where thinking what happens if we improve technology. If you improve technology, then everything is going to get, all the matching is going to get better. But the potential efficiency of the platform is going to rise faster than the potential efficiency on the outside market. I think, well, the welfare stuff, I think I explained where it's coming from. So we have some proposition that says, when is it that there's too much information disclosure? But again, the key idea is it happens when further improvement of the platform depresses the adoption of the seller so much that the platform can reap all the gains and more from the trader. And so this is how it ends up looking. I think that's a better summary of everything. Okay. So we have, I think most of the variables of interest here. And now, so here on this axis, I put X, right, the level of technology. And then here I'm showing you what I mean by efficiency gains. So the delta of the platform is in blue, the delta of the outside market is in red. So this is the extreme case where the delta of, so initially if you have better technology, if you have initially the outside market is more efficient, but it cannot leverage the new technology as much. So at some point, the platform becomes more efficient at using the information. The point where they cross here is X hat. So there's some level, so I think about the past 30 years, then we were in this region and we had, in that region, the outside market was more efficient. In fact, Amazon did not exist. And then at some point, we cross this threshold and the platforms become more efficient than the outside market and the platform enters. Now, the outside market does not disappear because there's a legacy sellers with the outside market. Okay, so that's kind of the comparative statistics I have in mind. Then we can plot the number of, well, it's a little, this one is easier. This is the number of buyers in the outside market. So of course, when you're below X hat, by definition, the buyers have only one place to go. So they all go to Walmart. So, and it's normalized to one. So this is 100%. Then when we cross that threshold, the platform enters. Now, remember here, because everything is cost of return and there is no time to build or anything. It's a discrete job. And immediately the platform steals, whatever, 80% of the market share. So the number of buyers on the outside market drops from 100 to 20. And then it's kind of flat. And even increasing after the number of buyers on the platform here is the opposite. The platform does not exist. So it's zero. And then it jumps up. And then it's kind of flat. And even going down a little bit. So what's going on? Well, here, that's entry of the platform. And then the number of sellers on the platform, of course, jumps up. The total number of sellers also jumps up. But then, so that's the big welfare improvement. Or that's the big shift in market share. Now, of course, when that happens, so that's welfare here. So welfare is continuous because when the platform enters at X hat by definition, they are exactly the same efficiency. So locally, there is no change in welfare. And then welfare keeps going up after if you keep increasing technology, because the platform gets more efficient. And then over that region, welfare still goes up with technology. After you after you reach that point here, which so this is just a numerical iteration. So this point here could be further right or further left, of course, depending on which part you use. But the key is that welfare goes up initially. And at some point, so here it happens here, further improvement in technology, while they do improve welfare, they do improve the match efficiency on the platform. The problem is they depress the outside option on the outside market so much that the platform can extract most of the gains. And therefore, the sellers are discouraged. And you can see the number of sellers on the platform going down relatively steeply here. That's what drives down welfare in this example. But the thing that I found striking is what seems to be often happening is that the platform, as soon as it enters and it achieves a significant market share, after that, for a while, at least the number of buyers and sellers on the platform remains kind of flat. And that's just a platform essentially using every extra gain of efficiency to just increase its margin, as opposed to increasing seller entry. So I'm out of time. So I think that I think that summarizes everything. So thank you so much. And I look forward to the discussion. Okay. Thank you, Tomah. The discussant is Shota Ichihashi. Shota, five minutes. Sure. Can you hear me well? Yes. Okay. Thanks, Tomah, for presentation. And thank you also for having me as a discussant. So today we saw the problem of excessive information disclosure and as one of the two sources, the gatekeeper effect. For the discussion, I'm going to discuss what this gatekeeper externality gatekeeper effect precisely captures. I will try to claim some generality of this new effect and also raises a couple of questions for later discussions. So first, I'd like to think of the gatekeeper effect as a combination of two forces, which correspond to the two choices consumers make in the model. So first, consumers choose whether to join the platform or outside market. And then if they join the platform, they're going to choose how much information to disclose. And my first point in the discussion is that even if we fix the level of information disclosure, consumers' participation decision still imposes an externality on other consumers. For example, if many other consumers join the platform, the outside option of sellers in the outside market deteriorates, and the platform exploits this lower outside option. As we saw today, this could discourage seller entry and hurt users on the platform. That's a negative effect across consumers about participation. But on top of this, the choice of delta information disclosure interacts with this participation effect, which is my second point. If I can provide my data and platform can use it to increase the value of transaction for me, then I'm more willing to use a platform, which makes the first participation, let me say first participation externality more relevant. So the interaction between the extensive margin decision, the participation, the intensive margin decision, how much information to provide creates a gatekeeper. And this is the composition means that the similar force like gatekeeper effect can work for also other activities on a platform that users can take to increase the benefits from using the platform service. So we learned today that providing personal information can be such an activity. But the same intuition could work for other activities, like for example, the mere usage of the digital service. If I use some digital service a lot, it could increase the quality of the service, possibly because of data-enabled learning, like a smart speaker, or learning by doing on my side with respect to the particular user interface. And this value-enhancing activity can encourage more consumers to join the platform. It can decrease the market tightness, as we saw in today's presentation. So I think in my, so my understanding is it may not be crucial whether the activity like providing information benefits centers, technically so long as the activity benefits consumers or the increase the utility of joining the platform, the negative gatekeeper effect will be relevant and restricting this kind of activity may be beneficial for the social welfare. So what I want to claim here, emphasize here, is the generality of this gatekeeper effect. And now the last point, the paper shows this that the amount of information disclosure can be socially excessive, so restricting data collection could help. And I think that part of the story here, this negative gatekeeper effect is also about a platform to hold up problem. Information disclosure could deter a setter entry because the platform cannot help exploiting the low outside option of setters and capturing most of the setter surplus through the today presentation, through the Nash bargain. And that's a problem because the entry cost is sunk when the platform and a setter bargain. So we may think of other solutions on top of the restriction of data collection to mitigate this whole problem. It could be the contractual solution like a platform committing to a fee M in advance, maybe that's what Thomas meant as the other monopoly pricing formulation. So this idea basically asked how the timing of committing to the fee or the split of surplus, how important assumptions or maintaining the whatever Nash bargaining or the monopoly pricing, the platform may be able to mitigate a whole the problem by making it easier for consumers and the setters to multi-home for the outside market and the platform. So this may mitigate a set, improve setters outside option, mitigate a whole that problem. So it might be interesting to think other potential solutions. Another related question is whether that this negative effect, negative gatekeeper effect can also halt the platform's profit. If that's the case, we could ask how the platform may self-regulate to improve profit, potentially restricting data collection or using other possible solutions. Now, I think overall the paper provides a novel and deep insight. So I really enjoyed reading it. Thank you so much.