 I'm very happy to present this paper, which is on platform liability and innovation. It's a paper with my great quarters, the Xinjiang and Yixing Lefoulis, who are also in the audience. So they may also help me with questions if I'm not able to see the chat box at some point. So let me try to motivate what is the main topic of this presentation and why we think this is important. So e-commerce platforms in recent years have become quite important. We buy goods online on platforms like Amazon, in Bay, and many others. But in recent years, something problematic has happened. According to ACD, the Organization for Economic Cooperation and Development, e-commerce platforms have become ideal storefronts for counterfeits, not only because they allow large numbers of potential customers to buy goods, but also because some of the sellers that are operating on this platform can sell goods from everywhere in the world and can be very hard to identify or to bring to courts. And the problem has become particularly important in recent years with multiple brands filling lawsuits against companies like Amazon and eBay because they were claiming that platforms were not doing enough to prevent the sale of counterfeited items on these platforms. And at some point, big brands like Nike and Birkenstock decided to pull their products from the platform. There is also a very interesting case that concerned a luxury brand in Europe a couple of weeks ago, Louboutin, that was complaining for the presence of high-infringing products on Amazon. And according to courts, Amazon was not found liable for the sale of these high-infringing products. Now, the overarching issue that we try to tackle with this paper is whether platforms should be liable for third parties' illegal conduct, the third parties' misconduct. And currently, digital platforms that are intermediaries benefit to a large extent from liability exemption. This is certainly the case in the US with section 230 of the Communication Decency Act. But it is also the case with some small differences with the Commerce Directive in the European Union. Platforms in the European Union benefit from liability exemption as long as they comply, they are considered, they are passive. At the same time, they act immediately the moment they become aware of illegal conduct that is present on their ecosystem. But in recent years, policy attention increased on this topic, and we now have the European Digital Services Act that was approved by the European Parliament last week. We have other piece of regulation that have been drafted in the UK, the UK Online Safety Bill, the Informed Consumers Act in the US, and a new law in China that try to intervene on this topic by granting platforms, some liability exemption, updating the current liability regime for some platforms, introducing in some cases some strict liability. So in this paper, what we are going to focus on is, first of all, on a specific type of platforms, e-commerce platforms, and eventually app stores, and a specific type of illegal misconduct, IPR infringements. So we are going to be focusing on trademark violation, design violation, and copyright. And it is very important that what I'm going to say now, this infringement are by non-deceptive third parties. So there is the products that are considered in our model are sold by copycats, but these products are neither harmful nor deceptive. In the sense that consumers know that buying not from the original seller means buying a low quality version, there is no deception. And the absence of a symmetric information is also quite important in our framework, because imagine a situation in which you buy something that you think is an original product, and then this is delivered to your place, then in most countries and also most platforms adopt this policy, you can simply return it back. So if there is a mismatch between what you thought you were buying and what you get in the end. So it also makes sense to focus on non-deceptive third parties. And a leading example is the one that I have in this slide. So you may imagine, for example, a branded product, Levi's, and a copycat, Love. Now for consumers, these products are really different. They look similar, but the consumer can perfectly understand that buying Love means not buying Levi's. So there is some differentiation here. Now, with this in mind, in this paper, we are going to answer this narrower question, which is what is the impact of making platforms liable for IP infringements by third parties on innovation and on consumers? And we are going to focus on the following negligence liability rule. So we are going to focus on the case in which lawmakers, policymakers, regulators impose some requirements that platforms have to comply with in order to benefit from liability exemption, the current safe harbor. And in our model, this means that platforms have to comply with a minimum screening requirement and the obligation to the least any IP infringing product that they identify on the marketplace. And the second part of this negligence rule that we are focusing on is pretty much similar to the current provision of the Commerce Directive that tells that platforms have to immediately intervene the moment they become aware of illegal conduct, illegal products, or illegal information that is present on the marketplaces. Now, with this, we try to contribute to the low and economic literature on liability, mostly to the literature on indirect liability when you want to make a party that is not directly involved in illegal activity liable for third parties in legal activities. And more importantly, on the topic of liability in digital markets, there are some formal contributions but there are, most importantly, two closely related paper, very two fascinating papers. One is by Xinxiu, my discussion. I'm very grateful for being here. And by Catherine Spear is a paper that was presented actually in this seminar series a couple of weeks ago that concerns liability in the presence of harmful products. And there is also another fascinating paper by Alessandro de Chiaraes-Termanina and co-authors on liability for roasting platforms in the presence of copyright violation. But this is a seminar on platform governance. And this paper try to speak to the community of platforms because in the end, the decision of a platform to the least IP infringing products is a decision concerning the governance of a platform. And platforms use different prices, pricing and un-pricing instruments to influence, for example, when there's competition and innovation, they may bias innovation towards one side of the market, curate the ecosystem or delict toxic content. And in one of the extensions that we have, we also focus on the interplay between the imposition of platform liability and the adoption of a high business model and many papers that I'm referring to have also been presented in this seminar series. Now, if there are no questions, I will start presenting the details of the model that we have in mind. So consider an economy in which all transactions between sellers and buyers take place on a marketplace, on a monopoly platform. And there are two types of sellers. We have innovators that can develop an original product and this has a cost, which is distributed, a fixed cost of innovation that is distributed according to a CDFF and a PDF small f. And the moment an innovator develops an innovation, a new product, this gives rise to a new product category. And for simplicity, we are going to assume that the marginal cost of production are equal to zero. Now, in each product category, a single imitator copies the innovative product at the non-cost. Now, with the probability new, this imitation is legitimate. And with the complementary probability, this imitation is infringing IPRs. Now, in the baseline model, we assume that this probability is exogenous, but we have an extension depending on time, I can spend some words about it. We also consider the case in which there is endogenous decision by imitators to be infringing, to infringe IPRs or not. And the presence of this endogeneity is particularly important because it gives rise to some additional interesting effect. Now, the platform sets an ad valorem commission rate, which is still on the seller side of the market and is committing to a screening effort, PHY. And PHY is a probability that the IP infringer is identified. Now, two things are very important here. First, we are considering a commitment on screening effort. In an extension, we also consider what happens in the absence of commitment, but we thought it is reasonable to assume that there is commitment because nowadays, very large platforms are subject to transparency obligations. So there is some observability in what they are doing in terms of moderation, in terms of screening. And the second is that the technology adopted by the platform is imperfect. So the higher the screening effort, the higher is the probability that the IP infringing product is identified. Now, the moment an IP infringing product is identified, it can be delisted by the platform. However, legitimate imitators cannot be delisted by the platform. And one reason would be, for example, that there is a platform to business regulation, like in the European Union, for which platforms are obliged to ensure some fair treatment to legitimate sellers. We assume that screening is costly, increasingly costly. So there is a complex function here, which automatically implies that if a platform is investing in screening, is increasing its screening effort and identifies an IP infringing product, then it has an incentive to delist it. So we can think about FI as the probability that there is the identification and the delisting of an IP infringing product. Now, the last agent in our model, the last set of agents are the buyers. We can see there a mass one of buyers. In the baseline model, we assume that all buyers joined the market place. Now, then later, and this is the core part actually of the paper, we focus on the case in which there is elastic buyer participation, which is particularly important because it's the way we model the presence of cross-group network effects. Buyers are ex-sante-symmetric. They have the same ex-sante utility from joining the platform, but they are exposed as symmetric. They discover their evaluations for innovators and imitators once on the platform. Now, in each product category, each product category that is there because an innovator generated a new product and this gave rise to a new product category. Now, each product category is by default, dual-polistic. There is the innovator and the imitator, but can become monopolistic because the platform can identify an IP infringing products and delist it. So in this case, the product category becomes monopolistic. In each product category, the innovator is getting Pi IM or Pi ID, depending on whether the product category is monopolistic or dual-polistic. The only assumption that we make here is that monopolistic profits are larger than dual-polistic profits. Then imitators obtain Pi CD if they are not delisted and here we model vertical differentiation. So Pi CD is lower than Pi ID. It makes sense to consider indeed the situation for which innovators make profit at a higher when they are alone in the product category than we are competing with innovators and branded products and innovators are different in terms of value and therefore they generate asymmetric profits. Now consumers obtain exante utility, which is UM if the product category is monopolistic or UD if the product category is dual-polistic. And given that we are considering IP infringing products that are not that are neither harmful nor deceptive, we assume that consumers prefer to gain more utility, the exante utility for a consumer is higher in a dual-polistic market structure. Now the timing is the following. The platform is setting its screening effort and the commission rate tau, second, innovators having observed these terms and conditions of the platform make their innovation decisions and join the marketplace, join the platform if they innovate. In each product category, a single limitator joins the platform and is delisted if it infringes IPRs and is identified with probability five. And finally buyers decide whether to join the platform. In the baseline model, we start with a situation in which all buyers are on the platform. So there is an elastic demand buyer participation. And upon joining the platform, they discovered their evaluations for the products and they make the purchasing decision in each product category. Now it's important here to clarify what are the expected payoffs of the sellers and the buyers. So for a given screening effort and innovators expected gross profit, it just a weighted average of the profit and innovator would get if there is a monopolistic industry structure per category structure and the profit would get if there is a duopoly structure. So one minus new is the probability that there is an IP infringing product is five and five is a probability death and IP infringing product is identified. The expected per category profit of an innovator is just dependent on the probability death. The imitator is not delisted either because it is infringing IPRs and it is not identified or because it is legitimate. And the expected utility per category of a buyer is once again a weighted average of utility obtain if there is a monopolistic market structure and if there is a duopoly stick market structure. Now, let me start introducing the baseline model and we're gonna focus, we're gonna start with an elastic buyer participation. All buyers are on the marketplace, all buyers are on the platform. And we assume for now that there is an exogenous commission rate. Now you can think about an exogenous commission rate as the result of a long-run decision strategy of a platform that decides about the commission rate or simply as a situation for which for the platform is quicker, it's easier to adjust the screening effort than the commission rate. Alternatively, you can think about an exogenous commission rate being there because there is exante or exposed regulation. For example, by competition policy that prohibits excessive pricing or alternatively because there is a direct channel that puts a constraint on how much a platform can charge innovators if the reservation utility of the innovators is sufficiently large. Then we are gonna relax this assumption. But let's focus now on what the platform would do in the last set of the regime. And this is particularly important because one of the complaints made by brand owners is that platforms do not have incentives to screen and delist IP infringers. Now, in this setting, we're gonna identify whether or not there are these incentives and then we focus on the impact of platform liability. Now, in the last set of the regime, the number of innovators that in the second stage develop a new product and join the platform is just a probability. It's the probability that the net expected profit of an innovator is larger than its innovation cost that is fixed. And pi i phi is the expected gross profit that we've seen before, but then the innovator has to pay a commission to the platform. So this gives us an i, which is the number of innovators, but also the number of product categories because innovators give rise to new product categories. And the expected profit of a platform that the platform maximizes by choosing the screening effort is the following. So here we have the screening cost, omega, and the revenues are the commission rate that is charged on the NI product categories. And in each product category, the platform is collecting a portion because we are considering the commission rate of the per category total profit, which is basically the sum of the expected profit of an innovator and the expected profit of its copycat. Now, in the laissez-faire regime, the platform decides pi, the screening effort to maximize its expected profit, taking into account two main effects for a given cost. The fact that increasing pi impacts positively on the number of product categories in this baseline model, because by increasing the screening effort, the platform is reducing the probability that each product category is dual-polistic. Therefore, it is increasing the expected profit of an innovator and therefore, it gives more incentives to innovators to develop new product and therefore we have a higher number of product categories. So in the baseline model, this effect is always positive. And we are gonna call it later IP protection effect. But there is also another effect that the platform takes into account, which is the effect on increasing screening effort on the per category expected total profit. And this effect can be positive or negative. And that depends on whether a monopolistic market structure gives higher total profit than a dual-polistic market structure. And it is negative otherwise. And the two scenarios are present and can be micro-founded in different ways. Now, in the Lasseffel regime, therefore, if total profits are greater under a monopolistic industry structure, than a dual-polistic industry structure, the two effects are positive and the platform optimal screening effort is always positive. So there is an incentive for the platform to identify in the list IP infringing products. If the platform were not constrained by the cost of screening and by the possibility to screen out legitimate, the possibility to screen out legitimate imitators, the platform would have the interest in screening in removing goal imitators. Otherwise, if a dual-polistic industry structure gives rise to higher total profits than a monopolistic one, the optimal screening effort of the platform may even be zero, no screening at all. So the platform incentives to engage in screening tend to be higher if total profits are maximized under the monopolistic industry structure. But now let's focus on what happens if you impose platform liability. And we focus on the case in which the regulator, the lawmaker imposes a minimum screening requirement that are higher than the privately optimal level by start decided by the platform owner. And we focus on the case in which the platform finds it optimal to comply with this screening, minimum screening requirement. And you can think about it in two ways. First of all, litigation costs can be very high and therefore the platform has an incentive to comply or alternatively, there might be fines for non-compliance. So long story short, platform liability here means that the platform has to increase its screening effort. Now, this is going to lead to it in the very baseline model to the following effect on innovation. And this is the intended effect of platform liability on innovation. By increasing screening effort, the platform reduces the probability that each product category is globalistic. It's relaxes competition between the imitators and the innovators. This increases the expected profit of an innovator and therefore this leads to a positive effect on innovation. But what is the effect on consumers in the baseline model? Now, consumer surplus is given by the number of product categories and the per category utility that each consumer obtains. And so here platform liability has two opposite effects on consumer surplus. The first one is that it leads to more innovation, therefore more product categories. But at the same time, it is rendering each product category monopolistic, more likely to be monopolistic and therefore per category utility decreases. So depending on the relative magnitude of the different effects, the net effect can be positive or negative. And this boils down to a comparison of two different semi-elasticities. The semi-elasticity of the amount of innovation and the semi-elasticity of the per category utility. And the net effect is positive if consumer benefit more from an increase in the number of product categories than how much they are losing in each single product category because there is less competition. Taking a message is that platform liability in this baseline model benefits consumers if the effect on innovation is sufficiently strong. But let's start now relaxing the assumption of inelastic bio participation. And this is particularly important because it's a way to introduce cross group network effects. And we are gonna focus now on two different type of cross group network effects. A cross group network effect that goes from buyers to innovators and cross group network effects that go in both directions, from buyers to innovators and from innovators to buyers. In order to generate these two different types of cross group network effects, it is useful to write down the utility of a consumer that joins the platform, which is basically given by how many product categories are present times the utility in a given product category. Now here, this is particularly important. This is the gamma here is a category related opportunity cost. So for each product category that is present, the consumer has to incur an opportunity cost. You can think about time spent in order to understand each product category. And it's also quite in line with the recent literature. And then gamma Xi here represents a platform related opportunity cost. An opportunity cost that is born in order to join the marketplace, in order to join the platform. We are gonna focus now first on the case in which there are only one-sided cross group network effects. So there is no platform related opportunity cost. And this is quite in line with the recent paper by Andrew Tataute and Julia Wright in front. So there is a per category outside option in their model. In our case, it's the opportunity cost that is category specific. And therefore the consumer decision to join the platform only depends on how much utility the consumer obtains by joining a product category and the opportunity cost. So it does not depend on the number of innovators. It does not depend on the number of product categories. So there are no network effects from innovators to buyers, but there are network effects from buyers to innovators because depending on this relationship, we obtain the demand. And the demand is going to be the probability that the utility in a given product category is larger than the opportunity cost. Now, the key aspect here is that the demand of buyers is decreasing in the screening effort. And the reason is that each buyer decides to join the platform depending on how much surplus it gets. And if you screen more at the least more IP infringers, you render the product category more likely to be monopolistic and therefore this reduces the participation of users, of buyers. Now, the reason why we have one side of cross group network effects is that the demand is taken into account by innovators when deciding to develop an innovative product and sell it via the platform. And so here, platform liability differently from the baseline model has now two effects on innovation. The first one is what we've seen before. The positive IP protection effect. I screen more, I get rid of, I get rid of, I'm more likely to get rid of competitors of innovators and therefore I induce innovators to invest in innovative products. But there is an effect that is negative that is stemming from the reduction in buyer participation. And therefore the net effect is positive or negative depending on the prevailing effect. Also in this case, we can write down the relationship between these two effects in terms of semi-elasticities but the takeoff message is that platform liability can now lead to less innovation, which is a very important result given that platform liability is meant to protect innovators. Now, platform liability has therefore two effects on consumer surplus. There is a change in the number of product categories as before, but now the number of product categories can decrease because innovation can decrease. And in each product category, the utility decreases. So this implies that when we look at the prevailing effect the net effect is positive if the relationship holds. But now, differently from before, this effect, this relationship might not be, may fail to be too old because the number of innovators can actually decrease with platform liability. So in this case, there are conditions under which platform liability harm consumers and platform liability harms consumers if its impact on innovation is either negative or moderately positive, otherwise it is going to benefit consumers. Now, let's focus now on the other case where there are two sided cross-group network effects. So this basically means that we put to zero the category related opportunity cost and we focus on the platform opportunity cost. Now, buyers decide to join the platform, taking into account how much surplus is created, the utility generated in each product category but also the number of product categories. And if you increase the number of product categories you are more likely to increase buyer participation. So now given that there is a coordination problem here so the number of innovators and that the buyers are given by the following expression. So we need to look for a fixed point. And when we do so, we identify conditions under which buyer participation increases or decreases with a higher screening endpoint. So this implies that platform liability has two effects on innovation. Once again, the usual positive intended what actually is meant to generate platform liability and this is the IP protection effect but there are also two, there is another factor that can be positive or negative. And this is coming from the change in buyer participation and then at the fact that for platform liability on innovation is positive is if buyer participation increases or it does not decreases too much but it's negative otherwise and then at the fact that consumer surplus has the same sign as the effect on buyer participation. This is to tell you that the presence of gross group network effects is particularly important in order to identify the impact of platform liability on innovation and consumers but the presence of network effects from but also the direction is particularly important. The presence of network effects that go from innovators to buyers tends to make platform liability more likely to benefit innovators and consumers. Now, let us relax the other assumption that we have made at the very beginning. We assume that the commission rate was exogenous. Now, let us suppose that the platform decides also about the commission rate and we are interested in understanding how does inducing the platform to screen more to increase its screening effort impacts the marginal benefit from an increase in the commission rate. And in order to answer this question we need to identify what is the trade-off that the platform has to deal with when deciding about the commission rate. Now, the platform when deciding the commission rate takes into account two opposite effects. If increases the commission rate it gets more from more revenues in each product category. So this is the intensive margin effect but it also reduces the number of product categories. So this is an extensive margin effect. It turns out that if you use a platform to invest more in a screening effort then a change in the screening effort impacts both effects. And the impact on the intensive margin depends on the elasticity of the CDF and the impact of the extensive margin depends on the elasticity of the PDF. And so we can write conditions for which a platform liability leads to an increase in the commission rate. And so this is a quite intuitive result. I mean, think about the fact that if you have to screen more, if you need to spend more effort that this is costly for you and then you want to recoup the resources that you have spent by increasing the commission rate. But interestingly and also quite surprisingly we find that platform liability might lead to a reduction in the commission rate. So the platform reacts by lowering the commission rate in order to stimulate more innovators participation to the platform and therefore enlarging the number of product categories at that price. So what is going to be now the impact on innovation even that we are interested on the impact of platform liability. Now we have the usual IP protection effect that is positive, but now the platform reacts by changing the commission rate. So if more screening means that the platform lowers the commission rate, there is a new positive effect of platform liability on innovation. So platform liability, positive effects on innovation are amplified because there is a new channel and this is therefore also more likely to benefit consumers. On the other hand, if more screening leads to a change in the commission rate that is now higher, this generates a new negative effect of platform liability on innovation. But what we show in the paper is that this indirect effect, the margin effect is lower than the positive effect or the positive effect protection effect as long as the second one, that the former one is negative and therefore the net effect remains positive, innovation continues to increase with platform liability, but to a lower extent. Now, let me tell you very quickly what we also do in the paper and we try first to identify new channels through which platform liability can affect innovation and consumers. First, we focus on the case in which the infringement is endogenous. So imagine a situation in which you have imitators that have to decide whether to infringe or to be legitimate and imagine a situation in which being infringer is cheaper. Now, if you introduce platform liability under some conditions you have the same results as now under some other conditions this is an interesting effect. You induce potential like infringers to become legitimate but this can have a negative effect on innovation because the legitimate sellers cannot be removed by the platform. And so if platform liability increases this conversion, it is more likely to render each product category duopolistic and this exert competitive pressure on innovators that might decide to invest less on innovation. The second extension that we consider is the hybrid business model. You can imagine a scenario in which there is a pure marketplace like the one we have considered now but also the platform and in this case platform liability certainly harms the platform because it's forcing the platform to do something that is suboptimal. So suboptimal. On the other hand, the platform that adopts a hybrid business model if it is forced to identify and the lease type infringers that identifies can still restore a duopolistic market structure by introducing its own legitimate copy cuts. And so platform liability here means that the platform is more likely to change from a pure market place to a hybrid one. And finally, the third extension that we consider is the absence of commitment. Platform liability can mitigate the old app, have the platform to commit and therefore increase the platform profits. Now it's time to wrap up. So with this paper, we tried to look at the potential unintended effects on a platform liability where platform liability implies a higher screening gap over the platform on innovation and consumer service. And we find that these unintended effects come from the impact that platform liability has on buyer participation and on the commission rate. So these unintended effects can either be positive or negative. So if buyer participation decreases and we find conditions under which this is possible, then this may lead to less innovation and lower consumer service. But there are also positive unintended effects that come from, for example, from the case in which the platform reacts by changing, reacts to platform liability by changing the commission rate, reducing the commission rate, this force more innovation and leads to a higher consumer surplus. And we also find that it is important not only to understand the relevance of cross-group network effects because results can change dramatically, but it's very important also to consider the direction of these network effects. And the cross-group network effects from innovators to buyers crucially affect the deserability of platform liability. And in particular, if these effects are strong enough, then platform liability is more likely to induce more innovation to benefit innovators and also consumers. Otherwise, there are cases in which platform liability leads to a lower consumer surplus, therefore harming consumers. And in some cases, my even harm innovators, which is basically what policy makers don't want because the idea of introducing customer liability in this scenario in which the online misconduct come from the presence of IP infringing products is probably to protect innovation. Thanks a lot for your attention and I really look forward to your comments and discussion. Thanks very much, Leonardo. So let's go straight to Shin-Yu for the discussion. Thanks. I still have one slide. I know it's not must, so let me just share my slide. All right, so I very much enjoy reading this paper and I think it's a very nice piece of study which covers some important topic with very interesting policy implications. Now, okay, as Leonardo mentions, this paper certainly contributes to the literature about law and economics, as well as the one on platforms. But beside those, I think it's also complements the literature on IPR protection and piracy. Actually, Kathy and I, we also have another paper about piracy, but total difference. So we know there in that literature, there are some studies showing that sometimes accommodating piracy can actually increase brand owners' profits, which in turn may promote innovation. And we have seen here, when there are margin effects in this current paper, sometimes the lower screening efforts at the platform may also increase the number of innovations. So in that regard, it can actually also contribute to that literature on IPR protection. I think some discussions along this line would be kind of useful. And also this paper identified many interesting and subtle effects. Okay, as we have heard, there could be IP protection effects versus the monopoly distortion within each category. Also, there could be demand effects due to the bias, the changes of bias participation and finally the margin effects, which is very interesting. And my comments are mostly about potential extensions and maybe a further analysis. So we see that, first of all, if there's no regulation or liability, while the paper derives the platform's optimal screening efforts, okay, which is intuitive and we saw the intuition, but it's not clear to me what the socially optimal screen level should be and whether the private level is socially excessive or insufficient. Okay, I think the answer to this question will be useful, especially when I think about for such actions-based rules, liability rules or regulation, while the social planner in choosing Phi Zeta may need such kind of information, right, okay. And related to the first comments, I think it'd be also useful to have more welfare analysis. So currently the analysis focuses on the impacts on innovation and consumer supplies, okay, which is useful. But I'm wondering what would be the total welfare changes when there's regulation, the minimum screening requirements. I know given so many subtle effects, it's kind of hard to derive general conditions, but perhaps it's useful to provide some numerical examples to illustrate the effects. For example, I really like this final marching effects. Okay, and we know that when, with uniform distribution, the commission rates is independent of the platform's screening efforts, okay. But I was wondering, could there be any other familiar distributions under which the commission rates increases or decreases in screening efforts? I think having those numerical examples may give us more policy or welfare implications. And then for potential extensions, the current paper, okay, considered the platform's action to verify IPR violations. And I was wondering sometimes in practice, maybe brand owners might be in better position to do so, given their expertise or knowledge about products. If that's the case, we may have a kind of a double-sided more hazards framework. And also I was thinking about the pricing schemes. I saw there were some discussions in the chat box about the commission rate. So currently, I think the marching effects partly depends on this assumption that the platform can only charge a uniform commission rate for all the firms. So, and the paper also provides some discussions about price discrimination. I was wondering what happens if the platform could set commission rates based on market structure. I'm not sure whether we see this in practice, but theoretically it's possible. For example, the monopolist and duopolist, they may pay different commission rates. So it seemed to me in that case, the regulation or liability could be more desirable. Or alternatively, we may think about the flat fee for each transaction per transaction fee instead of a percentage fee based on profit or revenue. And also finally, I think this is, well, currently the screen costs are fixed costs. So I was also wondering what would happen if part of the screen costs are variable. So currently the screen costs are independent of the number of categories or the number of firms. But perhaps some of the screen costs could be performed. So in that case, maybe some of the welfare effect would be different. Now, I mean, most of the comments about future extensions, but again, as I mentioned earlier, I really liked the study and I think there must be a lot to follow up and the related studies in this direction. Thank you.