 This week we have a talk from Shotta Ichihashi from the Bank of Canada. The format for those of you who don't know is that Shotta is going to talk for about 40 minutes. He said that he's very happy to take questions as he goes along so you can just pop those into the chat. And then after Shotta's talk we will have a discussion from Tomasir Valletti for about five minutes and then time for some open Q&A. And as usual at the one hour mark I will stop the recording but anybody who wants to hang around a little bit longer for an informal chat is welcome to do so. So to get the ball rolling let me hand over to Shotta who's going to talk to us about addictive platforms. Alright so thanks Greg for the introduction. Thanks everyone for coming to my presentation. So today I'm going to talk about competition for consumers' attention. This is my joint work with Byon Choukin. We are surrounded by these amazing digital products and they have a monetary price of zero because they are supported by advertising revenue. So the more time we spend on the service the more ads they can display and are a higher revenue. Their incentive will be to provide a service on which we want to spend more time or in other words more attention. But there is recently a growing concern for all consumers, policy makers and even for the tech industries about this firm's incentive to capture users' attention. Roughly speaking the idea is that these firms may have an incentive to design various aspects of their services to increase users' attention in a way that may not necessarily benefit users. For example, a platform may adopt a certain content recommendation algorithm which just learns and display whichever content I'm most likely to click regardless of the underlying quality of the news like it's credibility. Or a platform, a social media platform may adopt a certain notification system which keeps telling teen users how great their classmates are doing every single minute. At least intuitively these features may increase the time that users spend on the platform but it's unclear whether it should be regarded as high quality and it benefits users. Now motivated by this recent discussion we are considered a model of competition for consumers' attention. A novelty is that a firm has a strategic variable with which they can degrade the service quality and make it more capable of capturing consumers' attention. So we allow a firm to sacrifice quality for consumer attention and examine the impact of competition. In particular I'm going to show you a condition under which competition harms consumers compared to monopoly. I'm going to also talk about potential policy remedies as well as the importance of the platform's revenue models in deriving our conclusion. Alright so let me jump into the model. There are K platforms. I use K for the number and the set of the platforms and there is a single consumer. Let me just say up front we are not going to see any uncertainty or any behavioral component although in the extension we consider a particular behavioral assumption. For most of the talk we consider a perfect information plus rational concern. Now in the stage one of this model each platform's small K chooses the strategic variable called addictiveness denoted by D over K which is at any non-negative scale. Then the consumer joins the platforms and allocates our attention. So suppose each platform has already determined this DK and let me focus on the detail of the consumers participation and attention allocation. In the second stage consumer chooses the set of platforms to join any set J and for each platform she has joined the consumer decides how much attention AK to allocate. We allow multi-homing so the consumer can potentially join any set of platforms. The consumers eventual payoff is the benefit of using the service minus what we call attention cost. So the consumers benefit of joining platforms in K is a sum of the utility coming from each platform she has joined. This UAKDK depends on how much time the consumer spends on the platform K and this DK chosen by the platform K. But the consumer also incurs a attention cost which is a function only of the total attention the consumer has spent across the services. And this is a weekly increasing weekly convex and differential. In addition, the consumer faces the attention constraint, which is there is some model parameter a bar such that consumer can spend at most a bar amount of total attention across the platforms. And this is going to be the key parameter of the model. We're going to show you that a lot of comparative studies with respect to a bar. So please keep this in mind a bar is the attention cap. Now, so this is the consumers decision and in equilibrium one step back, each platform sets this addictiveness DK to maximize the amount of attention going to the platform. So that means one possible specification of each platform case payoff is just equal to AK. So generally platform case payoff can depend on the entire attention allocation profile, as long as it is increasing in AK. But to solve the model clearly we do not allow platforms case profit to directly depend on DK. So choice of DK affects platform as a profit only indirectly through the consumers behavior, which is the main channel that we want to study. So before going to the assumption on you AD, either any question about timing or informational assumption sounds good. So let me show the assumption on you AD. This is the benefit that consumer obtains from using a given platform, which depends on how much attention she allocates on this addictiveness. As a function of attention, this service utility is increasing and concave. U00 is non-negative, namely compared to the outside option of zero, the consumers weekly better off by joining the platform with zero addictiveness. But point two says the level of the benefit of joining a platform is decreasing indeed, and it becomes negative for a sufficiently large deal. For conditional on joining, consumer will face a higher marginal utility of allocating attention when D is a high. So pick any platform and plot the attention that consumers allocating on the horizontal axis and the vertical axis is a service utility. As a platform increases the low to the high, then overall service utility function shifts downward, but gets everywhere steeper. So roughly exactly, consumer views the platform as a low quality, less willing to join when D is a high. But conditional on joining, what determines the consumers incentive to spend time is the marginal utility. So higher D gives the stronger incentive to the consumer to spend time. Now before, if this mathematical conditions are clear, before going to the more general discussion, I'd like to show you one application under which these conditions hold. And I hope this application will also tell you our model can fit the situation which is not exactly about what we imagine from the world addiction. Okay, so the example I'm going to show you is the one of data collection. So pick any platform and suppose that upon participation, the platform requests the amount D of consumers personal data for registration, which can be the location or demographic characteristics or the contact of friends. And platform can use that information to personalize content. However, the consumer anticipates some negative consequence from collection of personal information, so consumer have a preference over how much information the platform requests. In particular, if the consumer joins the platform that collects amount D of data, consumer incurs a privacy cost of L, so for simplicity linear positive L times D. But a platform can use data to improve the other aspects of the service. So without any data collection, consumer will face the baseline value of service V of A other than the privacy cost. But platform can use the collected information to increase the value from VA, increasing concave to one plus D, V of A. Now, given this simple functional form, if L is higher than the supremum of this bounded function V, then the level of the benefit of joining the platform is decreasing. But marginal utility of allocating attention is increasing in D. So what I mean is that exactly consumer views platform as low quality when it asks for more personal information. But once the consumer joins in this application, privacy costs become the sunk, so the consumer has a stronger incentive to spend more time on the platform that has more information. So in that case, D is not really about addictiveness, but simply how much information the platform asks for for registering user. Now, more generally, we want to use this D as any choice of a firm to sacrifice the service quality for consumers' attention. Now, our paper cannot give you the direct answer to the question of how the firm achieves such an objective. But such a choice is likely to appear in the very complex choice of the design of user interface or the recommendation algorithm or other platform design. We summarize this complicated choice as simply a shift of the level of the utilities and marginal utilities. This is somewhat in the spirit of competition in utilities framework. Now, this shift or divergence of U and marginal U will be different from the competition or other dimension like price or advertising load. For example, if a platform decides to increase advertising intensity, then so long as I view add as this utility, this change will likely to shift both U and marginal U down. Now, in the paper, in addition to the previous data collection application, we also have another application based on the rational addiction. This downward shift of U and upward shift of marginal utility may remind you of the rational addiction, then if that's the case, you are on the point. So we consider a super simple two-period model of rational addiction in which the consumer's platform consumption exhibits habit formation. So if I use platform service today, that will lower my tomorrow utility but increase my marginal utility of spending time just like in this Baker Murphy paper. In that case, D becomes the intensity of habit formation. So higher D means by today's service consumption affects my tomorrow utility and marginal utility a lot. This application also uses a certain kind of time inconsistent agent and we derive UAD as the example. Now, it's a little bit long application and I don't have time to go through this but I'm happy to talk more maybe after the talk. Okay, so here is a quick motivation and then let me go to the model. So remember platform to choose simply addictiveness to maximize attention and then consumer join the platforms and allocates attention. I'd like to begin with a simplest case of a monopoly. So monopoly chooses D to maximize consumer attention and a conditional on joining consumer chooses A to maximize this utility. And because A and D, the higher D increases marginal utility, so the consumer would choose higher A given the higher addictiveness. Of course, consumer joins only if she anticipates the non-negative payoff. So this consumer's participation incentive will bound the possibility or possibly optimal. So remember a bar is the attention cap of this consumer side. So to sum up platform maximizes attention given consumers incentive. Now monopoly may have multiple optimal choices of the addictiveness, but we focus on the equilibrium in which SBE in which the platform breaks tie in favor of the consumer. Or equivalently we focus on the Pareto and dominated SP. What I'm going to show you is to show the monopolist choice of addictiveness as a comparative statistics with respect to the exogenous attention cap. So attention cap is this upper bound of the total attention. Now, so here is the result. When a bar is relatively small, then even if platform sets zero addictiveness, attention constraint is so tight that consumers going to spend all of her attention. In that case, there is no point for the monopolist the degraded service quality for attention. So D is zero. When a bar is extremely high, so think of a bar equal to infinity. Then attention constraint doesn't exist. Then only attention cost exists. So monopolist wants to increase addictiveness all the way up to the point at which the consumer just gets surplus with zero, so but still joins the platform. In that case, consumer allocates a high amount of attention, but service quality is so low that consumer surplus is zero. When a bar is somewhere in the middle, then monopolist said positive, but not too high level of addictiveness under which the consumer will strictly prefer to join the platform. So overall as a function of an attention cap, the monopolist D, so this is the extent to which the platform sacrifice quality for attention is weekly increasing. Now, what's the welfare implication? So let me put this on the top right corner. As a bar increases, on the one hand, consumers attention constraint gets relaxed, which is good, but monopolist degrades service quality, which is bad for the consumers perspective. So what we can show is that consumers equilibrium payoff as a function of the attention cap is no monotone single peak. Now, but what I want you to remember for that talk is when a bar is relatively low, attention is relatively scarce. Then as we saw in the previous slide, monopolist is going to set zero addictiveness. So for whenever primary force in this range below a one, we get consumer optimal outcome, namely monopoly equilibrium maximizes the consumers payoff across all the strategy profile. So this is the basic observation of the monopoly. Let me see whether there is any question. Any questions I think. Oh, sure. Okay, so, so here we consider now competition. There are two or more platforms. Each platform maximizes attention given the participation constraints, namely, each platform incentive is qualitatively the same as a monopoly. We consider a model of a perfect information. So each platform wants to increase addictiveness so long as the consumer is willing to join. And all the consumers they are symmetric and do the same calculation. So here's what we have. So here we have a unique SBE with a little bit work we can show uniqueness. And they are all the platform choose the same positive addictiveness, which makes the consumer just in different between joining all and all but one platform. In equilibrium, consumer joins all platforms and allocates the same amount of attention to each of them. Now, so main point here is that for any parameter platform to choose positive addictiveness, they degrade service quality for attention. And this is in contrast to the monopoly, which sets zero addictiveness for a small A bar. And this is because competing platforms has business stealing incentive. When a bar is very small, then monopolist has no incentive to raise D because it doesn't expand consumers total attention. But if I have as a platform, I have a competitor, then by increasing addictiveness, I can capture a greater fraction of consumers available attention. So this captures the fraction or the capture the attention that consumer would have allocated to my rivals gives me an extra incentive to increase addictiveness. Now, of course, there is a competition force which is I cannot increase the too much because then consumer will just stick to my rivals. But on balance, there is still a non-trivial business stealing incentive across all parameters leading to a positive service degradation. And this result gives a hint that there is something, some downside, maybe some downside of competition as we move from monopoly. And as a starting point, I'd like to show you the comparison of one versus two platforms. Now everything else equal, the consumer trivially prefers duopoly because there are two services and they are differentiated. But in equilibrium, the result depends on the primary. So this is only a partial comparison for the subset of primary. When a bar is below some threshold, the consumer is strictly better off under a monopoly. When a bar is above another cutoff, the consumer is weakly better off under a duopoly. Meaning, so here is the ketika graph we get, even though this is a little bit more than what we are formally claiming. Now when a bar is relatively small, the main reason for the platform to capture consumers attention under competition is the business stealing incentive. In that case, competition reduces consumer service quality and reduces consumer welfare compared to monopoly. When a bar is relatively high, then monopolists bad incentive of increasing total attention to capture more of the consumers total attention becomes dominant. In that case, the monopoly is worse for the consumer compared to duopoly. Now, why do I have this even though duopoly has more services? Now, this is a very simple. Consumer surplus under duopoly is same as the consumer surplus of just joining one platform because of the indifference condition. So consumers pay off is greater under monopoly when never monopoly sets lower addictiveness than any of the duopoly platform. And that's the case when attention constraint is tight or attention is relatively scarce. Right, so any question I might have seen something in the chat box. Yep, so there's a question from Mariam CD who asks whether you thought about the case where it's costly for firms to change the level of addictiveness. Yes, so I have two answers. When each platform sets a very small but positive epsilon cost of choosing a positive addictiveness, so like a discrete investment in choosing positive addictiveness, then all the result continues to hold. Indeed, we get a unique equilibrium even under monopoly. And I think it's natural also to think increasing say convex addictiveness. In that case, we haven't obtained clear results. Yeah, just that monopolies are the platform taking into account consumers that part attention allocation incentive. So we have to tweak around the first order condition and get second or third order derivative. So we haven't obtained a clear equilibrium prediction. Yeah, thank you. So I just think that in your second case, then, especially with duopoly, you probably will have multiple equilibria with one within lower efforts with lower level of tea and the other with high so you might have multiple equilibria in that case. Yeah, or the costly investment. Yeah, especially if like it's costier to increase the level of tea. As, as another paper for all. Yeah, yeah, yeah, that's a good point. Right. Well was introduced cost. We see that like, I don't have an immediate intuition of whether a choice of these become a complement or substitute. Yeah, I can imagine the intuition where there could be multiple or asymmetric. Thank you. Thank you. So I've shown you this monopoly duopoly companies. Now more generally, one step ahead, we can ask, can monopoly continue to dominate more competitive markets. Or once we consider sufficiently high degree of competition, are we going to see vanishing addictiveness in equilibria. So that's the high degree of competition eliminates this problem. We could keep adding more and more platforms so consider more and more market entry and consider the bigger and bigger market. But we didn't take this approach. Instead, what I'm going to show you from now on is to consider a fixed market size. And then imagine consider the sequence of markets, which gets more and more competitive, namely, I'm going to see more and more platforms with a smaller and smaller insights. The purpose is to exclude the variety expansion effect of competition, a focus on the other effect of the competition, which is each firm has a smaller influence on the aggregate market. And here is the formalization. So we consider a sequence of markets, one, two, they have the same size, but as the index increases, they get growingly complete. In any given market, the model is exactly the same as a monopoly as before, but we just normalize markets across different index indices to capture the idea of constant market size. Now, market one is what we saw at the beginning, monopoly market with service utility UAD. For any positive integer K, market K has K platforms. Each platform offers not UAD, but one over K times U over KA times D. Now, this, the paper we show that this is indeed a unique way of normalizing the primitive service utility to capture the idea of constant market size. Now, one way to see this is that if the consumer is in market K, and she picked total attention A and divides it equally across the K platforms, then direct substitution shows the consumers gross total utility is U of capital A of D. And super importantly, this is independent of the K. This is the sense in which this is constant market size formulation. For example, maximum consumers are plus doesn't change even if we increase K. The consumer side of primitive like attention cost a constraint continue to be the same. For any given market, we can apply the previous result to solve equilibrium. Then let's see how the equilibrium changes across K. This is clear last bit of notation. A of D is the total attention the consumer is going to choose when she is in any market K and platform set same addictiveness D. For example, in market say 20, if the older platforms choose the same D, consumer allocates AD over 20 to each of the 20 platform. Now, beyond duopoly, the equilibrium addictiveness is weakly decreasing K. And it eventually converges to some positive level that uniquely solves this equation. So competition beyond the duopoly weakly improve the situation for the consumer, but even in the limit, we are going to the D infinity, some positive limit addictiveness. So imagine captures the consumers participation incentive in limit economy. So imagine consumer faces a large number of infinitesimal firms. Now, if the consumer decides not to join a platform one platform, consumer is going to lose the service utility over you. But there is a game. Let's say consumer decides not to join one platform, and she saves 10 minutes. We allocate the saved 10 minutes to other services that consumer has already joined and are 10 minutes times marginal utility from other platforms. Now, in equilibrium, the consumer is indifferent between joining and not joining each platform conditional on joining all other platforms. So these two terms must coincide. Namely, there is no net gain or loss of walking away from each platform. You can also see that this equation basically says average utility is equal to the marginal utility. And for this to be true for the concave function, there has to be some downward shift to for this equality to satisfy. Okay, so in addition to this qualitative insight, what's good about this result is that this equation is very trackable. In any finite k, there are lots of the problem of which constraint binds. But for the limit, we can directly solve this equation in some special cases. In the paper, we consider several assumption on the functional form and solve the analytically solve the equilibrium for the limit outcome. But here I'm going to show the welfare implication on the consumer space. So what I'm going to do is to derive the infinity, calculate consumer surplus, call this the consumer surplus in the limit economy, and compare it with monopoly. Now, first, let's consider a quadratic attention cost CA squared over two with exponential utility. So this A minus D captures all the assumption that I introduced at the beginning. Now, consumer surplus is a greater under monopoly than the limit economy, if and only if this total amount of attention available to the consumer is above some known threshold. So this is again constant market size formation. And this is the typical graph we get. Namely, as a function of attention capacity, both consumer surpluses and their monopoly and limit economy are non-mono, a single peak. But there is a unique cutoff at which monopoly curve crosses the limit economy consumer surplus from above only once. So if and only if attention is relatively scarce, then downside of the competition of this business stealing becomes a dominant force, in which case as we move from monopoly to the limit economy, consumer surplus gets lower. Otherwise, monopoly is better. Indeed, eventually limit economy gives a positive surplus, but monopoly gives consumer zero surplus. So this is one instance, just to show the full comparison across all possible A bar. We also consider the linear attention cost, because we have a slightly different welfare implication. So large C A is small C times A, and UAD is V of A minus T for some increasing and concave V with some condition on the derivative at zero to get non-trivial result. In that case, we get the ambiguous welfare comparison. There is a unique cutoff A star such that when attention capacity is below the threshold, consumer is strictly better off under monopoly than the limit economy. And remember, beyond the duopoly, more competition leads to lower addictiveness and higher service quality. So point one implies whenever A bar is below A star, consumer surplus is a higher under monopoly than any market cake. Otherwise, if A bar is above A star, consumer surplus is zero in all markets. So this is a typical graph. So the main difference from the previous one is that as we move from a monopoly to a more competitive market, consumer surplus curve shifts downward uniformly. So the competition never strictly benefits the consumer across all the planet. Now it's kind of intuitive that why linear attention cost makes competition less effective. For example, if attention cost is linear, namely, even if I use one platform, I continue to face the same marginal cost C of using other platforms. Then when A bar is extremely high, then consumers participation and attention allocation decision become the separable across the platforms, in which case each platform acts like a monopolist and consumer gets zero surplus, but allocates high attention. But indeed, this kind of comparison uniformly hold for all A bar. All right, so this is the basic result on the impact of competition. We saw that relative to monopoly competition for scarce attention can harm consumers. Because when firms compete for a smaller pie, their main incentive to increase addictiveness is to steal attention from their rivals. Now, so what can we do in terms of the policy? So here we fixed market structure and asked what kind of policy can improve consumer surplus, assuming we cannot directly control D. We're going to show you two somewhat unconventional policies. One is to restrict consumers' platform usage, sometimes called digital curfew. So this is one of the graphs I showed you before. We can see that from a high A bar, as we reduce A bar to a smaller number, then this increases consumer surplus. And this policy is more effective for a monopoly than in the more competitive market. What we show in the paper is that the condition under which exogenously reducing attention cap upfront can improve consumers' equilibrium welfare. And that's the sense in which this reducing A bar tends to be more effective in a less competitive market. Now, the consumer in our model is rational, so there is no self-control problem. But reducing A bar still discourages firms from increasing D. So lower A bar can go to the lower D, higher service quality and higher consumer welfare. The other policy implication would be that if we see the result literally, it means that under a certain condition, namely where A bar is small, merger to a monopoly can improve consumer welfare. Maybe tech CEO love this. This may sound very extreme, but main takeaway is that a merger could mitigate firms' business-stating incentive, which in turn can mitigate their incentive to degrade service quality for capturing consumer attention, which may eventually do the better consumer surplus. In the paper, we consider a bit more general class of mergers and discuss what kind of merger can benefit or harm the consumer. Now, finally, we discuss the role of the platform's business model. For the moment, we consider a very simple comparison. Previously, we started with a model in which platform earned revenue only from attention. Here, we consider a model in which platform can set the participation fee, monetary price that consumer has to pay, upon joining platform K. And also, we modified a platform's pay-off function so that it no longer earns revenue from consumers' attention. So this is not the model in which we add monetary price as an additional revenue source to our original model because platform don't get any revenue from attention. Now, in equilibrium, platform always prefer to decrease addictiveness over higher service quality and charge higher monetary price. So we're going to see zero addictiveness with a positive monetary price. Previously, Monopoly now minimizes the consumer surplus because Monopoly sets price equal to the consumer's gain of joining the service, leaving the surplus of zero to the consumer. Because again, we are in the perfect information model. But now, one question which is non-trivial is how does the consumer welfare change as we move from attention competition model to this pure price competition model? On the one hand, consumers are going to see better service quality, but on the other hand, they have to pay. Here is a condition under which consumers better off under attention competition. And a normalized market K consumes strictly better off under attention competition if the attention cost is strictly complex, say quadratic, and K is sufficiently large, so market is sufficiently competitive. Or market is Monopoly and attention is relatively scarce. In that case, we get strict welfare comparison. Now, so let me show the intuition of point one. When market is competitive, consumers better off under attention competition. Idea is that whichever attention competition or price competition we consider, consumers net utility from any given platform is determined by her outside option. For example, consumer pay off from a platform under price competition, this is a service utility minus price, is determined by the benefit of walking away and reallocating attention to other platforms she has already joined. Now, under attention competition, so we have the similar expression, but attention competition has a higher addictiveness, which leads to a higher marginal utility, which implies higher incremental gain of walking away from a platform and continuing to use other services. So this better outside option forces the platforms to offer a better net utility, either net of the service degradation or net of the monetary price. So as a result, consumer can be better off under attention competition in the competitive market. But now this particular result, price versus attention depends on the consumer being rational. So it misses a force under which we may think, well, there may still a good point about price competition. In the paper, we consider a naive consumer in a sense that the consumer wrongly underestimate the true addictiveness D as S of D for some exogenous parameter S between zero and one. This underestimation generally increases the equilibrium addictiveness, but qualitatively we get pretty much the same result. Except if S is small, namely consumer is naive, consumer surplus tends to be higher under attention price competition than attention competition. Okay, so I think it's a good time to recap. So the literature, I don't think I have time to go through this, but if you have any existing economic intuition that we can relate our result to, we'd love to hear your thoughts. Now, I think there have been an idea that attention economy could distort the kind of services provided to the market. We try to formulate this idea and speak to it by introducing a new strategic variable, capturing the firm's incentive to degrade the quality and make it more effective in capturing consumers attention. Competition could mitigate or exacerbate this problem, but probably the novel part is competition for scarce attention, tight attention constraint can lead to the more service degradation and lower consumer welfare. Among other things, restricting consumers' platform usage could mitigate a problem, even though the consumers rush. This is all I have. Thank you for your attention. I'm looking forward to the Thomas's discussion. Thank you very much, Shota. So yes, now we will have a brief discussion from Thomas Avaleti. Thank you. Thank you very much for the organizers for having me discuss this great paper by Shota. So it is about the attention economy. It's a very important topic. In a sense, attention is the ultimate scarce resource. It's our time. We've got 24 hours a day, and if you think about recent transactions, for instance, the recent merger between Google and Fitbit, you're talking about a wearable operation system which is attached to our body 24 hours a day, which we'll try, according to some, to understand our mood, our emotions, and some argue that they will even be able to manipulate that mood and those emotions. So this is not a dystopic future. This is happening right now. If you think about the business model of YouTube or Facebook, it's about engagement, as the companies call it. It's about showing us stuff that keep us hooked as long as possible, as long as the right signal is extracted to show us some ads. And so, and typically this content is related to very divisive politics or sex or violence. And so you may not even like it, but it's really difficult to get away from it. And the big tech companies are engaging continuously in AB experimental testing to uncover some behavioral biases. They can even target particular consumers at a particular point in time when they are more likely to give good reviews about products that is steering. So people are thinking, is there or is there not discrimination? But we think about price discrimination, but there is different kinds of discrimination. So it can be steering, showing you things that other cannot see, showing you things that when you are in a certain emotional state, there is even a branch in marketing, which is called vulnerable marketing. So which is about, you know, it's marketing devoted to people which are either vulnerable as a group or in a vulnerable state. So it's important that economists are aware that this is happening is not just a theoretical possibility. If you're interested in many of these examples, there is a very recent informative report by the UK CMA, the Competition and Market Authority, called Algorithms. How can they, how they can reduce competition and harm consumers? So again, it's an excellent document because it opens up a lot of research questions for us economists that have not been answered yet. As I said, companies themselves are interested in addiction. They would never call it addiction, of course, a college engagement. It's a fine line between addiction and engagement, but it's the first metric, it's the first KPI that companies have is engagement. So how much time can you keep people online? And just, and these numbers are very relevant. If you think of Facebook, on average, an American consumer spends about an hour and a half on Facebook, over an hour and something on Instagram, which is owned by the same company and a bit less on WhatsApp. We're talking about the average, okay, and then there is lots of originating about three hours a day on a certain platform ecosystem. That's a lot of. So this is, it's very important. I've been doing recent work with Andre Vega recently. We team up with a software company called Lumen, and this is eye tracking software which is trying to understand whether or not you dwell on an ad according to the content that is shown next to the ad. So, and this is a typical technology, which is used a lot by the marketeers. So it's really relevant in practice. The paper itself is, in a sense, is simple, and it generates a lot of results. So this is what a good model is about. So not doing something complicated, it's extremely rich, the set of results that you can get. And it also has the right ingredients that we are thinking about in economics. The business model matters. Is it about advertising funded platforms versus paid for business models? What's missing there is what is leading a particular company to adopt one business model. We are just positing exogenous, if they are all had funded or all paid for, and we would like to understand what is leading the choice for business model. Some more specific remarks about the paper. It's a great title. I love the title. In terms of the literature, you, of course, you do, to the first generation of seminal works on two-sided markets, but I do remember that the work of Simon Anderson, Stephen Colt, Mark Armstrong, I think they were also using those models to think about public sector broadcasting. So advertising funded television, the type of news that people can actually watch, the reasons for imposing particular restrictions on PSP, public sector broadcasting that could have made sense in the olden days where people had a single channel, I think, of the discussion here in the UK about the license fee to the BBC. Some regulation made sense, whether we had very few channels available as opposed to a multi-platform world. So I was wondering whether your model can also let us think about those important questions which are still out there. A question, you have to give some answer to, obviously, it's a paper which has advertising, and there is no discussion about the welfare implications of advertising, so you have to say something. So it's just as exogenous are, we don't know what happens to the advertiser, we don't know what happens to the people buying advertised products, so you have to think a little bit about what's in the welfare function, because currently it's just a positive R for any unit of attention, and there may be a bit more. So more specific details, and then I'm done. The attention constraint matters a lot in your results, and of course we do have 24 hours a day, so I do see the practical implication. But I was thinking, why is that? Usually some similar results you could get by making the attention cost function more convex. So I was wondering, or do you really need this boundary solution? That wasn't entirely clear to me. It would be good. You have a representative agent, you have one consumer, which is representative of the economy. It would be good somehow to think about some dimension of heterogeneity, especially when it comes to monopoly, we do think that monopoly typically reduces demand. I know this is difficult in a zero price market, but to think about the typical effect of monopoly is generating some meaningful elastic demand could be useful. The way you deal with competition wasn't too obvious to me. So you're talking about this limiting sequence of markets and where attention is spread equally, that's a very ingenious way. You refer to some literature from the 80s that I have to admit I'm not familiar with from financial markets, apologies for that. But it wasn't the obvious way, the most obvious ways to think of competition. In particular, since we're talking about attention, if a consumer allocates attention across a certain number of platforms, the number of platforms is irrelevant. The level of utility is the same. One of my recent work with Andrea Pratt on attentional egopolies, instead, it's a very different mechanism, of course, it's a different model. But there, if you can spread your attention across different platforms, basically attention is not a bottleneck, which means advertising is going to be cheaper, which in our model means that new products can be seen and can be known and consumers are better off. Instead, when attention is spread over a very concentrated, very limited number of platforms, the incumbent product firms can just hoard, can just preempt to enter from happening. So in our model, for instance, attention, sorry, the number of platforms directly benefits consumers, which you don't have, even if you don't have a variety, etc. So in a sense, you have a model which is geared against the benefits of competition we typically think about. Maybe that's what you want to have, but having that monopoly can be best is also because you're ignoring some more typical channels. And finally, I didn't get probably due to my very quick reading. When there is competition, you seem to always have multi-homing. And it is always multi-homing. It's a bit counter-intuitive because we know that multi-homing is feasible in theory, but in practice it doesn't happen very often. So if you could also put some more nuances into that question, I think it would be useful. But it's a great paper, which I enjoyed very much. I was very happy to have the opportunity to discuss it. Thank you so much. Thank you, Thomas. Shota, I didn't know if you want to reply. Otherwise, we will have some questions in the chat. Sure. Yeah, yeah. Thank you so much for the discussion. I think we have a lot to think. Yeah, I think for modeling the advertising market side and be richer welfare implication beyond consumer welfare. Yeah, I think we are hopeful in the sense that platforms pay off function can be quite general, generally depend on the attention profile. I think we haven't tried, but I think it would be natural to think that, yeah, detailed model of advertising or the matching between the background producer and the consumer. Right. And also one technical point of whether why don't we replace attention constraint with a very steep cost function. So that's a little bit a weak point of our model that we have to have this varying attention constraint. Our hope have been that even though we drop off attention constraint replace it with say steep attention cost. I think we introduced a costly choice of addictiveness that I got question we still get that different magnitude incentive to introduce increase D and continue to get the same similar qualitatively the similar result, but that's more of a content. Yeah, yeah, I think I also got a many other valuable feedback. So yeah, let me thank you. So we have a couple of questions in the chat. I don't know if you guys want to unmute yourselves and ask them in turn. As long as I can read the question out. So it says young Kim asked whether you thought about the effect that network effects have in the model of whether they changed the results at all. I maybe depends on how we model the network effect but I don't have immediate intuition that network effect kills our results but it should be possible to extend to that continuum of as a certain point identical consumers and each consumers pay off also depends on the average attention that other consumers are allocating