 Thank you very much for having me here. It's a pleasure to be presenting in this platform online seminar series. This is joint work with Alex White and Shanwall. All right, good. So there's a big public debate about Big Tech and every other person that you may encounter will tell you that how they are worried about Big Tech being so dominant and getting all our information and will be just going to be ruling all our lives. Here is a pattern of debate about the Big Tech, the concerns about Big Tech. Some people will say, well, we need to break up these Big Tech companies, say Facebook. And then somebody else will say, well, do we really want two Facebooks instead of one? How about instead we regulate them? And then people will be asking questions like, do we really think regulation will improve things? Will that lead to some unintended consequences? And our field economics is actually well suited to address questions of this sort. In particular, economics of platforms can address questions of the sort. What level of market concentration is optimal? Can competition policy interventions help? And what are the likely effects of regulation? And these are sort of the broader questions. In this project, what we want to do is we want to ask whether competition or a specific type of regulation that we will call interoperability alleviate dominance. And in doing so, we are going to offer a modeling approach that will be useful to answer these questions in the platform form context, but also that may be useful to answer other related questions in the platform context. So we're going to offer a tractable model. And since we're going to be looking at dominance issues, we need a model that can handle asymmetries. And what I'll do in this talk is I'll present the net fee model. I'll show our propositions regarding how competition may increase dominance and how interoperability regulation can decrease dominance. Good. So we're going to look at a model where there are J platforms and an outside option. Each user will make a choice of joining a platform or just choosing the outside option. For the sake of this talk, I'm going to present you the model with only one side in each platform. So there won't be males and females. There won't be buyers and sellers. Okay. Everyone is on one side of the platform. In the paper, we actually present the model with multiple size and we have some of our results with multiple size. For the sake of this talk, I'll focus on a single-sided platform. Users. I'll have a bunch of users and each user will be identified with a vector of membership values theta. What this means is that this vector will tell me the payoff I will get. I will enjoy from joining a platform. Okay. Theta J will denote that payoff from joining platform J. That will also be an outside option. Theta naught will denote the membership, the value I will enjoy from not joining to any platform. Joining a platform will give user theta utility that is equal to the membership value plus a component that measures the externality benefits that come from possible instructions in the platform minus all the payments made to the platform. So we're going to the externality component here will be a linear function of the number of users in the platform. There will be a platform specific interaction value parameter gamma J. And the more is the number of people that are using the platform, the higher the externality benefits will be if gamma is posted. Very good. And now here is the sort of the net fee structure. The competition conduct of our model. And this is what is highlighted in the title. So this is going to be an important concept for us. The platforms in our model will be competing by what we call net fees. And net fee is what a user pays to the platform in addition to other payments that the user makes that are related to externality payments. In particular, the total price that a user pays to the platform will be the sum of the net fees, plus all of the externality benefits. So what this implies is that if a user is contemplating on joining a platform, then her payoff from joining the platform, her net payoff from joining the platform will be her membership value minus the net fee. Now, let me a little bit motivate what this means. So in general, pricing strategies of platforms can take a very complicated form. They can be quite arbitrary. There are platforms where we pay fees for just signing up to the platform. Think about mesh.com. There are platforms where we pay fees for signing up to the platform, and then we may be paying fees based on every interaction that we have on the platform. Some write apps may be examples of this. Furthermore, these payments that we make the users make to the platform can be quite dynamic and complicated. They may depend on various factors like the frequency of interactions at that very moment in the platform. So obviously this pricing strategies are going to take a very complicated form. Well, we make some abstractions to simplify these prices, to both simplify these pricing strategies and also to focus on certain aspects of these pricing strategies. In our model, our firms are using this signing up membership fee as the only strategic component or the only strategic variable in their strategies. And we are assuming that all of the externality benefits that are created in the platform will be extracted by the platform. I see there are some chess, so what do I do here, Greg? Yes, so one question is whether you could give an example or to how people should think about the membership value, what sort of platform should we have in mind, I guess. Right, so these are the values that you enjoy from just being on the platform itself. Okay, sometimes I go to a platform and Right, so you can think of these as, you know, I For example, join to my phone company. So let me think about it. So what is it? Let me try to think about a good example. Hmm, very good. So imagine the choice between the video consoles, okay, game consoles. You can think of these membership values as the comparative value of joining to one platform versus the other one. And also I can do a lot of things that are like communicating with my friends on the game console. Okay. So that could be an example of a membership value. Thanks. And then we have two other quick questions if we could. So Heskey asks, is this a static model and do she and asks whether the net fee is equivalent to a quality adjusted price. So, right, so the first answer is that this is a static model. It's not a dynamic model. Okay, but right. And what was the second question again, whether we can think of the net fee as a quality adjusted price quality adjusted price. What do you mean by quality adjusted price. I guess what is meant is if we take the price and subtract from it the quality then what is left is the net fee. It seems to be what you have on the slide that where I think of quality as being a network benefits that are specific to the platform. Yeah, I don't really see it as a quality adjusted price in that way. I just see it as a membership fee. So, some fee that sort of the net pay off that will be left to the user. Sounds good. Sure. Thank you. So here is the timing of the model. Platform simultaneously post net fees. And then demand will be realized based on the user's choices. And then the profits will be realized. So, so here is what will be what will be sort of important and firms firms profit maximizing problem. First, I'm going to talk about the demand. Okay, so when a user chooses which platform to join. The users pay off from joining platform j is just going to be her membership value minus the net fee. In particular the users pay off from joining the platform will be independent of other users platform choices. So this makes the demand calculation in our model. This is a straightforward demand system calculation. Okay, this is going to be a standard and this great choice problem. So given a net fee vector, we can calculate the demand vector. Now the second thing is that now let's write down the profits earned by platform j. The platform profits will be the demand the second term multiplied by the marginal profit. The marginal profit will have the net fees. The externality payments extracted from the user minus the marginal cost. So what I want to highlight here is that the externalities will impact the firm's profit via affecting their marginal profit. So the marginal profit will include terms related to the demand in the firms demand for firm. Now when we do the do the profit maximization from j is a pretty straightforward exercise algebraically we arrive at the following formula. What this says is the following so that the optimal net view will be composed of three components. The first one is the marginal cost. The second one is the standard differentiated by Trump market power. And the third term is what we will call externality discount. So this is algebraically very straightforward, but let me sort of explain to you the idea behind this. Let's do the following thought experiment where the platform is contemplating on increasing is net fee. Now the first, sorry, increasing, sorry decreasing is net fee in order to attract an additional user. So let's see what are the costs of doing this exercise. Well first there will be an increase in the marginal cost. Okay, that there will be an additional marginal cost due to this user. The second term will capture the fact that the platform will need to decrease its net fee in order to attract this additional user. Now the third term is going to be the externality benefits because we have this new user. And as you can see there's a two in front of it. Where is this two coming from. Now, if I am decreasing my net fee in order to attract Alex. Now first Alex will also enjoy a lot of externality benefits here and I will be extracting them. So that's one. Moreover, all of my existing users will have an increase in their externality payments because there's now an additional user in the platform. What I want to highlight here is that the, the externality discount is increasing in the market demand. And more so with higher externality interaction value come on. And we're going to look at pure strategy Nash equilibrium where it's going to be a net fee profile where each firm will maximize their profits, even others net fees. Like I see. Yes, two more questions. I guess the first question could be put as do you allow gamma to be negative so it can never be negative network effects. It can be. It is allowed in general. And you wish asked. Sorry, but I will focus on gamma positive in my policy analysis. You wish asked whether you have a result or assumption that guarantees uniqueness of demand, given that we have network effects here. Excuse me. So do we know that the demand is unique. You know, sometimes in models with network effect you have equilibrium where nobody joins. Right. In our model demand is well defined and unique. Because of the net fee contact that's the advantage of the net fee contact. So a user knows the pay of that the user will get from joining any platform and then the user just goes to the pay of maximizing platform. Okay. Thank you. Very good. Now, so this is the model. Now let me go to some analysis. Okay, our analysis. The first one will be about the relationship between competition and dominance. The second one will be about the relationship between interoperability at specific type of regulation and dominance. Now I want to briefly argue why we focus on dominance. Well, the first one is that people talk about dominance. This is something that people worry about or wonder about. And we want to be able to have a model that says something about dominance. The second one is that there may be some unmodeled implications of dominance that people are worried about. We are writing down these static models and we may want to worry that well, dominance may have some long term implications on our lives. And, you know, it's not unheard that sometimes people make claims or sentences of the following form. Because the platform is dominant in one market, it will also dominate other markets. When AI is advanced, these companies will start ruling our lives. Okay, so we're going to take dominance as a separate issue, as an issue on its own, and we're going to look at the relationship between competition and dominance and this regulation and dominance. By dominance, I mean a market having a large market, a firm having a large market share. Good. For the analysis, I'm going to assume the demand is legit. So we are allowing an outside option and Z will capture the attractiveness of the outside option here. Platforms are going to be identical for this exercise that I'm doing. I promise you that this model can handle asymmetries and we'll see where the asymmetries will come in. And we're going to normalize the marginal cost to be zero. And here is our first proposition. Let me explain it to you with the graph first. So here what we are doing is we're looking at all equilibria of the tri-o poly model and all of the equilibria of the duopoly model. And we are going to compare the largest possible market share of any platform in any equilibrium in both models. And we want to see how they compare with each other. First, let me say that if you look at interaction values, gamma, that are less than 2.61, then in both models, we have a unique equilibrium. These are different equilibria, of course. They are going to be symmetric equilibria. So in the tri-o poly model, in the unique equilibrium, each firm will have one third of the market share. In the duopoly model, each firm will have half of the market share. Now, if we keep increasing gamma, say to 2.7, then the duopoly model will continue to have a unique equilibrium. Each firm will get half of the market share. Okay, just to make sure you were able to... Is there a question or shall I continue? I think Gary just had his microphone unmuted. Okay. Okay, so the duopoly model still has a unique equilibrium. On the other side, the tri-o poly model will start admitting a new type of equilibrium where there's a large firm and there are two smaller firms. And the large firms market share is larger than one third. As I keep increasing gamma, now the larger firms market share keeps rising. At some point around three, the duopoly model starts admitting a new asymmetric equilibrium where there's a large market, a large firm, and there's a smaller firm. And this proposition will say that the largest possible market share of any firm in the tri-o poly model will be larger than that in the duopoly model. Now what this implies is the following. Suppose initially the interaction value gamma is 3.25, let's say. And we have a duopoly model and there is a large firm that captures two-thirds of the market and a small firm that captures one-third of the market. And people are worried about it, about the dominance in this market. And they argue that let's bring in a new firm. Let's increase competition. What this result says is that when we go to a tri-o poly model by bringing in a new firm, it could be the case that actually dominance gets stronger. So I'd like to give you some intuition about what is going on here. And I'll give you the intuition by giving you one more proposition first, okay? And in this proposition, what I'm going to do is that I'm going to look at a model with an outside option and a monopolis and an outside option and two symmetric firms. And I will compare them. Essentially, why is this a sort of a nice benchmark to give to study and give an intuition about the other result is that you can think of the outside option as a firm, as a platform, who cannot do strategic choices, who cannot choose a net fee, okay? So it's not going to react to other changes that other platforms will do, okay? And the result here is that there's a value of, there's an interval of outside option parameters such that when you go from monopolis to duopoly, the total demand in the market will go down. So outside option will start attracting more users, okay? And this is a little bit perhaps counterintuitive in non-platform markets where we think of going to duopoly will increase the market size. So now let me convey the intuition in this symmetric market, in the symmetric model, okay? So recall the pricing formula, okay? So in a nutshell, the arguments will be of the following form. Well, when I bring in a new additional firm to the market, it's going to first have an initial shock to the system, initial impact of lowering the market, lowering the demands for each of the existing firms, okay? Well, lowering the demand will imply a lower externality discount. Remember that the last term externality discount is increasing in the market share in the demand. But then this means that there will be an upward pressure on the net fees and the equilibrium net fees will be larger and the total demand will be lower, okay? Now, of course, this is a very simplifying intuition. There are two caveats here. The first caveat is the following. That's not on the slide. If you look at the second term, the market power term, it is also proportional to the demand for Platform J. So all these arguments that I've been saying about the externality discount going down will also make the market power to go down. But it's also linear in the market demand. That's why I need a large gamma so that an increase in the demand or a decrease in the demand implies a lower and upward pressure on the net fees, okay? So large gum is needed for this reason that the externality discount is the dominant term. There's a second caveat, which is that when I bring in a new firm, it may very well be the case that there is now an increase in the match qualities. So the outside option becomes less attractive. So the total demand in the market may also go up. That's why we need to restrict attention to an interval of outside options, okay? It's not a global argument. I think it conveys the intuition. All right, good. Now, let me tell you how to think about the issue of bringing in a new firm, a new platform to the market, and how we arrive at a sort of a new equilibrium. Because initially we have the interaction value parameter in the range where the duopoly model has a unique equilibrium. Now, I'm bringing in a new platform, and I want to invite you to a thought experiment where we're going to start an iterative process of sort of best supplies of firms in a hand-wavy way, not in a formal iterative process, but in a hand-wavy way, think about this iterative process where initially the existing, the additional firm eats the user base of one of the existing firms, okay? The new firm eats the user base of one of the existing firms. So the initial market share configuration, as one firm gets half of the market share, and the other two firms are splitting the market share, the remaining market share. Now, the smaller firms will have lower externality discounts. So their net fees will tend to go up. If their net fees are coming to go up, their market shares will go down. This market share will go somewhere. It will go to the dominant firm. The dominant firm will get an even higher market share. Higher market share will imply a higher externality discount, so lower net fee, and so an increase in the market share. And so we have a process that is going to convert somewhere. And that somewhere is an asymmetric equilibrium with a larger market share for the dominant firm. Greg, I see, before I go to interoperability, I see some action on the chat. Yes, there's some help. I don't need them. I just read over there. The many people are discussing sort of big picture issues. So what I suggest is we wait until the end so that you can make some progress with the presentation. And then we can talk about interpretations of model if that's okay. Sounds good. Sounds good. Thank you. Okay. So what we have seen right now is that, well, adding competition may backfire if you were worried that, oh, we are in a duopoly where we have dominance issues, and we are going to bring in someone, some new firm, and then it may backfire. Okay, it may actually make dominance stronger. But some people argue that perhaps regulation is a better alternative, and one popular idea is interoperability. So we're going to use our model to do an analysis of interoperability issue. Interoperability refers to the issue where, you know, technically we're going to allow users across different platforms to be able to interact with each other and enjoy these external benefits. So can I just slip in one substantive question from Heskey who asked whether this sort of dominance is definitely bad news for consumers, or might they benefit? Very good. Good. I think that's a very good question. It is not. You can imagine dominance being driven by lower net fees. And so consumers may be better off. Although the welfare is not always being better for the consumers. Because the other firms, the smaller firms, net fees are going up. In general, one can actually, while here, let me talk a little bit about welfare here. We have thought about the welfare. One thing that comes up in our model is that we know the equilibrium. Okay, and we can calculate the welfare. One thing that prevents us from computing the welfare here computationally. It's just we cannot have a close form expression for the welfare. And we don't get very crisp results on whether welfare goes up or down. What is in the way, essentially, what the main difficulty is that, as I mentioned earlier, when we bring in a new firm. We can also increase the match values between the buyers and the firms and that makes the calculation sort of a little bit messy or having a crisp result. Not easy to get. But I want to emphasize that one can calculate the welfare. Okay, but we still take the we are now kind of taking dominance as an issue on its own, just because it is people are talking about. So let me introduce you to our approach to interoperability. So we're going to introduce a new parameter lambda. This is a number between zero and one is going to denote the degree of interoperability across the platforms. Okay, how much I can enjoy the benefits that would accrue in terms of from interacting with others in other platforms. And a user data J when contemplating on platform J will enjoy the following utility. She's going to get her membership value. She's going to get her externality benefits from interacting with users on platform J. No term here. This term is going to be the externality benefits that one could generate on platform K and the whole the total amount of externalities one could enjoy on all other platforms, but they are going to be discounted by this interoperability parameter lambda. Minus the total payments made to platform J. So we're going to extend the notion of net fee to this environment by assuming a particular competition conduct. Okay, we are the net fee here will be again any payment that is made to the platform in addition to all of the externality related payments. Okay, it's going to be so we're going to also the firm will also extract all the benefits that are coming from interactions with the other users of other platforms. This is an exercise of demand and nonprofits, given this given this given the models assumptions. Again, calculating the first order conditions. This is a forward algebraic exercise. Compared to my previous pricing formula. What I'm going to have is that the coefficient in front of the externality discount will be augmented by a new component new term that is lambda time side jet. So here, when I have interoperability equals to zero, the pricing formula is unchanged. When I have interoperability now I have a further externality discount. And this side J will be composed of two components. The first one is a function of the market share platform J. And the second term will be the diversion ratio. If I have a large platform who is dominant who has a large market share that side J will tend to be negative because the first component is going to be smaller if the market, the demand for platform J is large. And that side J will tend to be negative. For small firms, x i j will tend to be positive. Now the implication will be the following. If I have a large firm. And if I increase the interoperability lambda. Then this is going to lead to a smaller externality discount. Putting an upward pressure on the net fees. And the other side, if I have a small firm, increasing lambda will lead to a bigger externality discount. Well, that bigger externality discount means that a downward pressure on the net fees. Okay, now we are in a good position to do some of our exercises here. Suppose we have a duopoly, okay, and an equilibrium of the duopoly with say lambda equals to zero. That's magic equilibrium where there's a large firm, there's a smaller firm. And people are arguing that let's do some regulation and increase, add some interoperability. Okay, let's increase lambda. What is going to be the impact of increasing lambda? Well, for the large firm, increasing lambda will lead to an increase in the net fee. An increase in the net fee will imply a decrease in the market share or the demand. For the smaller firm, an increase in lambda will lead to an externality discount. So it's going to lower the net fee of the smaller firm, and hence will increase the smaller firms market demand. So it's going to equilibrate the market shares of the two firms. On the other side, suppose I've got, I'm looking at a symmetric equilibrium of a model. Then the firms are sharing the total market demand, and the market shares will tend to be small, and psi will tend to be large. Okay, and if I increase lambda, now net fees will tend to go down. And if I keep looking at the symmetric equilibrium, the market, if I look at the symmetric equilibrium, now suddenly I'm going to have lower net fees in the market. Okay, and an increased demand for the technology of the market itself, compared to the outside option. So we formalize these findings in two propositions. The first one looks at the symmetric environment. If you consider, if you compare two levels of interoperability, if you increase the interoperability, then in the symmetric equilibrium, the net fees will go down. This is just a formalization of this idea. The second one is saying that the dominance will, the dominant firms, market share will go down if interoperability increases. I think I've got one minute. Am I right, Greg? Yeah, one or two minutes. Okay, so let me then start to wrap up. Okay, so we have some additional results in the paper. We do a merger analysis where we allow for asymmetric firms and post savings in the merger. And we show that mergers actually can decrease dominance and more easily so for larger gamma. As I mentioned earlier, we do analysis, we present the model with multiple size, do some analysis with a multi-sided market. We have a general existence of equilibrium result in the paper. You know, there's a big literature on platforms that of course we are building on. The one paper that I want to mention here is Armstrong. And he, you know, he came up with the very influential hoteling model of competition. And a recent contribution in this line is by Tan and Joe. They identify a very interesting effect in these in platform markets where if you increase competition, actually the total prices may also increase. So they call this a perverse pattern. Compared to Tan, so Tan and Joe focuses attention on symmetric equilibria. So if you want to think about the market demand, what happens to the total demand in the market or to the market shares as you increase the number of firms. This approach is not going to be answering things related to dominance or the market shares. So let me conclude. So this in this talk I presented a model of platform computation in what we call net fees. And the advantages of this model include tractability and flexibility. In particular, now we can handle asymmetries relatively in a tractable way. It can accommodate demand forms that includes an outside option. We have some analysis for policy, increasing competition may increase dominance and increasing interoperability may alleviate dominance. And that's all I have to say. Thank you very much. So let's go straight over to Bruno to hear the discussion. Can I mute? Hi, can you hear me? Okay. Yes, we can hear you. Okay. So hello everybody. So thank you for the organizers for proposing me to discuss this paper. It's a real pleasure to read again a paper by Alex. It's been some time. So let me start with what is interesting, what I find interesting in the paper. Which essentially what is really attractive in this approach is that it does provide a very tractable model. And to my knowledge, it's the only one that really allows to deal with asymmetries in a simple way. Of course, we can always write the standard extension of the Armstrong model with this feature model with asymmetric platform, but we have no result at the end. So here they get results and they get some nice results. In particular, they get endogenous asymmetric equilibria with symmetric firms, which is a nice property. And given that this is a paper that can talk about dominance, you can talk about antitrust, you can provide insight. And that to my view, that the main strength of the paper and I would push to go more into this direction. I appreciate that this is done also in a very rigorous way with existence and uniqueness conditions. But I think really the value is to move in this direction. In this direction, I was missing and that was mentioned welfare analysis. I understand from the talk that this is not so easy to do, but maybe there are other demand functions that could provide easier welfare analysis. And I was missing one reading a bit on two-sided markets because the paper starts with multi-sided markets, but then all the insight that they have with one-sided markets. Remain to see whether the model can provide some insight on two-sided markets that are specific to two-sidedness. So that's really a very interesting aspect and it's important because it's been sometimes we've provided a model with network two-sided markets and network externalities. But if we want to have an impact on the policy and policy makers, we need to come with something that is tractable for them and which provides valuable insight. In this respect, if I were to push the paper, the paper is still a bit too much on the type, this is possible. So there is a possibility it would be good to go on toward under this condition, this will happen. Which is easier to read for economists that are in decision circle or anti-trust authority or consulting. So this is really the good aspect and there are illustrations with this kind of two interesting results. The one on increasing dominance and the one on interoperability. The slides were much more transparent, I think, than the paper. So you should go back on the slide and because of the explanation, I found it more transparent during the position. So then there is a drawback and everybody working on that knows that. So this is the concept as some drawback. I think one of the main drawback is that it's a combination of assumptions on price and model. So you need to assume that gamma is homogeneous. So there is an assumption on the model that is combined with a behavioral assumption on the pricing and that allows to get this simplicity. So understand that simplicity comes with a cost or raise. So this is a cost. As a comment, you should relate that to the work of Greg actually and Alex the cornoir on competition and utility. Because I think in your model it is equivalent. Probably I didn't check but looks like it is equivalent. So that essentially the main comment on that. I will leave the conceptual discussion for the after talk because good talk and less about concepts and things. Just one comment on the model and the assumption of Netflix. Technically it transforms the model into a multiproduct competition model with increasing return. So every result that you obtain with network externality here can be applied in the context of multiproduct with increasing return. Even interoperability because interoperability could be interpreted as learning by doing with below us. So we always find some equivalent. So this is a way to keep in mind the thing. That's all I wanted to say on the concept. I have a couple of suggestions for the authors. Three mostly one on the merger analysis of the merger analysis assumes that you merge to platform and you get to one new platform which actually has the same demand as each individual platform before which is in the district choice model. It's there is an issue of interpretation. But what you could do is to keep the two platforms. There is no reason to shut down the platform and to make them interoperable. And to ask yourself whether this type of merger would have a different effect and maybe this type of merger may be more efficient at curbing market power than the former one. So and this would be quite easy to do. A second question I had is that whether we can relate interoperability and entry. So and so one of the questions would be if we mandate interoperability, are we going to have entry of platforms and we know it can be good or bad. So it could be that interoperability backfired by market fragmentation in a sense, especially for partial London. So that's something that could be looked at. And a third suggestion is that if we have a triopoly the two small ones and an asymmetric equilibrium, the two small one may voluntarily become interoperable. And this in order to resist and to gain market power and this also will probably raise the value of the small one. So these are the three suggestions I had in mind. And I will stop just on the last point, which is something that was bothering me more, which is when we discuss about interoperability. The first thing that comes is multi-homing. So there is a direct question multi-homing as a substitute or as a complement to interoperability. So we would like the model to help to discuss also the question of multi-homing. But I was trying to think about that and then it raised some conceptual issues of the interaction of net fees and multi-homing. I don't know how you view it and whether you have the view on how to do it or your thought about it. But that would be something that would be interesting to see. And I'll stop here because I was instructed to be short.