 Yeah, can everyone see the slides. Yes. Okay, good. All right. So I'm going to, you know, present a paper today, tying in markets with network effects. It's joint with Jail Troy and Doshin, John, who are both attending. So hopefully they can chime in if I'm messing something up, or if they have things to add. And we'll take it from here. So, okay. So I'm going to just start with just a couple of slides just on, on tying. And, you know, I think most of this audience will be familiar with these things, but at least it will make sure we're all on the same page. So, you know, what do I, what do we mean by tying? So tying involves conditioning the sale of one product called tying good on a buyer agreeing to behavior regarding another quote tied product. So tying contracts, you know, can take a couple of different forms. In some cases they're, you know, gets referred to as a tie in, which is really kind of just purchase, you know, require, you know, the sale of the two products together. And that is that if you want to purchase, say product B, you have to buy my product A. And that doesn't, you know, have anything to do directly with what you're doing with other firms products. In contrast, there's also, you know, tying agreements that are referred to as tie outs, which involve not purchasing from a tied product rival. So if you want to buy my A, you have to agree to buy B from a rival B producer. So in essence, a tie out is a tie of an exclusivity provision to the sale of product of a product, say product A. So, you know, in the, there's a very long history, especially, you know, in the US for sure of very harsh treatment of courts under what was known as the leverage theory of tying. And the basic idea in the leverage theory, what and the concern was that a firm that had monopoly power or great deal of market power in one market, say A, might be able to leverage or extend that market power through tying and bundling to another market B, which is competitive or oligopolistic, and thereby monopolize that market. So, you know, the history of this, the intellectual history in the US was very harsh treatment by courts for many years. The Chicago School came along in the fifties and sixties and, you know, basic and critique this with what became known as kind of the one monopoly profit critique. That is that if you, you know, you can't extend, you know, you only have one monopoly power, and you can't use it to gain two monopolies. And, you know, they had, you know, in some sense, I always have thought of it as a real piece of demonstration of how powerful theory can be that, you know, what they had were some very simple competitive, you know, very simple examples and models that, you know, theoretical models, but very simple ones in which they made this point. And, you know, this point ended up being extremely influential. And, you know, what they then did. So basically it was kind of a two-step critique. One will show you a simple model that, you know, destroys your loose, you know, hand-wavy story about leverage and then we'll point to other reasons why tying might be used. In particular, they pointed to the idea that it could be used as a price discrimination device as in, you know, the classic metering story of, you know, IBM and its punch cards for HP and its cartridges. Come the 1980s, you know, came to be a kind of post-Chicago game-theoretic rejuvenation. So papers, you know, paper that I wrote, Jay had a paper as well, Carter and Waldman and others, all put together models that were game theoretic models in which this leverage theory kind of made sense. So, you know, kind of as in talking, just what the basic idea, for example, in my 1990 paper, there was a firm, it was a monopolist of product A that buyers value, and it faced a potential rival in market B. And what the paper showed is that if that firm, firm one, you know, the monopolist in A, could pre-commit to bundling, it could thereby profitably exclude rivals in some cases from market B and monopolize market B. And the basic mechanism was that a commitment to bundling made firm one more aggressive. And, you know, people why? Because it wanted to sell this very valuable product A. Once it committed to bundling, it would be aggressive in selling the bundle. And if there were scale economies in market B, something that the Chicago School had implicitly assumed away, that could lead to the exit of tie of good rivals or block entry of tie of good rivals and thereby change the market structure in the tie of good market. My paper kind of made a point of that, you know, this commitment assumption was important and, you know, showed that without that commitment assumption, you know, tie frequently could not serve as a leverage device. It did have some, you know, a couple of simple examples of where there wasn't pre-commitment, but I never regarded those examples as particularly successful. And, you know, at least that was my sense at the time. And in fact, the literature since then has mainly assumed commitment. And so, you know, in contrast, you know, without commitment tie in the question would be can tying arise, you know, tying can arise as a best response. You know, and we know it can because it can be a useful, bundling can for example be a useful price discrimination device. But, you know, in some sense, you know, as an antitrust story, you know, the effects in those cases you might think of as that is yes, I'm tying, you know, it's a useful price discrimination device. Yes, it could have effects on rivals, but that's not why I'm doing it. I'm just doing it because it's a more effective way to raise revenue. And so in this paper, what we have is a leverage theory of tying that doesn't rely on commitment. And in which time is adopted precisely because it can raise the perceived value of the tied product and lower the perceived qualities of tied product rivals. And by doing so, it leads to the monopolization of the tied market. And so that's basically what this paper will put together or puts together. I should mention, you know, one probably the closest paper to ours, and I think certainly the closest is a paper is the Carlton-Waldman paper. So, you know, as I'll say in a moment, our paper and the title already indicates it, you know, relies on there being network effects in the tied good market. And Carlton-Waldman, one of their two models does have network effects in the tied good market. And in that sense, it's similar to ours. What's different with Carlton-Waldman, their model is a model of compliments and perfect compliments. So it's a systems market. And the motivation for tying in their story is to protect the actually the tying market from future entry, you know, to protect that monopoly that you started out with. In contrast, in our paper, it's going to rather than a dynamic story about future entry into the tying market, it's going to be a story kind of going back to that leverage theory that, you know, in fact a one-period model where you're tying and successful, excuse me, and successfully monopolizing the tied good market. Okay. So what are the main ingredients of the model? The main ingredients are going to be two-fold. One is that there's going to be imperfect rent extraction in the tying market. So you have a monopoly in the tying market, but you know, you don't know everything about willingness to pay in that market. And as a result there are information that consumers in the tying market have. And you're going to basically use that and exploit that. The second piece of this is they're going to be, as I said a moment ago, network effects in the competitive quote or, you know, oligopolistic tied market. So the combination of these things is going, what we're going to show is that tying can be a mechanism to leverage that unexploited consumer surplus in the monopoly market to create a quasi-install base advantage in the competitive tied market. So basically you're going to have these consumers who are having information rents, but you're going to end up using, basically by tying you're going to get them to agree to buy your tied good market, your tied good, that's going to then lead to you know, get you the bandwagon going in the tied good market and let you monopolize that market even though you have an inferior good in that market. Okay. And that tying is going to be profitable and it's going to lead to exclusion of efficient rivals. And finally, as I kind of stressed already no pre-commitment is going to be needed to do this. So it's going to be a purely best response mechanism that to engage in tying in this way. I shouldn't say pre-commitment isn't needed, but if you can pre-commit a similar story would apply, it's just you don't need pre-commitment in order to get this strategy to work. I should mention in terms of imperfect rent extraction, there are other papers that focus other papers in this kind of foreclosure and I trust vertical practices literature that focus on unexploited consumer surplus. So for example, bursting had a very early paper on tying in which consumers had multi-unit demands for goods and for goods and the multi-unit demands, but pricing was linear. And so basically what his point was, well, you can use pricing time contracts in effect to extract some of the consumer surplus that you can't extract because you with just a linear price. And so in essence, it was basically like a form of Ramsey pricing. That's a mechanism that won't work in our paper because we rule it out by having unit demands in the tying good market. So that's not what's going on in our paper. But Chenzo has a paper that I'm sure many of you are familiar with, very nice paper in the AER, actually one of two papers. The one in the AER is focused on exclusive dealing. It has a similar, you know, it's similarly it points out that you can use information rents to get consumers, buyers to agree to terms. One, you know, there are kind of two differences between that paper and ours. One is that in that, you know, in our paper they're in essence externalities across the buyers because of the network effects. So, you know, in their paper, sometimes, you know, a monopolist can get everybody to just agree to these exclusivity terms for free because they have information rents. But nonetheless, the different types, you know, there's no externality among them. In our paper, there is this externality and what you do is you basically get these high, the high values in market A to agree to your tying contract. That then worsens the quality of the rival in the type good market that's available for other consumers and that's kind of how the bandwagon works. So, you know, that's one difference. The second difference which is related is, you know, in that paper, you know, exclusive dealing in equilibrium ends up being in essence price discrimination device. Low value buyers, you know, find exclusivity less costly than high type buyers and that's how the, you know, how it gets used. So, in a sense, it's kind of and in a sense, it's kind of a price discrimination story again for the use of exclusives. Here, for us as I said, we're going to worst, you know, adoption of time is going to worsen the terms that the rivals that the quality of rivals that's available to consumers in the type good market. Okay. Alright, so what's the plan for the talk? You know, going forward one, I'm going to talk about just a simple example that illustrates the mechanism. It really gives the basic idea of the paper, hopefully effectively. I'm then going to just describe, you know, in you know, without going into the details of proofs, the more general model of independent products that we then generalize the example to. I'm going to just have skipped the complimentary products case in essence. I just have one slide that just tells you what we do for that and then briefly talk about applications. So I guess I have about 25 minutes to do that. Okay. Any questions anyone have that before I get going? Okay. Alright, so here's the example. Pretty simple, you know, pretty simple example. We have, you know, two markets, A and B. A is the tying market. Firm one has a monopoly in A and there are two consumers in this model. There's a low type consumer and there's a high type consumer and the difference between them is the load is in their willingness to pay for product A. So, you know, UH is the high type utility willingness to pay that exceeds the low type consumers willingness to pay, which is UL. In market B, which is the tied market, we have two firms who compete. The two consumers have homogeneous preferences for the two products. There's no heterogeneity among consumers there. There's a standalone value for the two products. That is, by standalone, I mean ignoring any possible network effects. V2 and V1, V2 is the value willingness to pay for product two, which exceeds the value for product one. So, firm two, product B2 is better than product B1. There are also possibly network effects that could be realized and those network effects are such that if both consumers purchase the same product B, each consumer gets an additional value of N as a network benefit. And I'm going to normalize marginal cost to be zero for all the products. Okay. The first assumption, A1 says that two times UL is bigger than UH. And what this basically is saying is that the optimal, if you have independent pricing of A and B, the optimal monopoly price in market A is UL. That is, you'd rather sell, it's more profitable to sell to both consumers at a price of UL than to sell to just the high type consumer at a price of UH. And what that's going to do is it's going to mean that consumer H has information rents. Consumer H receives a surplus of what I'll call S, which is the difference between UH and UL. Okay. Assumption two is that N, the network benefit, is bigger than delta, defining delta here to be the quality difference in market B, V2 minus V1. And so what this says is that there's at least a potential network effects to exceed the quality differential. If you can get everyone on the bandwagon, you actually will have a better product than the rival if you're a perfect one. The third assumption is that this information rent S is large enough. That is, in particular, bigger than two times the network benefit. So it's saying that the unexploited surplus in market A for consumer H can exceed, and by enough, the possible network benefits in market B. And that's going to be what helps us get the band, allows us to get this bandwagon moving. Okay. All right. So let's first talk about what happens with independent pricing. That is, if we don't have time, well, in market A, like I just said, the monopoly price is going to be P, A star equals UL. What about in market B? Well, market B has network effects. There can be multiple Nash equilibria. So throughout the paper, we restrict, we allow consumers to coordinate formally by having their response via coalition proof equilibrium. And that, in the case of these in this example, the consumers in market B have are homogeneous. They have this, you know, the exactly the same preferences. So they're just going to coordinate in their response to whatever the prices are, they will respond to choose their Pareto optimal outcome. And so the, the result of that is that the pricing equilibrium in market B is such that firm two wins, it has the better product, its price, it can charge is exactly Delta, its quality differential. And firm B1 loses, you know, firm one loses and charges a price for B1 equal to zero. All consumers will buy the better quality product and real as a result, their full network effects being realized. Moreover, that network effect is redounding to the benefit of consumers. It's getting competed away because from the standpoint of the competition here the two firms, even though they have different qualities, they are in a similar position with regard to the network benefit and they competed away. Profits end up in this with independent pricing being that firm one's profit is two times UL firm twos is two times Delta the quality differential. Okay, so very straightforward happens with independent pricing. Okay, so now let's think about what happens if you're allowed to bundle what firm one can do. And in particular, what I want to show you is that if we start at this independent pricing equilibrium and allow bundling, that firm one has a profitable deviation to introduce a bundle. And actually introduce a bundle and in fact only offer a bundle. So let me go through that. And that's going to break that will break this independent pricing equilibrium and show you that we're going to end up having bundling happening. Okay, so let's consider firm one to introduce a bundle of A and B one at a price equal to its old monopoly, what the single market A monopoly price would have been namely UL. So imagine we're in this independent pricing equilibrium from one's losing in market B setting a price of zero from one in market A is charging this monopoly price equal to UL. It suddenly deviates, gets rid of its independent pricing introduces a bundle that's priced at UL. Okay, so the first point is if it does this, it's going to be a dominant strategy for consume under the assumptions I've made for consumer age to purchase the bundle to agree to purchase the bundle. And when I say a dominant strategy, what I'm going to show you in this next inequality is even if the price of product B two were zero and consumer and consumer age assumes that consumer L bought B two. So the bundle wasn't going to have any network benefits. It would still be worthwhile for consumer age to agree. Okay, so what's the inequality the left side here is the value of B two is zero when you have no network benefits by doing so which is UH plus V one minus the price of the bundle capital P which will be as I said up here is equal to UL is bigger than the value of buying B two and value buying B two is first the standalone value V two plus the network benefit end. Okay, well I just rewrite that condition that condition is equivalent to saying that S the surplus that type H gets from buying in market A UH minus UL is bigger than delta plus N. But the assumptions we can prove today that N is bigger than delta so two N is bigger than the right hand side and as well we assumed in assumption three that S is bigger than two N. So this inequality holds and consumer H finds it a dominant strategy to agree. Okay, all right now let's look at consumer L and apply iterative dominance. So given that consumer H is agreeing consumer L's going to purchase the bundle as well. Why? Well on the left hand side of this inequality is the value of buying the bundle which is UL plus V one. V one is the standalone value as well because if consumer L buys the bundle consumer L gets the network benefit end and then pays the bundle price P and on the right hand side of the inequality is the standalone value of buying the bundle of buying B two which is V two and I've assumed the best, the worst possible case for firm one which is that B two is priced at zero. So that inequality is equivalent to the inequality N bigger than delta which is something we've assumed. So once consumer H buys the bundle the bandwagon is started and consumer L is going to buy it as well. Okay, so both consumers by the bundle the price of the bundle is UL so the profit from doing so is two times UL which is exactly the same profit as under independent pricing except notice that these inequalities that we just went through were both strict inequalities and so I could have in fact charged a little more than UL for the bundle and gotten everyone on board and so in fact there's a bundle, a deviation to bundling where you price a little above UL that through iterated dominance is guaranteed to lead to an increase in profit compared to independent pricing. So that's basically the example. Okay, any questions anyone has on that? Okay. I can ask a question on that. I was wondering whether consumers would have a interest in buying both the bundle and oh yeah, perfect. Sorry, finish your question know what it is because with B buying B two they get a better standard value so they could combine that with the getting product rate. Thanks, I meant when I went through this first inequality I meant to say something about that. So yes that is that's an issue so you know what we're assuming here is that you know what you're doing when you bundle is a tie out okay you're explicitly saying you can't buy product B two okay it's not always necessary to do that so for example it is necessary when the costs marginal costs are in fact zero if the marginal costs were actually positive for these products it could be that without the explicit tie out you still would you know a consumer would never have an incentive to buy the bundle in order to just get a and then buy B two but in the case that I've assumed where I've normalized costs to zero you would have an explicit requirements contract a tie out that said you aren't going to buy B two so thanks very much for bringing that up okay model with independent product so I'm just going to hear here I'm just going to kind of give you a sense of the model and the structure of what we the results that we do that we show but the basic idea of that of everything is what I just showed you okay all right so what's the general model from what is a monopoly you are that represents consumers valuations for product a distributed an alpha to alpha plus you upper bar and we're going to define so the lowest possible value for product a is alpha which could be positive a consumers type is going to be defined as the difference between its value and alpha how much above alpha their value is and the distribution of that type is going to be according to a CDFG which has a monotone has a great condition the price of product a well off in the paper we often do a change of variables which states you know kind of a net price above alpha for product a and that lets us write the demand for product a is just one minus G of PA hat which is that next that net price profit maximization is just maximizing PA hat plus alpha that's the total price my times the demand one minus G of PA hat and we get standard first order condition and in some cases if alpha is big enough every the optimal monopoly price will be to sell to everyone which is the quote full coverage case one just quick remark you know in terms of interpretation you can interpret what's going on in market a equivalently as being that product a is a two sided platform and consumers valuations are those types but the platform also is getting advertising revenue of alpha per consumer and if you go back to its objective function you know here profit maximization you can see that that PA hat would be the price to consumers alpha here would be in essence the revenue earned per consumer or equivalently a negative marginal cost okay the tide market firms one and two compete consumers again at homogeneous valuations there's a standalone value VI and network benefits which are beta times NI where NI is the total number of consumers who use VI V2 is bigger than V1 so assumption one again delta is the quality differential that's positive beta is bigger than delta which is an assumption that like our previous assumption that network effects are important enough and there's a stability condition that we're assuming as well okay independent pricing game just as before there's a monopoly price PA star that now need not involve full coverage it could have just some consumers being you know being excluded in market pay and then again applying coalition proofness the equilibrium market be with independent pricing is that firm be firm to wins and charges its quality differential so in the general model we then you know and that analyze time we now say well suppose firm one is allowed to tie what's the effect of that we introduce assumption to here which is a condition that is a sufficient condition for the you know ban for this monopolization effect of time to go through and it's basically saying you know it more likely to hold if alpha is is large it's also more likely to hold if delta over beta over delta is large so if the network effect is much more important than the quality differential it's more likely to hold and it always holds if we have full coverage in market anyway I won't go and show you that but in the paper we point that out okay so first thing that we show is that you can effectively in this setting you know for firm one without some generality you can just think of firm one is either optimally best responding with an independent pricing or alternatively optimally responding with a bond with tying it's effectively a tying contract where it only offers a bundle at price capital P and product be one at a price P be one but it doesn't offer product a separately this figure kind of just gives you the idea of why this is true so this what I've done in this figure is arrayed consumers according to their type from left to right and I'm depicting a situation here where the bundle price P capital P is less than the sum of PA and PB one so that's why P minus PB one is to the left of PA so if you think about consumers types here you know consumers in set one are either going to buy B1 or B2 they're not going to buy the bundle because the incremental relative to buying B1 the incremental cost of going to the bundle which gives you product A is above of their types and so they're either going to buy B1 or B2 set two is either going to buy the bundle or B2 because for them buying the bundle is worthwhile the incremental cost of the bundle is bigger than the price differential relative and then finally in set three you're either going to a consumer there is either going to buy the bundle or a combination of A and B2 and the reason is their utility from A set price sold separately their utility from A is bigger than the price of A sold separately so if they buy B2 they're also going to buy A separately from the monopolist and so one you can see here is the only consumers who are going to buy just A by itself are in set three and if the the firm is in fact selling A separately at all what you can see here is that B you know it's doing so because A the AB2 combination is better than the bundle okay well if that's true it's also true that for set two B2 is better than the bundle and for set one B2 is better than just B1 and so that tells you that in that case the only sales that firm one is making are sales of product you know are sales of product A at three but if that's true the firm would be better off doing independent pricing and so you know weekly better off and so that's kind of how we see that one of these two things is going to be the best response is going to be a best response okay so that's a first thing we show the second thing we show is a similar result to the example so in the example we show that there was a deviation to bundling that breaks the independent pricing equilibrium we do the same thing in the general model in the general model what we do is we show that introducing deviating to just having a bundle that basically gets exactly the same set of consumers who would have been buying product A to buy the bundle is a profit increasing deviation and this is just the condition of what the bundle price would be which is the condition that says that a consumer whose type is exactly PA at star the net optimal monopoly price in market A with independent pricing that that type of consumer would be indifferent if everyone who had a higher value for product A bought the bundle and everyone's a lower value for product A to bought B2 and importantly the argument here is exactly as well an iterated dominance argument that is that we start at the top with the highest valuation consumers and they are for sure going to buy this bundle at this price that I've just described and then the bandwagon starts and everybody with a type all of the types that I've just said will buy the bundle will do so you know through a process of iterated deletion of dominance of iterated strategies so like the example that just shows you that independent pricing equilibrium is broken the neither the example nor this result tells you what the equilibrium actually is and so our main proposition which is a morass of words on this slide I apologize for that is basically telling you what the equilibrium is there are two cases case one says if alpha plus beta is bigger than one over G of zero then in that case the equilibrium is that firm one in fact only sells a bundle in equilibrium and it does so at a price of alpha plus beta minus delta it sells it to everyone so there's full coverage in terms of sales of the bundle and in doing so of course it monopolizes market B the second case is and that case I should say always holds when we have full coverage with independent pricing in market A the second case is a case is you know the converse case and in that case firm one actually sells both a bundle and product B one separately and so it sells the bundle to high enough value consumers in particular consumers who have a type above some critical type what I've called here X till the star which is given by equation one and it sells B one to lower value consumers and again it monopolizes market B so that's the main result let me take a few minutes to finish the rest of this so welfare can in principle can in general be ambiguous monopolization of market B is inefficient that's why you know because it's monopolizing a market where it's the less valuable product but in that second case I just described we also get an expansion of consumption in market A and that increases the inefficiency of market B however in the first case where we had full coverage in market A to start with we know that in fact in that case we get full we continue to get full coverage there isn't any expansion in market A so in that case we know that the result of the time is inefficient the slide on compliments is also just literally one sentence which is here what we do is we show that if you have an inferior product A then everything I just showed you for independent products actually ends up yielding we get the same thing with the case of compliments you know an A B system but where there's a less good product A than the monopolist and you can just think of the less good product like it you know before there was monopoly in product A but you could decide not to buy now instead you could decide to buy this inferior product so that's how the compliment case works in the paper potential applications so in the paper we just we talked about you know two cases that where the model can at least shed some light I think on this on the situation so one is the EU Google and Android case so in that case you know Google was found was accused and found guilty of tying the play store to search so another there was a the moda contract mobile application distribution agreement contract which required that distributors of mobile mobile carriers for example and putting Android mobile carriers I should say in order to get access to the play store where Google had tremendous amount has a tremendous amount of market power had to agree to make Google the exclusive out-of-the-box search engine on the phones there are definitely differences from the model to that situation and that that situation that just you know we have distributors not single product consumers for example but one thing I think is interesting about this is when you think about the moda you know you might ask yourself like why did Google tie the play store in order to get search exclusivity as opposed to just paying for exclusivity right and so you know potentially the model gives you some explanation for why those two things are different okay that you know if you just pay you're not taking advantage of these unexploited unexploited surplus a second example and you know the network effect in that case is that search you know arguably has evidence for I won't go say too much about this but you know search is a product where there are network effect direct network effects the more people are searching on a search engine the better the quality of the search engine will be in the EU Microsoft case Microsoft was had tied the windows media player to windows and windows media player has indirect network effects in that application the more people have the media player the more applications are written that are compatible with the media player okay so conclusion just we had a leverage theory of tying in the presence of network effects in the tied product market tying enables the leverage of an exploited consumer surplus in the monopolized product to build a quasi install base advantage in the tied product market and tying in these circumstances can be profitable without any commitment and in particular what it does is it raises by starting this bandwagon it raises the perceived quality of the tied product and lowers the perceived quality of tied product rights so thanks very much sorry for going a little bit long I will unshare first of all I would like to thank the organizers for letting me and discuss this very nice paper I learned a lot by by starting this paper it's a great contribution to the time I must say that as far as I can tell the analytics is fine so in my discussion I will focus on the ideas underlying this this paper and the basic mechanism as Mike explained is based on the notion of an exploited consumer surplus so the idea is that for some reason dominant thermo monopolies cannot extract all the surplus from consumers in the market and therefore that creates scope for imposing contract restrictions in other markets or related restrictions that that may be profitable now when you want to tell a story which is based on this unexploited consumer surplus idea you have to address two key questions there are two key elements in any such story the first one you have to explain why the dominant thermo cannot extract fully the surplus from consumers and this in these time models is relatively simple as I will tell in a moment in other applications like for example exclusive dealing is more tricky is exactly what is the mechanism whereby you can leverage this exploited surplus to raise your profit so just to illustrate these two paths of this type of explanations let me contrast this paper with very early people by best thing which Mike also mentioned was actually the first to put forward this type of unexploited consumer surplus mechanism so there are differences in both aspects so based on as a model where consumers have variable demand and the reasons why the dominant firm cannot extract the surplus fully is that the dominant firm is restricted to linear pricing here instead we have a model with discrete demand so linear pricing is not restricted per se but what you assume basically is that the dominant firm cannot price discriminate perfectly so in this aspect I would say the differences are minor with Burstyn the most important differences in my opinion are in the way in which these unexploited consumer surplus is leveraged in market B because what Burstyn has is basically a model similar to a model of optimal taxation so the idea is that by tying the dominant firm can touch with the Burstyn price cost margin two goods or n goods instead of one and we know that touching more goods tends to be more efficient so it is basically kind of exploitative abuse which if I understand correctly in the US would be not able to say no abuse whereas in this paper what we have is that a more efficient competitor is affected because it is denied the scale which create which allow it to exploit the network externalities so having said this I have two comments the first one is I was wondering whether there may be other exclusionary stories like this but stories that are not based on the notion of network externality so I think for example of a setting which is often considered in the exclusion of dealing literature and precisely models of naked exclusion so the support that a competitor in market B is a potential entrant which overall that is even accounting for the entry cost could be more efficient than the dominant firm in market B but the idea is that by tying you can exploit the dominant firm can exploit the unexploited surplus basically to deny economies of scale to the competitor and to deny the entry so I was wondering given that you have given important contributions also to the theory of naked exclusion whether you consider this particular this twist it would be another application of the similar the same idea and the second comment is about this notion of unexploited surplus I think it's important to clarify that it has not been taken literally that it is not strictly necessary that consumers have positive rents what really matters is that the dominant firm cannot extract the rents efficiently so to to clarify because if the dominant firm cannot extract the rent efficiently then that means that the dominant firm can give up a euro of profits so and that would lead to the consumer more than one euro of surplus and then the dominant firm could use this more than one euro of surplus in the other market so for example think of this kind of situation in market A so this is a situation where your assumption would be violated because the optimal price would be 201 as in your example one consumer of type H and one consumer of type low low willingness to pay monopoly price would be 201 no unexploited surplus left but clearly you see that here if the dominant firm price at 100 it would lose one euro of profit but it will lead to consumer H which is 101 euro of rent and then it could exploit such rent in market B and it could be that that kind of exploit so large a rent could be exploited to gain more than one euro of profit and if I understand correctly this is what is actually happening in your model in the case of mixed bundling so when you'll notice that there are two conditions with one condition the market is covered in the other condition with independent products the market will not be covered and in that case what you have is that in equilibrium there is mixed bundling but I mean mixed bundling because the market A is not covered is quite mechanical effect to me what is more interesting of this case is that the price of product A actually goes down of course when I say this I'm saying something loose because it's not priced independently but if you define the price of product A as the difference between the price of the bundle and the price of product B that goes down compared to the case of independent products and the reason if I understand correctly is precisely this one that is with uncovered market the way rents are extracted is inefficient so the dominant firm may want to decrease a little bit or decrease the price of product A that creates at least more rent to the consumers and then the dominant firm can exploit these rents in the market for product B whereas if instead the market is covered and you reduce the price of product A that will transfer rents to the consumers on a one-to-one basis and of course you cannot profit from this because you cannot extract on a more than one-to-one basis in the market for product B so the point is more general this is an exploited surface mechanism is more general in my opinion you may tell a story like this whenever the pricing in the tying good market is inefficient it doesn't allow to extract rent in an efficient way thank you