 This is probably an unusual paper for this seminar in that it's really written for a law econ journal and it doesn't have a new theoretical model. So I think maybe for those watching today, you should think of this a little more as kind of organizing theoretical ideas, but also perhaps inspiring future modeling. And one of the things I'm actually very interested in from you all is input on where you think new formal models are really necessary. So I sort of invite you to join us in this journey and saying, you know, taking this critical look of, well, what of what I say today is obvious. What do you possibly disagree with? Or what do you think really needs a model to clarify when it's true and when it's false? And so I think with platform economics, actually very little is completely obvious. So it's probably a little bit, you know, almost certainly somewhere along the way, you're going to say, gosh, you know, that's a little strong statement that must be qualified. There must be conditions under which that's not exactly right. So that's what we'd really invite you to do. So apologies for the non-standard talk. Fiona was the one who agreed to it, so I'm going to blame her for accepting this invitation to speak to this audience here, but I'm not trying to insult your intelligence by not showing you not a model. I should say, I would say I'm too old to write theorems anymore, but I'm actually writing theorems about things like regret bounds for contextual bandits and things like that. So I'm writing different kinds of theorems these days. And maybe you can wrote me back into writing more IO theory theorems as well. Okay, so here we go. And I also just want to give a couple of quick disclosures because this is going to have some policy implications that I'm also going to use some specific examples. I apologize, but I'm going to use both the examples I'm going to use are both about Google. Many of you know I spent a lot of time thinking about Google and lobbying about Google, but it happens that these are the examples that have lawsuits associated with them. And so those are just the best examples that have a lot of public information from the lawsuits that I've been filed. I was, many of you know, consulting chief economist for Microsoft. I stopped doing that seven years ago. There have been two chief economists since then, but this still builds on things that I did there. And so that's, but I'm this is definitely they have nothing to do with this because I don't have a close relationship with them anymore. Okay, so we're going to talk about platform annexation and just as an introduction, the like old view on on integration generally can be kind of boiled down to some simple maxims. Horizontal bad horizontal integration reduces competition. You weigh the benefits, the cost against the potential benefits like scale economies and the cost benefit would go in favor of merger of weaker rivals. So, you know, the, the, the, in general, if we have scale economies, you might want to weaker rivals to merge. But that's, you know, a kind of a special case, although in platforms as we know, that's a relatively common issue that, you know, you might want number two and number three to merge in some things. If they're, if they're going to go out of business or if they don't have enough scale economies. Because you'd rather have, you know, two than one. But vertical, on the other hand, was typically good. And we thought of it as, you know, solving double marginalization problems. And for the context of this talk, I want to reframe the double marginalization, which we all kind of talk about the buzzword, but really the another way to put that same idea is that it resolves a conflict of interest between a supplier and a retailer or manufacturer. So, you know, they have a conflict of interest, they're trying to go after an overall margin between price and cost, and by, you know, by, by merging, they're going to, they're going to internalize that but if they're separate then they end up with too high a margin basically is in each of them attempt to get more of the margin so they each mark up a little bit more than they would. And so that conflict of interest is going to be what we're going to focus on in the platform annexation that that theme. Of course it also all sorts of other things which which this audience is deeply familiar with but you know it can align incentives for investments. And there's a, you know, a similar theory for for tying and bundling their the ideas, you know, while there is a single monopoly profit to be had in a polar case where two goods are consumed in fixed proportion. If there is market power for one of the goods, then charging more for, for, for one reduces the price that can be charged from the other. There's only one monopoly profit to be gone after, therefore bundling is fine. So there's no harm to tying. And for the single monopoly profit idea for for bundling there's of course many exceptions. Like, you know, the goods aren't consumed in fixed proportion I always think about the single monopoly profit theory for tying is being like left to left shoes and right shoes. But if, if they're not consumed in fixed proportion, then there's there's then the amount of the profit can vary depending on market structure. You know, consumers have tied products might also consume complimentary products from other firms. That's enough that that creates an externality. And especially market power or entry might be affected by tying. Those are some of the, some of the forces that lead to more complex setups. And there's a nice summary by Joe Farrell and Phil wiser from 2003 that law econ paper that surveys a lot of this literature. If you haven't read that that's kind of a nice, a nice paper and it's kind of interesting now that Phil wiser was attorney general of Colorado and is actually involved in some of these related antitrust cases. And see, it's unusual that the attorney general actually wrote some of the foundational articles. So, okay, so the modern antitrust view on vertical integration is that, you know, there, there are many reasons that it can be bad. And, you know, the one of them raising rivals cost we have Steve sell up here. So he pioneered that line of research and is still writing papers today that they relate to this, this, this issue. And as recently as last year there's a he has a nice paper summarizing some of these issues. So the rabid raising rivals cost. If a supplier upstream and a manufacturer downstream merge, the supplier might charge a higher price to the competing manufacturer. And in this model upstream firms indirectly support competition between downstream firms. That's going to be another theme that we're going to pick up in in this paper, the, the role of vertical integration of certain types for supporting competition, and that'll be a big, a big theme but we're going to kind of specialize that. And when their scale economies or entry barriers for closing arrival can have any competitive effects. More recently and I think sort of in the same similar spirit is the paper we're writing, we people because something called vertical manipulation has become a big thing from a practical perspective. People have specialized in on the problem of vertical manipulation and written targeted models. The theory is similar to raising rivals cost here vertical manipulation might be depriving a vertically related firm of their user base. And so this would be something like Amazon or Google doing vertical manipulation and search results. Now, there's similar to these other cases there's going to be examples where this is good or where it's bad vertical manipulation might not hurt welfare if the downstream firm is competitive or their load entry barriers. So, you know, we can be we can think about customer protection for Amazon sellers but if the battery market is competitive, then if Amazon, you know, preferences its batteries, then, you know, that's not necessarily going to be bad for consumers. As long as you know there's free entry and batteries and Amazon isn't going to tie up the world battery market. But if there are scale economies or important innovation considerations and this can be bad. Another area where vertical manipulation can be problematic is if the downstream firm is a nascent competitive threat, it might be a compliment today that grows into a substitute tomorrow. And so we might also worry about, you know, Google manipulating against, you know, shopping like Amazon, because they're worried that Amazon is a nascent competitive threat to Google and search. So there's also going to be an element of that in our in our paper as well where we're going to be talking about the role, you know, vertical vertical integration, affecting something that really turns out to affect overall competition in the market. So those are those are some of the modern views, but, you know, as you can see, there's a there's sort of a lot of moving parts in these models. And so we want to spend some time to specialize in on on a part that hasn't received as much special attention. So platforms and marketplaces everybody here knows this we're going to talk about platforms and intermediaries with indirect network effects and multi multi homing. We're going to focus a lot on multi homing as a important force in platform competition. And we'll use the term take rate to loosely to be associated with the fee charged by the platform. And one of the key ideas is that when platforms aren't differentiated and both sides multi home platform competition can under many circumstances lead to low take rates. So, you know, the platforms tax on this is is low. So just as an example of the role of multi homing. So I think Uber and Lyft are is one of the examples that we're all familiar with where there's pretty active multi homing on both sides of the market. You know, there's there's a market with indirect network effects but in in markets where there is, there are two platforms of relatively similar strength. A rider will typically actively multi home for each transaction while the the drivers also actively multi home. Now this is this is a situation where there are benefits to multi homing on both sides that motivate people to do it. You know if you find out Uber is going to take 10 minutes then you're going to look and see about the lift. And as we're getting back into the market now you're seeing this where there's really long delays for Uber is where I live now still. So it's especially beneficial to check both apps to see if there happens to be a car that's closer on the other app. While the drivers are also very motivated to multi home because if they're they they if they're sitting there they're they looking for for more riders. And so that leads to intense platform competition which can lower take rates and reduce intermediary profits. Now, some people are concerned about other issues with Uber and left around labor issues or whatever but from a just platform perspective, putting aside, you know, labor issues. This is generally beneficial. Of course if you're Uber and left you're going to be thinking about ways out of this and try to get some loyalty. But as so we as we see this evolve don't come back later and say oh Jesus and you said this is going to be competitive and it's not. They may find ways out of the out of the multi homing situation but it's one that in principle leads them to need to differentiate in terms of improving their platform and it keeps keeps take rates low. So then if you know given a multi homing can, you know, and I should say, you know, what are the mechanisms for how this works that in the end you know the they need to. If most of the riders are on both apps and if most of the drivers open both apps then clearly people can, you know, search for a better deal on the other platform. So, in terms of interfering with the multi homing. What are some of the things that get in the way. Well there can be natural reasons. And those can lead to kind of can lead to competition problems but they're sort of exogenous reasons that you have competition problems. Things like a long purchase cycle like if you're buying hardware like a console or a device that's that's purchased alongside a software platform, then you're going to be with that for a long time, and the consumers will be effectively single homing. But you can also have natural reasons related to time or location sensitive supply and or demand, things like a search engine, you're doing a search right now you're about to go to a website right now. So you're effectively single homing, even if over time you use different search engines, or also also like mobile activities. If you're out and you're looking for a coffee shop, your, your need will evaporate and so you're effectively single homing for that at that moment. But what we want to focus on our platform actions that reduce multi homing. And so there are many of these as well, but we're going to focus in on one. Some of the others include limiting access to users through long term exclusive contracts or technical provisions, loyalty programs, and that's something that you might see Uber and lift leaning into more other types of artificial switching costs, or, or either contractual or technical can be examples, but we're going to focus on our plot when the case for the platform expands into adjacent areas, or tools that create frictions for participant multi multi homing. So how does this work. So we'll, we'll think about a situation where there are platforms and intermediaries and there's in the initial condition, and there's at least two platforms. And, and so there's a possibility of multi homing and in situations like that. There's often demand side tools or supply side tools that help people plug in. And these tools can come into being also even if there's one but they're going to be especially important for analysis if there's two or there's or there's at least potentially two platforms. And so what is the role of these, these tools, these tools are going to basically help the supply or demand side compare prices and offers across platforms, and they may also actually just technically help them plug into multiple platforms through APIs, so that from the perspective of a market participant, they're interacting with the tool, and that in turn, lets them fairly seamlessly interact with multiple platforms. And so, you know what what what's the benefit of these potential tools, they can increase multi homing intensify competition, you know reduce search costs, things like make sure that people can find up prices. And they can also enhance buyer supplier power in a variety of ways. They aggregate consumers and they thus have bargaining power with the platforms. For example, they can not just in terms of price which is a less common role that they're actually really negotiating price, but more commonly, they can incentivize platforms to provide information data, etc. So if a tool is trying to help the the participants choose platforms they're going to need certain data in order to compare prices and they can say hey, if you don't provide this data we're providing it for, you know, your competing platform. And so the platform may actually miss out on on business if it doesn't, you know, provide this information to the tools. So they can they can do a lot to kind of restore a balance of power between concentrated platforms and less concentrated suppliers and and and and market participants. And they also are going to therefore affect the way competition works. Multi homing on at least one side of the market can, for example, reduce platform entry barriers. So if a platform somehow or another can attract one side of the market through differentiation or quality or pricing. If there's a tool on the other side of the market, then it can they can help solve this chicken and egg problem. If you if you come if you can somehow get one side on on board even a niche on one side, then the tools make it very easy for the other side to multi home. So it's essentially like, you know, aggregating one side of the market, and then they getting them all to multi home by just by getting the tool to turn on a switch in the in the ideal world. So they can really substantially reduce barriers to entry. And that also makes them particularly important in markets where entry is is hard. And you know sufficient multi homing on both sides can lead to low take rates enhanced competition and efficiency. And they can lead to an sort of an ideal scenario where network effects occur at the market level, rather than at the platform level. And so again, I think it's it's it's easy for a regulator to look and say to ask question, well, gee, if these indirect network effects are so large, why shouldn't there just be a single platform. But the point is that if if people are able to plug into to multiple platforms, then the network effects are at the market level and not the platform level. And so then there's little benefit of having a single platform. Of course, there's saving on the fixed costs. But they're there, you know, we always are willing to incur some extra fixed costs in order to get some competition and incentives for innovation. And so partly now I'll preview but you know for where we could use modeling. You know, this is actually a, even though it seems like a fairly simple story, there there are would be a lot of moving parts in a full theoretical model. So we need to have two sides of the market. We want to think about an incumbent platform and a competing platform and potential entrance. We're going to need to model the multi homing costs that direct connections are costly. We're going to have tools which are a separate product that facilitate connection or price comparison. You have to kind of build in what those benefits are reducing multi homing costs. And therefore we also have to have endogenous multi homing as part of this then the tools need to have some scale economies and or switching costs. And finally the platforms are going to have a larger dimensional choice set because platforms are going to be able to choose whether to and how to interoperate with tools. So one of the strategic variables on the part of a platform might be whether or not to allow a tool to access their API. So there's a lot of moving parts and a lot of choices here, which is part of the reason we didn't, we haven't yet written out like a full, a full model of all of this. So now let me dive into some specific examples. And these are examples that I've worked on from an antitrust perspective that have been the subject of any trust investigations and some cases and resolved investigations. But also things that I worked on from the business perspective where it was very clear that the tools played a really important role. So one of these was, and of course there's so many investigations now, but this was the original FTC investigation into search in the early 2000s, you know, brought out a lot of these facts. So in the search market, we, all of you are familiar with just using a search engine, but there's also a third party market for syndication and distribution. And the recent DOJ lawsuit is about the distribution side of that market, but there's also a syndication side of that market too. And so we think about the ad platforms at that time, Yahoo ads, Bing ads and Google AdWords, they were branded at the time, are ad platforms that bring together advertisers and third party publishers for providing search services. And so I put a little list on there to drive from CommScore data in 2009, which showed sort of the size of that market. That was about a third to about 40% of the search advertising business was part of this syndication market. So instead of it being that you did a search on Google.com, you did a search or something that was like a search on a third party property and those properties in turn used advertising from these search advertising platforms. So the search platforms both provided ads on first party like Google.com and Yahoo.com, but they also provided ads on third party sites. And so the reason that's important is that that's where part of this market was matching advertisers and publishers. And this is the case where while end users going to Google.com may not care directly about advertising revenue, these third parties were mainly motivated by advertising revenue. So the more advertisers you had, the more publishers you would get. And that was reflected in the market shares at the time. Google had about 10 times the market share of the other competitors in syndication, for example, and in syndication and distribution. So, and in Europe it's always been that way or more. So what were some of what were these tools? Well, from the perspective of an advertiser, you know, what they wanted to do was to serve an ad for someone who was searching for something so they might be searching for car insurance. So from an advertiser's perspective, these things were very similar across the different search advertising platforms. They were all doing basically the same thing, matching ads to keywords. And from the, so from the advertiser's perspective, the natural thing to do would be to manage all of their search advertising and manage it across platforms. And really on, there were a lot of software products that did that. And so an advertiser cared much more whether you had searched for auto insurance versus car insurance than whether you had placed that search on yahoo.com or Google.com. So the keywords were more of the unit of analysis rather than which platform you were on. So it was very natural for for advertisers to completely multi-home across different search platforms and use these tools. But there were, in this case, Google put on a bunch of API restrictions for tools that also accessed Google's AdWords. And the APIs were needed for this software to plug in and manage your search advertising at scale. So here, the benefit of the tools, what the tools did was they really helped an advertiser plug in to multiple search advertising platforms at the same time, help them manage their bids and manage their ROI. So there were a bunch of restrictions that were put on. The restrictions said that tools that collected and used advertisers' own data for use on other platforms or for comparison with data on other platforms were not allowed to be provided by tools. So a tool that, in principle, should be doing price comparison was actually not allowed to do price comparison to Google or else they couldn't plug into Google's platform. They prohibited advertisers from directly transferring or copying their own data from AdWords into another platform by any automated means, and they allowed Google to shut off API service for any breach. So that made it really hard for a tool to actually provide any value because the main value a tool would have would be to help you compare prices and go across different platforms. So a lot of these tools exited or they had their API access shut off if they violated Google's terms and conditions. And so then Google had its own tool, which then it developed and got a lot of advertisers onto there. Later on, some of those terms and conditions were dropped in response to an investigation, but at that point a lot of advertisers were on using Google's tools. And then over time those tools would not plug in equally to other platforms. So this is an example where in the presence of the tool and independent tools that could plug into multiple platforms, a lot of the multi-homing problem by advertisers could have or should have been solved. And it was definitely what the advertisers wanted. They wanted to multi-home and they wanted to do this comparison. There's just like no real doubt about that from the evidence record and from advertisers' perspective. And if that multi-homing had been more complete, then the syndication and distribution markets also would have been more competitive, which in turn could have helped sponsor and tree or allowed competing platforms to grow. And there's a third part of this, which is the user search engines, Google.com and Bing.com or other search engines, which would have benefited from that as well. Okay, so that's one big example of this. And it's kind of surprising actually that there haven't been more papers about this, I think, because all of this came out in fairly gory detail 10 years ago. And this was a fairly big deal. But I think at the time, people, I probably, I tried to get economists to work on it at the time, but I think it was sort of viewed as sort of a niche topic and something that was so specialized that like people didn't necessarily care about it as a general interest matter. And I think now just people's interests have changed. So I still think there's room for looking at this. The second one is more complicated. I was also interested, this has been something that's been going on for the last 13 or 14 years. Many of you at some point in time heard me try to pitch you to work on this. But it was always hard to work on because there weren't a lot of facts out there. But if you read some of the recent lawsuits that have been filed, for example, by the state of Texas, they've actually laid out a lot of facts now that make it a little bit easier to wrap your head around what's going on. So this is the case of advertising exchanges. It's a similar setup and I did this on purpose. I focused here on the third party advertising market and search to help lead into advertising exchanges. So advertising exchanges are going to map not just for kind of search like advertising, but for display or video advertising publishers and advertisers. And in this case, you know, self-service isn't really so much of an option. Everybody needs tools to plug into these exchanges while in search there was some kind of self-service where you didn't necessarily have to use tools. And so these ad exchanges are then interoperate with tools that help both publishers and advertisers interact. And so independent tools compete for constituents in terms of quantity, service, or price. And they again are going to enable entry by facilitating multi-homing to smaller platforms and they'll support competition. So, well, annex tools in principle can steer business to their own platform. And this annexation can be implemented either through ownership or through contracts. In this case that I'm the example I'm showing here, it's through ownership. And they sometimes can attract customers by providing an advantage over other tools and interoperating with their own platform. In the case of publishers, the publishers would be like newspapers would be a key example of publishers, and they use something called a publisher ad server, which helps them interact with an ad exchange. And the ad exchange is holding an auction. On the other side, advertisers are plugging in and they're plugging in through something called a demand side platform. So if you read the antitrust complaint by Texas, it details a lot of the different behavior, particularly on the publisher side of the market. But basically Google acquired DoubleClick, which was an independent tools provider that helped publishers interoperate with ad exchanges. After Google took over the publisher ad server from DoubleClick, it started advantaging Google in auctions. For example, letting Google's ad exchange look at the bids of the other players before placing its own bid. And it also gave it differential access to information. And so what that does, I've kind of delineated that here in this picture, if you had a rival ad exchange, there's a kind of an orange arrow here with an X next to Google publisher ad server. That's indicating that Google's publisher ad server isn't equally interoperating with a rival ad exchange. And similarly, the Google ad exchange doesn't interoperate on equal footing in terms of, say, providing data, other things with rival DSPs, demand side platforms. And so what that does is it makes it hard for a rival ad exchange to enter. Now you might say, well, if these tools are so bad, why doesn't a new tool come in? So before we've got an arrow going in the other direction, Google's ad exchange was the largest ad exchange. And so it doesn't necessarily interoperate on equal terms with a rival tool. And that's where you can get this type of behavior to be robust to entry by rival tools providers, because if the platform can decide, not to interoperate with rival tools, then it's very hard for rival tools to enter, because what publisher wants an ad server that can't interoperate with the largest platform. And so you have this kind of reinforcing effects across the ad exchange and the publisher ad servers. So this is a current example that's getting litigated, and it's going to probably be litigated for a long time. And so it feels like, again, it could be worthwhile to have specialized models that focus on this kind of behavior. So Fiona and I kind of introduced this term platform annexation to kind of capture these types of examples. And we say it's a practice where a platform takes control of adjacent tools, products or services, and operates them in a way that interferes with efficient multi-homing. And it's going to use that to steer users to the integrated platform and away from rivals. And so why is this inefficient? How do we apply theory specifically to explain why this is inefficient? Well, first of all, there are externalities from multi-homing in tools. So the benefits will accrue to all participants if a competing platform is strong enough to reduce the take rate. So going back to an example like this, if we didn't have an annexation by, in this case, Google buying double click of the tools, then within these tools would serve the interest of publishers and they would help publishers choose between different ad exchanges. And if there was multi-homing on both sides, ad exchanges would have very low margins. And therefore a lot of the benefits would accrue to publishers were the people writing the news articles and doing the R&D. So the publishers are people who we should care about because they're also doing R&D. And if we had these tools helping facilitate competition, then take rates would be low and more of the surplus would go to the platform participants. But the individual participant bears the cost of multi-homing. And the tools providers, the entry and investment by the tools providers are also going to create positive externalities for the marketplace participants, whether or not an individual buys the tools. So the value of the tools to individuals for comparing platforms is really an externality. And actually if they succeed and platforms are competitive, also you may not need the tools as much because you're getting a good deal on both platforms. So there's a lot of positive externalities floating around when it comes to these tools. The tools are really creating the conditions that economists think of as ripe for competition like price comparison and low switching. The impact of platform annexation is it deprives rival platforms of access to constituents which harms competition in the short and long run. It also is going to deter entry and reduce competition in both tools and platforms. And it's going to maintain the ability of the platform to extract surplus from the constituents. So the impact is really if a platform annexes the local tools, they're going to change the nature of competition. And this is why the traditional kind of competitive theories why we shouldn't worry about integration don't apply because there's externalities and because the annexation affects competition. And the final thing we have to really think about, which I've already alluded to, but just to kind of summarize, why doesn't competition in some part of this take care of this problem? Like why don't participants switch to better tools if the tools are hurting them? And when you read through the litany of all the things that these publisher tools did to publishers, it's kind of amazing. You were buying a tool that was helping a publisher, in principle, helping a publisher make money, but those tools were actually rigging auctions and lowering revenue for publishers. And so the publishers actually fought that very hard and really didn't like these tools, so why didn't they switch? Well, in the short run, the participant can switch with sick with tools because the platform might offer exclusive access to the users of the annex tool on the other side of the market, and they can degrade interoperability with a competing tool. So if either the publishers sponsored their own tool, or if an independent tool came in, what they're worried about is that that tool might not interoperate with the largest platform because the biggest platform might refuse to interoperate with them. So you might go to all this effort to create a new tool and get people on it, and then it's not going to be useful because it can't access the other side of the market. So there's sort of this chicken and egg problem. And you can be blocked from getting the egg if there is unique access on the other side of the market, and that was the case with the advertising exchanges. And the incremental value to a participant of accessing a smaller platform is low. What's most important to the participants is getting access to the most users on the other side of the market. In the long run, the participant might stick with tools because the smaller platform might deteriorate, and so multi-homing just becomes less important if the other platforms are weak and don't provide enough users on the other side. So it can be a little bit like predation where you can degrade performance with your tool for the short term, but if you succeed in weakening the competing platform, then in the long run, you know, they're basically, in this case, inducing exit save or weakening rival ad exchanges, and once there aren't rivals, then there's no point in having another tool that helps you access those rivals. And why don't new tools enter? Again, tools, there may be switching costs for the users and scale economies, and the large platform has the threat to withdraw or reduce interoperability with new entrant tools. And so really, it's this kind of, if you can control both the biggest tool and the biggest platform, these dueling Xs here can reinforce each other and prevent entry and competition in either tools or the ad exchange. So that's the basic theory that we've laid out. And so, you know, we've talked, I've already kind of talked through what the, you know, welfare impacts are just to summarize from an antitrust perspective. It's more like horizontal than classic vertical conduct. It creates conflicts of interest rather than resolves them. And in its enables a platform to increase take rates. And again, this is a theme that Steve Salop has in has mentioned as well that sometimes a vertically related product really helps support competition. It's more likely to be any competitive if there's strong and direct network effects and scale economies, and if it's undertaken by the leading firm. Sometimes lagging firms need to build their own tools. So we shouldn't necessarily just blanket prohibit people from building their own tools, but but they're more likely to be using an anti competitive way from a smaller firm. And if there, and there's barrier to entry in tools and remedies could include preventing merger requiring divestiture or requiring interoperability and non-discrimination, or avoiding exclusive or exclusionary practices. So let me stop there I'm out of time. I should also mention though I didn't mention platform development by Eisenman I had a slide coming to that later and this also relates to that so I just didn't want to short change that reference. So let me stop here and we can have discussion. Thank you very much Susan so let's hear from Steve Salop for a few five minutes. Okay well I actually prepared comments on the paper, rather than on the talk the talk actually answered a lot of questions I had about about the paper. There's more geared towards the law group rather than the economics group and, you know, in that regard I thought it was a really terrific non technical explanation of the economic foundation of the Texas AG's case. It's a lot clearer than the complaint if you read the complaint you're going to find that this the papers a lot clearer. And so I certainly hope that the Texas AG and the Texas AG's team and their expert read this paper. Because it'll be a definite compliment to to their complaint. In terms of the, the, the economics. Well Susan laid it out very clearly I want to make it even, maybe even a little clearer. We talk if you start with the single monopoly profit idea. There's this question of why doesn't a monopoly exchange simply set high unbundled prices for the platform, rather than tying. And the idea is that the tying raises barriers to entry it prevents moldy homing and forces entrance in the in the simple vertical model to attempt to level entry. Now in the case of Google as you saw from Susan's presentation, it's not preventing to level entry it's really three level entry that an entry would need a rival platform and then tools on on both sides. Or in fact it's really maybe five level entry. Once you add add servers for search advertisers. And you separate out small advertisers and and large advertisers. So certainly harder to enter at five levels that it is to enter at one at just at one level. And you know, even aside from the fact of that they're switching cost network effects scale economies and uncertainty. I mean, my own story is I once asked John Malone who was a tech billionaire he owned the largest cable network in America TCI and he's now Liberty Global in Europe and Latin America and he had written a paper in the original bell journal of economics so I felt I could And I said well you know there's this single monopoly profit theory. Why don't you just raise the price on for TCI, rather than vertically integrate into content which he had done he owned a lot of a lot of content still does. And his answer was well if you just raise your price of the of the product of which you've got a lot of market power. That just puts a target on your back it's going to attract a lot of entry from people that see those hot that's high prices. It's better to expand your real estate that raises barriers to entry. And that's what this paper is all about is what Google does is it keeps expanding the real estate and that's what the other tech platforms do as well in order to raise barriers to entry. Regarding regarding the paper. Well, let me make one other one other remark about the economics. What Susan calls raising rivals cost I call in my own terminology input foreclosure and which he's calling vertical manipulation. I call customer foreclosure, which is Rasmussen and and Siegel and Winston but here in a dynamic context, rather in the static context to which they had it. The regarding the you know the paper itself. I would have liked to have seen in the paper. If you had gone back to Microsoft, because the original tool the original manipulation of the tools was Microsoft's killing Java and Netscape, which were tools to create multi homing I thought that would help a lot in the paper. The only thing I really didn't like about the paper is something that Susan alluded to at the end, which is this pandering of saying, this isn't vertical it's horizontal. Now, the authors are quite explicit about that they just don't want to confuse or offend anyone that thinks that verticals good and horizontal is bad so if it's bad we're going to call it horizontal if it's good we're going to call it vertical. While I appreciate the goal I'd prefer that we educate our audience and teach them my formulation is to say, well the conduct is vertical the anti competitive effects are horizontal. And that seems like a pretty straightforward way to say it. And it connects to this idea that Susan alluded to in my new paper with Sirj Muresi to show how the indirect competition is eliminated but when when there's input foreclosure. We actually show in this new paper which is on SSRN that input you can treat input foreclosure as as increasing what we call an effective HHI in the downstream market. We create a modified HHI that captures the effect of the of the foreclosure. So one other comment I've got one of the comment on potential research. The monopoly platform that is compensated on the basis of a fraction of the buyers of the buyers price, or based on the number of you have successful matches. That monopolist does not, in order to, in order to maximize its revenue it does not want to maximize its take rate for transaction, rather it might want to maximize the number of transactions. So let me give you an example, simple example. Suppose you've got three buyers, advertisers if you will, with willingness to pay a $5, $4 and $3. And suppose you've got three sellers, publishers if you will, that have willingness to offer of $2, $3 and $4. So $5, $4, $3 on the demand curve, $2, $3, $4 on the supply curve. I should have mirrored, I'm sorry. And so, you know, the optimal number, the efficient number of matches is $2. And the gross surplus would be $4 if you actually do the arithmetic. That is, you can imagine the way the matching would take place. You'd match buyer number five with seller number two, and buyer number four with seller number three, but then buyer number three could not be matched with seller number four. So the efficient numbers two. But if the platform is paid per successful match, if you want to think about it that way, they want to match buyer number, buyer number five with seller number four, buyer number four with seller number three, buyer number three with seller number two. They could, the monopoly platform could create three matches. It would then get paid for three matches and certainly on its percentage, it could make more money that way. But yet now there are too many matches. We have outputs exceeds the competitive level and surplus falls. So what this means I think in terms of antitrust, in terms of economics, you can work out the the maximum number of transactions of successful transactions, depending on the distribution of buyers and sellers. As a matter of antitrust, we should not be using total output as a measure of welfare, because in this case you get more than the competitive level of output. And this actually came up in the, in the US, the sort of abysmal American Express case in which the, the court said well output of credit cards went up, not down. And therefore, it must be pro competitive, but in fact it ignored the fact that the way in which the structure with the no steering and created a prisoner's dilemma, and that leads to a greater than competitive level of credit card transactions. So that's, those are my comments.