 Good afternoon to our friends in America. Good afternoon to our friends in Europe. Good evening to those of you who are in Asia. My name is Alexander Karnier. And on behalf of the organizing committee composed of Jacques Trimaire, Daniel Erschoff, and Paul C. Bright, I'm very happy to welcome you to this 14th edition of the TSE Digital Economics Conference. By now I'm assuming that most of you have seen the program and even though circumstances prevent us from holding this event in Toulouse, we are very excited by the program of these next two days. The format of this conference is a bit unusual, but we hope it will be conducive to interactive sessions. So presentations will be shorter than usual. And so let me remind you that most presenters have also submitted a 15 video of their presentation available on the conference website. The organization of this event would not have been possible without the extraordinary work of our administrative staff, in particular, Florence Chauvet and Christophe Rocher, who have been of great help with all the logistics for an unusual format. Thank you. We also thank the various partners of TSE and of the Digital Center. This conference will be recorded. So before we put anything online, we will ask the various presenters for their approval. Our first event is the Susan Scotchmer Memorial Lecture, which is going to be given by John Vickers. We're very honored to have John. And the session will be moderated by Jean Thierryle. So without further ado, John, I'll see you. Thank you, Alexandre. Welcome, everybody, to the Susan Scotchmer Memorial Lecture. We all remember our fantastic research and being such a great human being. It's always a pleasure to honor our memory. I couldn't think of a better person to give that lecture than John Vickers. So John is a professor of economics at Oxford and the warden of Osall's College. He has at least two lives, probably more, but the life as an academic was done very pioneering research in industrial organization and regulation and banking. And personally, I've learned a huge amount from his work and actually have used it. Actually, most recently, the Vickers rule my last paper, published paper with Emmanuel Fari was partly on the Vickers rule, actually. And he has also had a life as a very important policymaker. Again, in many fields, he was head of the Office for Fair Trading. He was a chief economist of the Bank of England. He was part of the member of the Monetary Policy Committee, also the Bank of England. He was a chair of the Independent Commission on Banking. And despite all this, he's still doing terrific research. Often when people go and do other things, they stop doing research and John is still doing fabulous research as you'll notice today. So without further ado, I would like to, we don't have that much time. I could speak for hours about John, but I think it's much better to listen to him. John, the floor is yours. You're going to talk about patterns of competition, information and price dispersion. And thank you so much for doing it. We are very honored. Thank you so much, Jean and the organizers for giving me the opportunity to speak at this event. And in particular, to give the lecture named for Suzanne Scotchma. Let me pull up slides if I can and outline what I plan to talk about in the time we have ahead. But first, I want to, this is all conferences about digital, but I'm going to begin with a picture of how the world used to be before digital economics. This, if you don't recognize it immediately, is the cathedral, the Duomo in Siena. And it is a place where I received some particularly important career advice, and it was from you, Jean. I don't know if you remember this. It was the second of December 2004, which I know because I found in a pilot paper the program for the then second annual conference of the Association of Competition Economics, which many of you belong to and know, and it brings together economists from universities, from the competition agencies, and from consulting firms and so on. And the first session had the two of us in it, together with David Evans, well-known in Toulouse and elsewhere. And I was coming to the end of my time at the Office of Fair Trading when this conference happened. And before that, I'd had two and a half years at the Bank of England, as you had mentioned. So I had this sort of daunting prospect in front of me. I said, how on earth did I get back productively into academic life? And because I saw us on the program together, I asked for the huge favor. Could we meet on the steps of that cathedral at noon and have lunch before the three o'clock start of this conference? And my question was, what have I missed in IO, particularly IO theory? And you said many things, but the two of the two of the core remarks were very relevant to our topic today were that two things that had happened were economics of two-sided markets, which had got underway at that turn of the century phase. That was one. And the other was bounded rationality meets industrial organization. Now, 2004 digital was there, but it was nothing like what we've seen in the last decade and a half. Now, at almost exactly the same time as that, and I do want to mention this, was the Suzanne Scotchman book, I think, was published November 2004. So almost exactly that. And her body of work and others work on innovation and incentives is, of course, hugely pertinent to the issues about the digital economy that are the subject of this conference. It's also an area that I used to work on as game theory models with Chris Harris, and we teamed up with Philippe Baguio subsequently. But that's not the aspect which I want to talk about today. I do, however, want to pay tribute to Suzanne's work in this area, which I think has had a huge influence on all of us, and an especially admirable part of that. And I did notice, as we were gathering in the, on this call is Stephen Mora, who was a co-author of some of the chapters in there. It's not just economics that you get from her work and from this book, but it's also economics together with the historical and legal context. And I think that combination, which very few people successfully bring together, she is a shining light in many ways, but in part for doing that. So let me now try and zoom in on some of the issues I do want to talk about. On this slide, I'm not going to cover this whole agenda at all. In fact, I'm not going to talk explicitly about two-sided markets, which was one of Jean's two points that he mentioned to me in that Sienna discussion 16 years ago. But the other two were the bounded rationality point. And I think of this more generally as imperfect consumers, consumers who are not like economics 101 textbook consumers. They have limitations, they have limited awareness of what's on offer, and they perhaps search, do or don't search around to try and find better deals. And one of the points about digital, I mean, this isn't specifically for digital, but it's relevant to digital, is that search technology for consumers and of course for businesses has enormously improved. So on the one hand, we have a transformation, positive transformation in the ability consumers to become more aware and to search around. But on the other hand, and this is the third block here, the information that sellers have about consumers is also enormously expanded. And so too, in conjunction with that, have the opportunities, if permitted, for various kinds of tailoring deals, price discrimination, and so on. And this isn't in a standard pure monopoly setting where most the earliest work on price discrimination happened, it's in more competitive settings. So what I want to talk about a little aspects of the second and third of those elements there and put it into the wider theme of the information structure of markets, which is quite a hot search here at the moment, as indeed some papers later in this conference will illustrate. So I'll talk about those things and the plan I'll begin by talking about the notion of prominence and linking that to price dispersion. Price dispersion we see very much all around us, quite diverse prices, often for exactly the same product or service, despite the digital transformation. So how can that happen? Why does that happen? Sometimes happens in markets which on the supply side look reasonably competitive, not brilliant, but not terrible. And prominence has, if you like, become more prominent with digital because the way information is presented to consumers, particularly search engine results, the framing of the choice structure seems to be tremendously influential. So the economics of search and prominence seems one good topic. Then I'll talk a little bit about an aspect of price discrimination where firms, sellers, can identify who doesn't have much choice and who does, so against captive customers. Then third on this list, give a sketch of some work underway with Mark Armstrong on patterns of competitive interaction, how patterns of consumer awareness relates in theory models to patterns of pricing, and again the good deals, bad deals point. Then fourth talk about some work we've got underway now, multi-brand firms. And of those four things at the top there, the first two are published and I'll say where. The third one is available in a working paper form and the fourth one is unwritten. Now I underline and highlight just how important Mark has been to the collaboration on all these strands of work. This is joint work that I'll talk about and some of it is also with Mark's former student but now at Yale, Zhigong Xu. So triple underlining of thanks to them and in particular to Mark. Okay so begin with provenance and price dispersion and I want now just to mention and give a sketch of two issues that surfaced in the literature 10 plus years ago. I should stress I am not giving a balanced literature review. This is all very selective, enormous bias in favor of focus of work that Mark and I have been doing. It's just one angle into this much wider set of issues and I want to try and convey the essence of it and what seem to be the key points coming out of our current work. So let me begin with with provenance and price dispersion. As I've mentioned and this is an old point I mean in the economy centuries ago some sellers would be more prominent than others in marketplaces but with digital with search engine results presentation of results prominent seems ever more important. So a good question I think a good set of questions is whether prominent firms which often seem to charge different prices from less prominent firms do they tend to give good or bad deals? Now ultimately that's an empirical question and I'm not going to be talking about the empirical side of things today but I want to draw out two underlying points that go in different directions that bear on that. For a general survey of this of ordered consumer search I recommend Mark's Marshall Lectures of European Economic Association 2016 which appeared in GIA 2017. So to try and see what the underlying economics is let's take a super simple setting where there's a bunch of sellers and let us suppose that one of them is prominent it's seen before other firms and let's say that's true for all consumers to keep it really simple. You could obviously generalize to other settings. So Mark Shadong and I had a paper came out in round general 2009 in which in a model with that key asymmetry between sellers but otherwise with but with symmetry among consumers particularly with respect to search costs it turned out that the prominent firm the one that everybody goes to first offers a relatively good deal a better deal than the other firms because of the following economic effect. I won't spell out the details of the model because of the time pressure that we we all have but the basic idea was symmetric consumers a sequential search model so each consumer can pay an amount s and it's the same for all consumers to have a look at one more firm down the the list of firms let's say. It's a match utility model I need to go into the details here but the upshot was that if the only asymmetry is the prominence asymmetry among the sellers turns out that the prominent firm has more elastic demand than firms further down the queue so tends to price lower and be a better deal relative to the others so that in a sense made the search order that everybody going to that firm first a rational thing to do because chances were you get a somewhat better deal from the first firm than the later firms. What's the intuition and this is the point I want to try and get across I think it's best conveyed in the two firm case the two firm case the people that go to the second firm by their revealed behavior didn't much like what was on offer at the first firm that gives the second firm a kind of market power over the people that eventually get to it even though they might just be a minority of consumers and that that less elastic demand causes a higher price to be the equilibrium outcome for that firm than the prominent firm and what determines what's prominent well in the otherwise symmetric model it could be arbitrary any firm could be prominent and that would be self-reinforcing the the search order that could prevail but of course there are differences between firms in fact some might have better value underlying better brand value or lower costs than others and in the main line of analysis in the paper I just mentioned it's sort of fairly benign result those firms would have more incentive to become prominent than others Mark and Chidong sometimes we had a paper on paying for prominence in that line however a completely different effect contrasting effect I want to say more about in what is to come first by reference to a paper by Albert Skyros around journal a couple of years earlier and here was a very different kind of asymmetry it was asymmetry among search costs across consumers and here you got the opposite kind of result from the different kind of asymmetry here and she described it as as consumers go into the bizarre the sellers near the entrance which even the consumers with relatively high search costs would sample and sample first they would give a relatively bad deal because as you go deeper into the bizarre or down the list of search results then the high search cost means that the high search cost consumers that only sample the early firms those have less elastic demand and they will tend to get relatively bad deals relative to the others so that's a very different point and we're going to pick up echoes of it in some of the models to come later on so this is a sort of hold the point for now in that ran journal paper Mark Chidong and I did have an example of the Albert Skyar type which chimes with what I'm about to talk with just next so let me say a little bit about that an extreme example of different asymmetry among consumers with respect to search costs so here's suppose um fraction lambda of consumers have no search costs at all they can look at all the offers no problem at all no cost whereas other consumers can only see the first firm they come to and suppose that firm is common to all consumers then if you've got three or more firms you get this very very stark result which is that the prominent firm in a sense just rips off the non-searchers those for whom search is prohibitively costly all the other consumers no search costs they have consumers competing perfect competition to supply them so they all get great deals so even though no firm is discriminating in that simple little story that parable it is equivalent to a model and I'm now going to come to an explicit model like that of perfect discrimination against the captive customers that is to say those who have the prohibitively high cost of searching beyond the first firm that they all come to and that's going to be the next topic and I want to talk about some of the simple welfare economics of discrimination against captive customers so as I mentioned in the introduction price dispersion variation among of price among firms or even single firm charging very different prices apparently for the same product to different consumer groups that seems a pervasive feature of markets digital transformation has not banished that phenomenon at all there's good reason to think that in a number of settings it has exacerbated it so what what economics can can we think about in terms of economics of price dispersion either between different firms or and or by one firm for essentially the similar or same varieties of the same product well one place to look and this is what I'm going to focus on today is that consumer awareness of what deals are on offer seems to vary greatly and there's an empirical literature documenting this too so the line of work I'm going to talk about is one where consumers differ consumers groups differ in respect of their so-called consideration sets some consumers might easily be able to see all the offerings in the market their consideration set is all the offers in the market other consumers think of them as the captives they can only see an extreme start form the offering of one firm and there are clearly a whole range of possibilities in between so how all these consideration sets relate to each other and what that means for market outcomes that seems to us a potentially interesting research topic where there's a literature from about 40 years ago which makes a very good start into that and I'll mention a few papers in passing as we go but what Mark and I are trying to do is to push the envelope a bit further in the line of that literature so forms of discrimination of that kind they seem pretty common there are some examples there are some UK competition inquiry examples loyalty pricing you see that in many markets for example again with more time I could document more and more examples of that and a very natural response of policy makers when they see the captive customers the vulnerable customers those who don't shop around those who appear to be disengaged from the marketplace getting poor deals a very natural responses to say well why don't we ban discrimination even though it's a more or less competitive market in general why don't we say that firms can't charge higher prices to the vulnerable than the others they've got to have a kind of constraint that firms do not discriminate on the basis of vulnerability or lack of shopping around activity of those who are disengaged from the market and there's clearly some appeal to that including if the vulnerable tend to be poorer consumers including on distributional grounds as well as efficiency grounds but kind of warning is that the literature on price discrimination in oligopoly and I mentioned a couple of papers at the bottom of that slide does show that banning discrimination can quite easily soften competition to the detriment of consumers in general so there's not a there's not a no-brainer here so in a paper published a year or so ago in AER Insights Mark and I looked in a very simple model with these consideration sets at some of these issues about discrimination on the basis of captivity and I want to link that to this wider set of work which many are engaged with and I'll mention just one or two examples looking at how information structures in markets that's what firms know about consumers what consumers know about firms how these patterns of information can can play into market outcomes in quite strong ways let me sketch and this is only going to be sketch and headlines and intuitions let me sketch the framework that we look at in that paper so let's suppose we have a representative consumer where you can generalize it to heterogeneous consumers provided that dimension of heterogeneity is independent from whether consumers are captive or not let's normalize cost to zero going to do that in everything I talk about henceforth just for simplicity let's suppose that profit per consumer so that's this profit function here assume that is single peaked up to the monopoly price so we've got downward sloping demands it's all very standard and we're going to suppose for most of the analysis that it's going to be duopoly though I'm going to state one result a bit more some things come true more generally so consumers either consider just one firm could be firm one they look at could be firm two each of those firms in general have some captives and then some consumers will look at both so if the fraction sigma i consider firm i then the others fraction one minus sigma i those are going to be captives to the other firm to firm j let's label firms so that firm one is the larger of the two though they might be symmetrical and then a key thing to hold on to in all these models is row i that is the captive to reach ratio of firm i and given that firm i is the larger firm that has the higher ratio that than does firm j so is it a good thing or a bad thing for consumers for welfare to allow firms to discriminate on the basis of captivity if they can so the extreme form of price discrimination would say firms can identify precisely who their captives are they can charge rip them off charge them the monopoly price so then those consumers would get surplus v of p star whereas if they're doing perfect price discrimination the non captives those are going to get a great deal because there'll be virtual competition for their custom between the firms price will be driven down to cost zero and you'll get this much higher surplus level and in that world if perfect price discrimination on the basis of captivity is both possible and allowed then each firm will get its captive profit that's the monopoly profit on the fraction of consumers alpha i which are captive to it now what happens in the other environment where firms either cannot observe his captive or they can but they're not allowed to discriminate on the basis of captivity here we're in the world of mixed strategy equilibrium in prices the literature of 40 years ago roughly which is a taking off point for this would include the papers in the review economic study symposium 1977 butters for example it would very much include Hal Varian's model of sales AER 1980 and then a very important paper in this line is Burdett and Judd econometric 1983 on equilibrium price dispersion price dispersion the very term which is the centerpiece of what i'm talking about today so what happens there is that you have mixed strategies both firms will price in this interval P naught up to the monopoly price where P naught meets this condition the profit per consumer at that price is equal to the monopoly profit per consumer times the larger firms captive to reach ratio and in this world in this environment the larger firm gets its captive profit in expectation so exactly the same as it would have got with price discrimination whereas the smaller firm does better than with perfect price discrimination the intuitive reason is that the larger firm doesn't want a price too low because it would do better just by gouging its captives and this kind of holds a price umbrella up over the smaller firm which allows that firm to make more profit than it would have done otherwise so what's the deal for consumers well the firms are making more profit except in this metric case when uniform pricing happens on the other hand with uniform pricing consumers get more similar deals to each other you still get price dispersion because in general the firms will charge different prices but you won't get the stark difference in the deals that consumers get under price discrimination so obviously if you're a captive you do much better with uniform pricing if you're a contested consumer you do much worse which way does the overall effect go and the key point here this is the kind of a heart of the paper is don't think about prices directly but think about consumer surplus as a function of profit so whereas consumer surplus as a function of price is convex with demand curve slope down consumer surplus as a function of profit is not entirely generally but pretty broadly a concave function so one way to think about that is consumers are risk averse about profit variation if I didn't know whether I was going to be a low profit consumer or high profit consumer I'd be risk averse about that under a mild condition on demand in particular it's the condition that demand elasticity with price defined net of cost is increasing with price and what the thing that corresponds to risk neutrality is unit demand where not sloping down but just the vertical demand so this brings out the trade-off and really quite clearly firms cannot gain from this form of price discrimination pricing on the basis of captives we established that earlier but for consumers if we have a very symmetric more or less symmetric market consumers are harmed by discrimination because the profit gained to firms is small whereas the riskiness lost to consumers under the stated assumption is high on the other hand with sufficiently asymmetric markets under mild conditions it goes the other way the profit benefits to firms from discrimination which is a loss to consumers outweighs this riskiness point so what that paper is about is to compare the levels effect with the risk effect when one flips between the discrimination regime and the uniform pricing ratio what we do towards the end of the paper and this takes us into this burgeoning literature now on information structures is to say well look that's very stark that form of price discrimination can't we look more generally at information structures in markets and discrimination based on whether somebody is captive or not there could be many other kinds of discrimination less perfect we could think of partitioning consumers into submarkets let's say it's public signals with firms able to condition their pricing strategies on those public signals what happens then and then you have a link to the work on monopoly by bergamot and others and very much to their their recent work and I think there are papers later on in this very conference which are in this line on search information and prices and the analysis can be expanded to more than two firms to private signals as well but just to explain with a simple example in the setting mark and I looked at if you start off with a symmetric overall market and of course that's a strong assumption then any segmentation of the market into partitions is going to be bad for consumers that's good for firms can't be bad for them and it's bad for consumers now if the market as a whole starts off high in a highly asymmetric way you can get the opposite so a lot of this is about moving between symmetry and asymmetry but let me give an example of what I'm sorry to call it a theorem it's so pompous I meant I couldn't work out how to call it a proposition in the software but anyway um here's an illustration of it if you look at that picture um the these to pick consideration sets and let me tell a story as though these are regional monopolists in let's say an energy market which is a an issue we had a long inquiry competition inquiry in the UK so suppose we start off um with uniform pricing and there's a northern firm which is the upper circle and a southern firm which is the lower circle so the consumers diagrammatically here are captive to the northern firm the ones down here are captive to the southern firm and the ones in the middle are contested so if you pretend you've got equal density of consumers in each of those four areas that would be captive to reach ratio of each firm of one over three because those are the northern captives and these two areas with the dotted line are the contested but imagine firms now can discriminate on the basis of geography whether consumers are in the north or the south above the equator or south of the equator if they can do that kind of segmentation then in each sub market in each of these partitions captive to reach ratio is now a half and we end up less competitive uh in that situation in this example prices rise for all consumers and all consumers lose a hand from that form of price discrimination so this example is no more than an appetizer and there's this much wider literature and I think there are some very good questions about what are the maximally and minimally profitable or the maximally and minimally um good for consumers information structures in markets so my point in all this in a way is just to sell that question um which only in a way in toy examples did mark get into in that paper and the work by bergamot brooks morris and and many others now is looking at questions of that kind it's not specifically digital but it very much relates to it now let me move on i want to move away for a moment from questions about price discrimination by firms to look at issues about price dispersion with as it were in inter firm uh variation of prices different firms supplying different prices and talk more about this patterns of competition point i'm not going to delve into the details of the modeling i am going to come back to the prominence point which i flagged earlier but i really want to give more of flavor again by way of appetizers of um this line of work so now assume each firm does uniform pricing at the end i'm going to change that assumption but hold that for now suppose it's unit demands so we get away from that convex point we just had earlier one can generalize this but it keeps it simple let's look at this consideration set model so each consumer is going to buy from the lowest price firm in her consideration set it's going to be exogenous which offers which consumers see and notation is going to be that an exogenous fraction alpha s of consumers see precisely the firms the offers in set s so let me hop forward to a little diagram this is a three firm example then diagram so these people alpha alpha one they see only the offer of firm one likewise alpha two alpha three these people here they see both one and two but not three and these people in the middle see all three offers so you could draw these diagrams in all sorts of different ways but i hope that conveys the general idea now it will be lovely to have these sets endogenous whether by search behavior advertising by firms word of mouth or whatever um we could build a story about that but to make progress to begin with let's ask the question of how the patterns of consumers might relate into enterprise outcomes um as i indicated earlier this is in in a line of literature that goes back to those papers and i highlight specifically howls and the burlett and jud econometric of paper so the sort of question we ask is how do the range of prices that different firms offer how how do those relate how do the resulting market outcomes relate to the underlying patterns of consumer consideration and how would things like entry by new firms exit by firms mergers of firms how might that change those outcomes again we're in the world of mixed strategies we know that there's a mixed strategy equilibrium from uh desktop to masking what do those equilibrium outcomes look like well it took um us a long time to arrive at what we now think is the key to this problem and the key to the problem we suggest is this variable here gamma s which is a measure for each set of firms set of products s of um the intensity of interaction between the um uh the firms how much they interact within that set so what it is it's that gamma is the proportion of consumers that see the firms that's in in that set and possibly other firms too divided by the product of the overall reaches of each firm in that set so it's hard initially to get a grip on it for um any any singleton set that gamma is one it's also one if we have the um setting of independent reach whether it's um independent probabilities about whether a consumer will see particular products and the literature in this line and there are some 1990s papers um many of them assume independent reach which is which is a very elegant setting if the firms in this set compete more than averagely intensely they interact particularly strongly then that gamma variable um parameter is greater than one in the opposite extreme of disjoint reach if there are no consumers who see both firm i and firm j then then it is zero so let me sketch how this comes into play we say that a market has symmetric interactions if that parameter gamma s depends only on the number of firms in that set this class includes essentially all the models looked at in the 80s and 90s line of literature in this area it includes duopoly including asymmetric it includes symmetric models it includes independent reach and so on however it's broad enough to allow firms to be um quite entirely different from each other in size what happens if we have a setting like this well in fact equilibrium and payoffs i'm not going to detail what the mixed strategies are it is really quite simple and intuitive so under the stated assumptions of that theorem which i think are mild we have a unique equilibrium each firm mixes use mixed strategy from the same common minimum price p0 up to the firm i pi where that p0 is the captive to reach ratio of the largest firm and each firm's expected profit is that p0 multiplied by its reach the maximum prices they are in an increasing sequence so the largest firms they price all the way up to the top uh the monopoly price under remember this is inelastic demand up to um choke price one smaller firms don't go so high so this in another way is how the larger firms kind of the more prominent ones on average charge higher prices than smaller less prominent firms those seen by fewer consumers so it's a kind of stochastic thing but all the firms are competing with each other in some of the price range so it's head to head competition among everybody comparative statics for exit and for merger i won't do more than give you the headline which is they're what you would expect exit of the firm raises the base price raises profits bad for consumers a profitable merger again does the same raises the base price raises everybody's pricing and in this setting reduces consumer surplus but what if we are away from that world of symmetric interactions what if the Venn diagram instead of anything like the earlier one looks like this this is sort of darts players model so this is the case of nested reach this corresponds if you like to audit search again takes us back to the prominent point you can think of people going down results on a internet search results page and the idea here is that um in this simple picture there are some consumers those in the entirety of the big circle um sorry what there's one firm that everybody sees then there's a smaller firm that not everybody sees only a medium group of consumer see and then the smaller firm is a smallest firm is seen only by a subset of consumers so here the only captives there in the outer ring they are captives to the larger firm and the smaller ones don't have any captives at all because anyone that sees them also sees firms larger than them so this is a radical departure from what we had before again one could tell a story about prominence and search results here we get something that can be completely different so what happens here is that each firm prices in a price interval but there's a sort of potentially a ladder that goes up that the larger firms even though the underlying product is identical cost structure is identical they price higher than the um uh than the smaller ones and while it might be that all firms price at the at the bottom so they're competing head to head what you could easily get is this almost partitioned price structure which we call overlapping duopoly so if the increments of the reaches are increasing as in that inequality chain in the middle of that proposition stated there then we get the pattern we call overlapping geographies in which each firm as it were competes with its neighbor in size but not even with its next door but one neighbor so each firm uses a price range and it's sort of duopolistic competition but the larger firms price in an entirely different upper bit of the price range than the smaller ones so the head to head competition is only between neighbors and not between those who are other than next door neighbors the comparative statics when we move away from symmetric interactions can also be entirely different from what we had before and from earlier intuition so here and it's a particular information structure but I think it has some intuitive appeal imagine that diagram at the top without the entrant to begin with symmetric duopoly then suppose we have an entrant who comes into precisely the contested area it doesn't compete for any of the captives firm one or a firm two it's only in the contested area in this class of models that form of entry is bad for consumers because it does nothing to dent the profit of the erstwhile incumbents the entrant makes positive profits so it's bad for consumers so what's going on here is that the entry causes the erstwhile incumbents to retreat back towards their captive segments and I mentioned it here not as sort of again these are all little toy models toy examples but to get across the point that the information structure the patterns about which consumers can see which firms can drive results in a simple setting like this entirely contrary to the intuition that one might have in other settings finally this is the work in progress multi-brand firms so I talked about some of the above but in the my eerie lecture at the end of august and one of the comments in emails afterwards came from at Andrew Rhodes who's probably on on here was well okay that's all very well for mergers but why assume the merged firm charges just a uniform price why don't you allow firms to charge if they're multi-brand firms allow them allow them to charge different prices so that's what mark and I working on now is the same framework as just discussed but now ij and so on those areas in the in the Venn diagram think of them as distinct brands and allow the possibility that some of those multiple brands are co-owned by the same firm what what happens then very basic question is would such firms want to use discriminatory pricing or not if they had the freedom to do so now potentially this is quite complicated because this is could be multi-dimensional mixed strategies we're a little bit offshore from the desktop to mask an existence theorem so we can't even be sure that equilibrium exists though and we've been in touch with power that we think it does but let's take this question will they use discriminatory prices or not what would what's your guess i think a natural guess so it turns out to be wrong you might think well it's only in a knife edge case would affirm want to use uniform pricing if it had the freedom to discriminate that in fact turns out to be wrong and i want to illustrate why so again i'm going to talk about captive to reach ratios and here this is just the same definitions before for firm a row a is the portion of consumers captive to a divided by the proportion of consumers that see firm a in some form who see at least one of firm a's brands so here's a very simple result to get started you get this one for free if each firm has the same overall captive to reach ratio then with uniform pricing where they can't or don't do the price discrimination each firm's payoff will equal its proportion of captives if you allow firms to do price discrimination then they can do at least that well just by gouging their captives so they can clearly do equally or better and this is just like the earlier result um from that bit of the a our insights paper where the overall where an overall market gets segmented more generally though um there are more interesting things that one can say so let me take um a two firm case some of this generalizes some we don't know how to generalize let's suppose that firm a is a two brand firm and now define a kind of modified captive to reach ratio row i this is for the for brand i its consumers captive to firm a the owner of brand i divided by the reach of brand i the number of consumers who consider that brand let's think about firm a's best response to firm b under the assumption that firm b the other competing firm is pricing uniformly it might be a one brand firm so it has to price uniformly or it might be a multi-brand firm that is doing uniform pricing will firm a want to do uniform pricing charge its two brands the same price or might or will it want to go different for the two prices maybe have a high price one and a low price one even though they're intrinsically the same well the answer is that uniform pricing is the best response if and only if the condition in that proposition holds for both brands it is a very very simply stated condition and if it does not hold if the some brand or both brands for whom it's not true that inequality then intuitively that brand in isolation has more elastic demand in effect than brad then firm a does overall if it prices the brands the same so brand a would want so a would want to price the two brands apart whereas if the condition in the theorem does hold firm a would not wish to price them apart it would do better by gluing them together so this is a kind of do the elasticities go the right way or the wrong way kind of a point so if we now have brand B as a two brand firm as well then if that condition holds for both brands of both firms then we have a uniform pricing equilibrium but what if it doesn't what does equilibrium look like first I should say though what does it hinge on whether that condition holds it's partly to do with whether the probability of a consumer that sees both my brands whether the chance of that consumer being captive to me is greater than for a consumer that just sees one of my brand that's one point up at the top the second issue is the asymmetry between brands if my own brands are asymmetric there is more chance of that condition in the theorem failing and then we know we don't have the uniform pricing equilibrium forgive me racing ahead but given the time I have to so one type of equilibrium that you get quite often when that condition for uniform pricing fails we call segmented equilibrium where each of a again two brand firms each firm prices one of its brands high and what in a high interval in the range and one of its brands low so even though there's no intrinsic difference between the two brands in terms of quality or cost one is a kind of fighting brand essentially aimed at the consumers who have a lot of choice and the other is a high price brand aiming at those who have less choice so this is a kind of intra firm price dispersion price discrimination but there are a number there are many settings where you get neither that form of equilibrium nor the uniform pricing equilibrium you might get a kind of mixture of those two pricing strategies or and there isn't time to explain it today you can get some quite well to us surprising things which are neither of the above we have found some equilibria which are neither the segmented pricing just described nor the uniform pricing I should end with concluding remarks the meta theme of all this has been that one of the many things the digital transformation has done is to enhance both consumers ability to discover and compare different deals and sellers ability to discriminate among consumers I think it's highlighted how the way that information about market offerings is presented can be tremendously important determinant of market performance price dispersion is clearly highly pervasive has not been eliminated by any means by digital developments and we see many markets whether which are not monopolistic whether sort of some competition at least where we get dispersion discrimination going on which has all sorts of effects which are a priori non-obvious I think it makes information structures a very good research topic I've been running through some theory lines of theory literature largely toy examples but trying to give the flavor of a research agenda and of course it will be wonderful to make all these things endogenous but that is for another day thanks very much