 Hi everyone. Welcome to the online economics of platforms seminar. Today we have Andrew Robes presenting from the School of Economics presenting platform design when sellers use pricing algorithms. And Alex McKay discussing. Andrew will have 40 minutes for his presentation with clarifying questions from the audience. Alex will have five minutes for his discussion and then we'll move on to a general Q&A. I will stop recording after an hour but we welcome the discussion to continue and I will stay here as long as it's needed. Before we move to the presentation let me just remind that if anyone in the audience has a paper on platforms that they would want to present please contact us and especially Julian Wright and Andre Hadjou. And with that let's move to the presentation. Andrew the floor is yours and you're welcome to share the screen with your slides. And also unmute yourself. Okay can you hear me? Okay so thanks very much for the invitation and thanks everyone for attending. This is joined with Justin Johnson from Cornell and Matthias Wildenbeest from Indiana. Okay so in the interest of time let me be pretty brief with the motivation. So many products are sold through online marketplaces and increasingly sellers on those marketplaces have access to software which use algorithms to set and then change prices. So for example as far back as 2015 it was estimated that around 30% of the best selling products on the Amazon marketplace were priced by algorithms a number which is probably significantly increased in the last couple of years. Now this increased use of algorithms has prompted a debate. So on the one hand there are some people who might argue that algorithms could lead to fiercer competition. They make it easier to adjust prices in response to changes in cost or demand conditions. On the other hand there are other people who are concerned that algorithms may lead to collusive outcomes. So there are a couple of cases where algorithms were used to implement collusive schemes designed by humans. But arguably more interestingly there's recent evidence from economists showing that algorithms may learn to play collusive strategies even when they haven't been designed explicitly to do that. So our contribution to this debate is to note that irrespective of whether algorithms lead to more or less competition platforms are not passive participants. Platforms can design certain features of their marketplaces to influence the way that sellers and their algorithms price. Okay so for example platforms can affect the way in which sellers are ordered and ultimately displayed to consumers. Okay so just to give a concrete example of what we have in mind consider the Amazon buybox. So the Amazon buybox shows very prominently one seller amongst many of a particular product and then if consumers want to look at other sellers of that product they have to hover or click elsewhere on the page. Now winning the buybox is known to be very important. It's believed that on average over 80% of the demand of a product that goes to the firm that wins the buybox. At the same time the exact procedure that determines who wins the buybox is not known. What we do know is that the seller with the lowest price doesn't always win but based on some studies that have scraped and analyzed data from Amazon Marketplace we know that having a low price and having good recent past performance does help affirm to win the buybox. Okay so I want to keep the introduction very brief so I can get through a little bit more about what we do but let me just give a quick overview. So what do we do in this paper? Well we consider simple design policies which are a little bit inspired by the buybox and which steer demand to a subset of the sellers. Then first of all we examine in theory how these design policies might affect various market outcomes. We show that it is indeed important to distinguish between whether sellers are behaving competitively or cooperatively and we also show that design policies can completely destabilize collusion even as sellers become infinitely patient. So even as we would think collusion would be easiest to sustain. Then we look at what happens when prices are set by algorithms. We examine the effect of these design policies and we highlight some similarities but also what we think are some quite interesting differences between what is predicted by theory and what happens when the algorithms are at play. Okay given it's a very short talk I propose that I won't say very much about the literature but let me maybe just mention that the theory part of this talk relates to a literature on steering. One important difference is that we're going to look at steering in context where sellers may be colluding. And let me also say that the second part of the talk will be very related to this recent AR paper by Calvano and co-authors. So what they do is they simulate AI pressing algorithms and they show that they learn to sustain high prices by playing by supporting collusive strategies reward punishment strategies. So what we do is we take a very similar setting but then we look at how a platform might be able to design the marketplace to guide the behavior of those algorithms potentially undermining those collusive strategies. Okay so I know it's a bit early but maybe let me just briefly pause and see if there are any quick questions otherwise I'll go into the model. Okay so there are no questions. Okay so let me move to the theory part of the paper. So I'll start by introducing our model. So this is a very simple game between n greater than or equal to two firms that sell differentiated products at a common constant marginal cost c. These firms interact repeatedly over an infinite horizon on a monopoly retail platform and in each period t of this game the firms are able to observe all past prices and other market outcomes and by that I mean in particular the result of any platform intervention. Okay exactly what I mean by that will become clearer in the next few slides but in any given period firms observe the whole history and then they simultaneously set a price they will charge in that particular period. Firms also have a common discount factor delta strictly between zero and one. So this is the firm side of the market place. Then on the other side in each period we have a unit mass of consumers. Consumers enter the market stay for one period and then exit and are replaced by a new unit mass of consumers and in each period consumers wish to buy at most one of these products. Okay we're going to assume that if a consumer buys product i in period t then she gets a payoff u it which is equal to a so we can think of this as the quality of the product minus the price that she pays plus a z to i which is some random taste shock reflecting product differentiation. Similarly if the consumer instead takes the outside option in period t she gets a utility u zero t which is equal to a constant a naught plus again a preference shock z to naught. Okay throughout the talk we're going to focus on the logit model and so we're going to assume that z to naught and z to i each of these z to i are iid draws from a type one extreme value distribution with scout parameter mu and therefore mu is going to index the amount of product differentiation in this product category. Okay lastly as i suggested in the introduction we're also going to have a platform so we're going to focus on very simple design policies in particular in each period of this marketplace the platform will display a subset of the products to consumers. Now in this very stark theory model we're going to assume that the platform chooses some subset of products to show and consumers can only take the outside option or buy from that subset of products but when we move to the experiments with the algorithms will allow for a much richer setup. Okay but just bear in mind in the theory model we have this quite stark assumption so consumers have shown a particular subset of products they can only choose amongst that subset and as in the paper i'm going to look at two very simple ways in which this subset of products could be generated and then examine the consequences of that from market outcomes. Okay so that's the model i'm now going to introduce two different design features that we examine so the first one is called price directed prominence or pdp and this one is very very simple under pdp in any period the platform will simply pick out k firms who have the lowest prices and it will display only those to consumers. If there are any ties for the kth lowest price these ties are both in randomly and then as I said in this very stark theory version of the model once we've picked those k firms the other n minus k firms are discarded and consumers are unable to choose them. Okay so let me first we'll start with this very simple design policy and then i'll look at a subtler one later on and compare and contrast. Okay but given this very simple policy let me now look at the implications for market outcomes. So given that this is a short talk i'm going to focus almost exclusively on implications for prices and consumer surplus but in the paper we also look at other things such as platform profits and perhaps i'll say a word about that at the end of the talk if i have time. Okay now again as i alluded to earlier when we look at the the effect of these interventions it's important to distinguish between whether sellers are playing competitively or cooperatively. Okay so let's start with the case where sellers behave competitively by which we mean in any period sellers act as if this were the only period in which they're around in the marketplace so they just pay static. Okay so first of all clearly if there were no intervention by the platform then consumers would see all firms okay and we know that firms will then charge a Bertrand Nash price PVN star which is strictly greater than C because there is some product differentiation by assumption. On the other hand with price directed prominence only k strictly less than n firms are going to be displayed okay and so it's easy to see that the firms are going to Bertrand compete for the right to be shown. Okay so very simply this intervention creates a trade-off for consumers on the one hand PDP means that consumers are exposed to less variety they have less options to choose from but on the other hand each option that they can choose from now has a lower price. Okay and so not too surprisingly what one can show is that if i start with the case where there is no intervention and then i introduce PDP into the marketplace consumers benefit from this intervention if and only if the the proportion k over n of sellers that is displayed exceeds the threshold. Now in the paper of course we examine that threshold in much more detail. Let me just point out here that obviously conditional using PDP because prices are at marginal cost due to this competition to be displayed consumers obviously prefer it if there is more variety being displayed to them nevertheless one can show in this particular loget model that consumers benefit from this intervention even if almost two-thirds of the firms are obscured. In other words this the increased price competition is so strong that even if you if you lose almost two-thirds of the varieties you're still better off and in particular one can show that consumers are always better off if k is equal to n-1 such that only one firm is hidden. Okay so that's what happens in a competitive market so in a competitive market this intervention may work quite well that unfortunately is not necessarily true in a cartilized market so to illustrate that as simply as possible let me just focus on what we call a full collusion benchmark meaning that sellers collude in such a way that in each period they choose prices to maximize total industry profit or equivalently they choose the same prices as would a k product monopolist where again k is just the number of cheaper sellers who are displayed to consumers. Now for the usual reasons collusion in this model is sustainable if and only if sellers are sufficiently patient so in particular if we have pdp with k firms being shown then there exists some critical discount factor delta k hat such a collusion is sustained full collusion sustainable if and only if delta exceeds that threshold and what one can show is that again conditional using pdp as we display fewer firms this critical discount factor increases and so the range of delta for which full collusion is sustainable decreases in other words a more aggressive implementation this policy makes it harder for firms to sustain full collusion. The intuition behind this result is quite simple and comes in two parts so firstly of course if fewer firms are being shown then fully collusive profits or in other words monopoly profits are lower and so each firm's benefit of sticking with the fully collusive agreement is lower at the same time you can also show that each firm's optimal payoff if they deviate from full collusion is higher when fewer firms are being displayed intuitively this is this is just because if fewer firms are being displayed then you face less competition so your demand condition on deviating is higher okay so so in cartilized markets if we focus on full collusion pdp a more aggressive implementation of that makes it harder to sustain collusion okay at the same time however one might think that if algorithms can move very quickly so set prices very quickly then that's effectively meaning that time periods are very short okay so that's kind of the same as saying that delta agency's patient's level may be high okay so again just to illustrate the result let's assume that delta is actually very high okay so delta is so high that full collusion would be sustainable even with this platform intervention okay then what we can show is the following simple result which is that a more aggressive implementation of pdp so k the number of firms being shown is lower well first of all at least to lower prices but now it also leads to lower consumer surplus okay lower prices is very intuitive because these are just monopoly prices if a multi-product monopolist has fewer products is less worried about cannibalization so it charges less but here it turns out that these lower prices are not enough to compensate consumers for the loss in variety and so we get a very different conclusion compared to what we saw in competitive models okay so just to wrap up with this particular intervention what we see is that this very simple intervention could work well in a competitive market but could behave quite poorly potentially in cutlery markets okay and so for that reason we then look at a another uh sufferer intervention which we call dynamic price-directed prominence so before I give the formal details the idea behind this policy is to try and reward firms that charge low prices today not just with extra demand today but also demand in the future okay and we'll show that with this policy it's much easier to undermine collusive schemes even when sellers are very patient okay so now let me go through the formal definition so dynamic price-directed prominence or D or DPDP works as follows so firstly in in the initial period zero all of the firms set a price and the platform chooses one firm with the lowest price it displays that firm to consumers and then it confers an advantage on that firm for the following period for period one okay so now let me explain a little bit more what this advantage means so consider some later period period t and suppose that going into that period firm i has the advantage well in period t this firm with the advantage firm i will again be the one shown to consumers and will keep that advantage for the following period if two conditions are satisfied one condition is that firm i should not in this period have raised its price relative to the previous period so firm i has either kept its price the same or has cut it and secondly firm i should not have been undercut by any other firm by too much and when we say too much we mean in particular a fixed level ADV which is controlled by the platform so this allows so firm i could be undercut a little bit but as long as it's not undercut by too much by other firms then it keeps it's still the only firm being displayed and it keeps this advantage going into the next period okay so again just to just to recap what is going on here in the first period so period zero the platform looks at all of the sellers looks at their prices and picks out one of them that has the lowest price it displays that firm to consumers like in PDP but it also confers an advantage on that firm for the next period in period one and all subsequent periods going into the period there's going to be one firm that has this advantage so the platform looks at who that firm is and it checks first of all has that firm not raised its price compared to the previous period and secondly has it not been undercut by too much by some fixed enough ADV that the platform specifies up from if that's true firm i keeps the advantage for the next period and is the only firm that is displayed if either of these two conditions is violated so firm i has raised its price or if it's been undercut by a large amount so more than adv then the advantage is taken away from firm i and it's as if we're back in the initial period so again the platform looks at all of the sellers looks at their prices picks out one firm that has the lowest price displays that firm and gives the advantage to that firm in the following period okay so i hope so i hope that's more or less clear so again just to stress the idea here is that this policy is aiming to reward sellers who charge low prices not just in the period where they do it i think particularly the first period but other periods where this advantage is up for grabs reward them not just in that period but in later periods as well okay so what we can show given this policy is the following result so again collusion in order to look at a sustainable collusion there's going to be some critical discount factor delta hat so there exists a delta hat such that if delta is less than delta hat then in any pure strategy sub game perfect Nash equilibrium of this game the transaction price either price charged by the displayed seller equals marginal cost in all periods moreover we can show two interesting things so firstly as you increase adv remember this adv is the cushion that the advantaged firm has right it keeps it advantage unless it's undercut by more than adv okay so as we increase that cushion as we increase adv this critical discount factor delta hat increases okay meaning that the range of delta for which we get marginal cost pricing increases moreover one can prove that for adv above a threshold this critical discount factor delta hat is actually equal to one okay what does that mean well that means that if adv is sufficiently high even as delta tends to one so even as firms become infinitely patient in the equilibrium of this game the firm that is displayed to consumers always charges marginal cost so in other words for sufficiently high adv collusion is completely destabilized okay so what is the intuition for this when it comes back to what i said on the previous page if you think about it dynamic pdp makes collusion harder because it's more difficult for firms in the industry to punish firms at cut price so for example suppose that the firms were trying to engage in full collusion if one firm cheats and undercuts today on that agreement it'll still demand today but because of this adv cushion it will also be able if adv is high enough to price above marginal cost in future periods still makes some profit and none of the other firms can compete it out of the market plus and this is why for adv sufficiently large collusion can become impossible even as delta tends to one but notice though that even if this adv is very high in equilibrium the firm that transacts with consumers charges marginal cost and so adv doesn't actually bestow prices in any way it just pushes them down to marginal cost i haven't put the details on the slide but it's easy to see that in cartilized markets where delta is very high dynamic price directed prominence could be very beneficial for consumers again there is the same variety loss that we had with the first intervention but now prices may be brought down from monopoly levels to marginal cost even when when firms are very attention okay so the next thing i want to do in the talk so this is so just to sum up so we've looked at two simple interventions the first one could work well in competitive markets less well in cartilized markets then we have this subtler intervention which seeks to reward firms with low prices not just today but in the future turns out that has very similar properties to pdp in competitive markets but it can work very well in cartilized markets so the next thing we want to do is then see how we can ask a question please yeah there is i know that there is a break for question just after this slide okay thank you hence i was i was i was holding off on that question so so andrew there is a question in the chat and so asking whether the mechanism would work with heterogeneous consumers which means that the lowest quality adjusted price may be different for different consumers so you mean if products different terms of quality is that the question well if consumer what i mean is think of a model of horizontal differentiation not only vertical differentiation so consumer are heterogeneous and if you just prices by quality then different consumers may have different products with with the lowest quality adjusted price well i mean so here we do have the horizontal differentiation because we have the the loget shock i think it would work if we also had some both types of differentiation i don't see why not provided that that vertical differentiation was not too large of course one would have to then think about products differing in cost as well an important assumption here is that the products have the same cost so that simplifies things a little bit is there another question or should i go on yes please i'm not entirely sure but your second mechanism looks very much like selling the telling the firms you can bid now and then you can sell forever at the price which you bid and in this case of course you make collusion is there is there a difference so selling the market in the first period yeah um so i think i think that's a fair comment i mean remember the theory model is very stylized so i mean if you thought about a richer model where maybe in the future you could have firms coming in with lower costs there will be some innovation then i think that this model would still allow those firms to compete if they're if they're sufficiently strong so this model works by having this this adv so you need adb to be positive of course it may not necessarily be so large of course this is also very stark i mean you might think that you would give this advantage away for some number of periods and then you would allow firms to compete again so i'm sure you could fine-tune this this is just to show in a very stark setting uh the kind of trade-offs that arise but i agree in this very simple setting you're correct yeah that's effectively what happens and uh Bruno asks in the chart what happens if our costs change randomly that is a good question i'm not sure we haven't we haven't checked that again presumably i mean presuming that there's not too much variation in costs one can imagine that the same trade-offs will come out and so probably if this policy works well for consumers if there are a little bit of randomness in costs i'm sure that it would also work work fine if there were large variation then we're not sure but that's a good question thanks should i should i go on yeah i think yeah okay so i have about how long do i have left uh you have about 13 minutes left 13 13 13 yeah okay so um now let me move on and just discuss very quickly um a little bit about the algorithms that we use um so to set the scene um consider the following abstract setting so suppose there's an agent facing a finite action set x and some finite space s okay imagine that if this agent takes action x in state s she gets some payoff pi s of x okay and imagine that transitions between states which could be probabilistic depend on both the current action and the state now this agent is a long-lived player and she wants to choose actions to maximize her totally expected discounted payoff the problem is that at least initially she's uninformed both of this pi function and potentially about the transitions between states okay so she wants to learn that information we're going to follow many other papers both in recent economics literature and also computer science by looking at a class of algorithms called q-learning algorithms so i'll give a little bit more detail on the next slide but the idea is that these algorithms seek to iteratively estimate what is known as an action value function q star s of x which gives the value to the agent of playing action x in state s given that she's going to behave optimally in the future okay so and just notice that if the agent is able to estimate this matrix this q star matrix then she will know what optimal policy she should play in each state okay so in particular if we're in state s the agent can just take this matrix and read off either the appropriate row or column look at the value of taking each of the actions and find the action x tilde to maximize her payoff okay so how in practice would you implement this well you start with some initial perhaps arbitrary matrix q and then you want to iteratively update this over time okay so just very quickly to give you a flavor of how this works imagine that the agent is in state s at time t the agent can do one of two things according to q-learning so firstly she can experiment with some probability epsilon t which is specified by the agent upfront and when she experiments the simplest thing to do would just be to choose randomly choose an action see what payoff she gets in which state she moves to with complementary probability one minus epsilon t the agent may also exploit in which case she chooses the action which she thinks is best given the current q matrix available to her now whether she experiments or she exploits the agent will take some action x she'll get some realized payoff and she'll transit to a new state s prime having done that she then uses this new information to update this q matrix up here that she started with in particular she's going to update the cell corresponding to the state s that she was in and the action x that she just took and this updating depends on a parameter alpha which again that the agent sets up from okay and so all this equation says is that the way in which you update the cell is as follows so you start off with some value in the q matrix given by this and you get some new information about the value of taking this action in that particular state which is the flow payoff you just got and a discounted value of what you what you read off from the q matrix given that you've transited to state s prime what the agent then does is take some convex combination of those two things depending on this way alpha and then this arrow just means you then update that that the former cell in the q matrix with this new information this is an iterative procedure so the agent then keeps doing this in the next period she does this from state s prime and so on and so forth in single agent problems where you're just playing against nature under mild conditions you're guaranteed to converge to an optimal policy in most studies including ours in multi-agent settings you get convergence even though in theory there's nothing that guarantees that typically it does it right so i guess i don't have much time but let me just briefly say so why why use q learning well a lot of other recent papers and economics have used this one advantage is that there are not too many parameters that you have to specify so you don't have too much wiggle room when you set up the algorithm but it's also true that reinforcement learning techniques like q learning are a simple building block of many algorithms which are used in more complex real-life settings so this is just a picture of lisa doll a very well-known player of the board game go who was beaten for one by a google deep mine computer which was using ai including q learning to learn how to play that game okay in terms of how we implement this in our game i probably don't want to spend too much time with this because i want to have enough time to go through the results let me just say that the basic setup without the platform design and the parameterizations that we use are very similar to this recent ar paper by calvano and co-authors as i mentioned earlier we build on the theory model in a couple of important ways one is that we introduce a parameter gamma that captures the degree of platform design so in particular when we run our simulations we assume that a fraction one minus gamma of the population just sees all of the firms regardless of what process they charge or have charged in the past and the remaining gamma consumers are exposed to either pdp or dynamic pdp okay and so obviously if gamma is equal to zero there's no intervention consumer seal firms if gamma is equal to one that's like the theory model but we also allow for anything in between those two extremes just a few details before i get to the results so we look at prices between one which in our parameterizations is marginal cost and 2.1 which is a little bit above the fully collusive level we discretize that into 15 elements and then as in the calvano paper we use a one period memory so the state space is just a set of possible prices that were charged in the previous period each firm has its own q matrix and it updates it in the way that i showed on the previous slide we run the algorithms until their strategy has been stable for 100 000 periods we average over those periods and then we do a thousand runs for each set of parameters just to smooth out the results okay so i know that was a bit quick but given given that i don't have much time i won't say anything more about that i'll pause again if there are any questions otherwise i will or maybe i should go through some results and then pause for questions after that no questions in the chat for this part so okay so i'll keep going okay so in the paper we run a lot of experiments here i'm just going to pick out a few to give you a flavor of some of the results um so for this talk i'm going to focus on a setting where there are two firms uh discount factor of 0.95 and the logic parameter is a quarter okay and just as a first step it's of course important to look at what happens if there is no platform intervention so there's no pdp or dynamic pdp so in other words this gamma parameter is just equal to zero um so some simple computations show that the batron nash price in this setting in theory is about 1.5 fully collusive price would be about 1.9 and when we run our algorithms they tend to settle on a price of about 1.7 okay so roughly halfway between competition and collusion and so of course this is very much in line with the results of calvano and corvus okay then the next step is of course to introduce into these into the setting our two design features okay so let me start with price directed prominence um so what these two graphs are doing is on the x axis we're plotting remember we only have two firms here so k is equal to one so a fraction gamma of the population just sees the cheapest firm and proportion one minus gamma sees both of the firms so we're plotting that proportion gamma and then on the y axis here we have the share weighted prices and here consumer surplus now in both of these diagrams the red line is showing what theory would predict for a fully collusive cartel and the blue line is showing as we vary uh gamma what happens to the price charged by algorithms so what you can see here is that as we increase gamma initially the price increases then eventually it decreases and price ends up about 7% lower then with full intervention compared to no intervention similarly consumer surplus ends up about 7% lower so this is if you remember this is very much consistent with what we said in theory for full collusion we expect that this intervention reduces prices but not by enough to offset the loss in variety and so consumers are made worse off okay let me skip that for now so now let me look at the second intervention dynamic price directed prominence so again here we're just plotting on the x axis the extent of platform intervention gamma and then the prices and consumer surplus the blue lines are what happens with pdp that's just copied from the previous slide and the red line is showing what happens when we implement dynamic price directed prominence and what you can see again very much consistent with the theory once gamma is above about 0.2 dynamic price directed prominence leads to much stronger price decreases and much stronger consumer surplus increases so again consistent with the theory dynamic pdp leads to much lower prices and higher consumer surplus now of course one difference with the theory is that although prices are lower they don't fall all the way to marginal costs but they do fall quite significantly now if you look at these graphs you'll see one interesting feature is that when we move to gamma equals to one under dynamic price directed prominence prices jump up very strongly and consumer surplus jumps down very strongly so we attribute this as i mentioned here to a learning challenge so if you think about what does gamma equal to one mean it means that one of these firms gets no demand moreover because you have this pricing advantage the firm without the advantage may get zero demand even for a broad range of prices that it might charge it charges high prices but even if it charges prices they're a little bit below those charged by the advantage firm right because it doesn't charge enough to to to pull back the advantage so in that case if a firm is getting zero demand for a broad range of prices it might be quite hard for it to learn so i don't have time to go through the details but in the paper we show what happens if we have what we call a smarter ai where we augment the state space with more information we avoid this big jump here and actually we get even nicer stronger results again let me skip that for for now okay so i i guess i only have a few minutes left but let me just summarize so far so what so what we've seen is that both with pdp and dynamic pdp although there are some differences with what theory predicts qualitatively the predictions are what what happens in practice is not too far from what theory suggested one more thing that i want to discuss very quickly so remember in the theory model i said it was important to distinguish between whether sellers will be having competitively or conclusively okay so we also try to get at that in our simulations so again we take the same setup here with two firms and logic parameter of a quarter but now we're going to vary seller discount factors okay and the idea would be that if the discount factor is quite low that might proxy for a more competitive market and if delta is high that may proxy for a more collusive market so the first panel here is just a heat map showing on the x-axis again the proportion of consumers who only see one price or the amount of platform intervention and on the y-axis we have the discount factor delta and what you can see is that if i were to fix a particular level of gamma as i increase the discount factor this is showing consumer surplus so if you if you read off here red numbers mean that consumer surplus is very high um green means that consumer surplus kind of intermediate and blue colors mean that consumer surplus is quite low okay and very nicely as you increase the discount factor you can see that consumer surplus seems to monotonically full which is which is kind of i guess a sanity check it's suggesting that the algorithms are managing to sustain higher prices and therefore push consumer surplus down more in markets where the discount factor is higher okay another thing that we do so this is all about consumer surplus level then we look at the percentage change in consumer surplus due to the intervention okay so just to illustrate what we mean by this take for example gamma equals 0.7 and delta equals 0.5 so what does this point here represent this point says suppose that we fix delta at 0.5 this is the percentage change in consumer surplus if we go from no intervention so gamma equals 0 up to gamma 0.7 and again um dark red colors mean that consumer surplus is going up and going up by a lot um green means that it's not changing very much at all and blue means that it's decreasing and again if i were to take a slice at this graph so for example i looked at gamma equals 0.7 um in markets where the discount factor is quite low which we might think of as competitive markets we see that this intervention works very well um but it can work quite badly when delta is very high which we take as a proxy for a cartilized market so again this is kind of qualitatively consistent with the theory that i went through um earlier okay i probably don't have time to to show that but we get very similar patterns that are also very much consistent with theory when we look at dynamic price directive problems okay so i don't know whether you want to whether i should take some questions or whether i should just do some extensions so so and i mean there are several interesting questions that are showing up in the chart but i think most of them are more proper for a general q and a asking about the incentive of platform to to to limit collusion and others but one clarifying question so is the q learning algorithm simple enough that we could have analytical predictions that's from uh Daniel Garrett like for instance could we predict a price bounded away from the collusive price without the simulations i think it's not not as far as i'm aware i mean it looks simple but actually it's not so simple okay so i think now uh it's better for you to to kind of wrap up and then leave other interesting questions for q and a okay so maybe let me just spend one minute on this slide just to tell you some other things which we do which we think are interesting um so in the paper we also vary um the number of firms we allow for three firms um basically we find results again qualitatively consistent with the theory we also look at this dynamic price directed prominence but we vary the level of this adv this cushion that is given to the advantage firm and here interestingly we find something which is a little bit different from theory so theory would predict that once you increase adv enough you get marginal cost pricing and making adv even higher won't change that what we actually find when we run the algorithms is that consumer surplus is an inverted u shape in adv so in other words moderate increases in adv um push up consumer surplus but if you make adv too large if you give too large an advantage you may get stuck at high prices and consumers suffer okay and so we attribute this to a way into the fact that algorithms learn in a different way to how we derive the result from a game theoretic point of view so there's a difference in how the how the algorithms learn this may touch on some of the questions uh later throughout the talk i focused on how do these interventions affect prices and consumer surplus of course um you know platforms may feel that they have a responsibility to uh to target collusion on that platform they may may may view themselves as like a gatekeeper but even if they just care about profitability it's not so obvious not necessarily obvious that they might want very high prices so we show both in theory and in practice that these interventions can increase both the amount that is sold on the platform and also the revenue of uh sellers okay and so to the extent that the platform makes money um either from per unit fees or because it takes a fixed share of revenue the platform itself may want to carry out these interventions so in particular we show it's possible both in theory and in and the simulations for consumer surplus and platform profit to go up okay so i guess it's almost quarter two so let me so let me wrap up so we've considered two very simple policies which steer demands to certain firms we've shown that in theory effective those policies depends on whether or not the market is catalyzed in simulations we saw that broadly speaking the results are kind of consistent with theory but we think there are interests some interesting differences especially relating to differences in how algorithms learn compared to how we derive the theory results um very simple steering policies which depend only on current prices may not be enough to undermine collusion and algorithmic collusion um and subtle subtle policies might be needed now of course we've looked at two very simple policies here um but nevertheless we believe that these results are kind of a proof of concept that platform design can be used to raise consumer surplus and as i alluded to at the end also platform profit even when algorithms are being used and irrespective coming back to the debate that i mentioned at the beginning irrespective of whether those algorithms lead to more or less competitive outcomes okay so with that thank you for your attention and i look forward to the discussion uh thank you and real and uh we will have it seems quite a lot of discussion before then uh alex mckay uh from hbs we'll uh discuss thank you uh andrew and hannah so thank you and thank you for having me discuss this is a very nice paper from a great trio of scholars um and i'm happy to be doing the discussion um and uh you can hear me okay hannah excellent okay um so i was encouraged not to have slides no slides here's what i'm going to do first i'm going to go over high level motivation then i'm going to quickly summarize what i think this paper does um the third thing i'm going to do is actually talk about potential future directions for research based on this and then i'm going to come back to that a little bit with a few specific questions uh for andrew so high level motivation i think it's a really nice paper to help understand competition with platforms you know and in particular a really hot topic right now is sort of antitrust concerns related to steering and i think this is squarely in that area even more broadly what we're looking at we're looking at questions of what do platforms do and what should they do and i think this paper helps us understand that in sort of interesting and nuanced ways um what should they do both from perspective of you know antitrust but also from the motivations of the platform so i think that's really nice what this paper does is it's a rich theoretical investigation into a relevant and timely question and andrew sort of showed some extensions at the end there's a lot in this paper i think it's very thorough and some really nice features i want to say that the the key question they're kind of asking is does price arrested prominence i.e prioritizing low price products benefit consumers or harm consumers and we we sort of get two answers here really the first answer is it depends on whether or not firms are colluding and the second answer is it also depends on whether or not they're using machine learning algorithms so it's nice to kind of look at both of these dimensions with respect to that question and i think their solution of this dynamic policy is is really interesting and has this nice feature that it it sort of parallels what a collusive policy would look like from the firm side so fight a collusive dynamic policy with you know this platform's dynamic policy so i think there's some nice subtlety there so now stepping back a bit and just thinking okay where might other papers or other research go from here as related to it i again i think thinking about what do and what should platform forms do i mean i know there's a rich literature on this but i i also think this paper is an illustration there's still a lot of features that deserve you know additional consideration then when i think about the relation of algorithms to platforms there are a few things that come to mind one thing that you know this paper focuses on our learning algorithms and how do learning algorithms lead to certain pricing behaviors there you know a couple other features of algorithms that sort of have been acknowledged and and studied one is algorithms prediction power you know that can be related to learning but not you know that's not really the focus of this paper or the calvano at all paper so there's learning there's prediction there's also automation itself so when we think about you know and you sort of mentioned amazon marketplace when we look at the pricing strategies that a lot of these sellers actually use on the marketplace they're often very simple automated strategies you know and that's there's some relation to some work i've done but but moreover i think even thinking about on platforms would be really interesting to think about the intersections of these features of algorithms and sort of what platforms do so they're looking at one element but i think there's a there's a really rich space here i i also think you know for future research there are some sort of unanswered theoretical questions with respect to q learning i think daniel garrett asked about one of them earlier you know what what are some properties here you know i i just think there's a lot more to be done in this area you know i think one thing you might want to ask is why would you know sellers on a marketplace choose to adopt this sort of learning algorithm versus other kinds of learning algorithms i think there's you know there are a lot of questions in this area and they're they are they're targeting one i think they're executing on it well i just want to sort of motivate some additional research to build on this um i do have a few specific questions the first one is um maybe the broadest and and i'll just outline all the questions happy to get andrew's thoughts um i think you know one thing i think about this is kind of motivated by the marketplace in the buy box but if i think about the buy box on amazon there there are actually many features that i think of that aren't in this particular model um you know the first thing is that they're search frictions first you have to arrive at amazon's website then you have to search for a particular product and then it's only when you get to the product page that you actually see the buy box so they're actually like three steps for prominence in that market and they're sort of collapsing it all to one specific step you can think of it as an analogy for search what they're doing but again it's sort of one specific step but search frictions are actually really important right in in the model that andrew and co-authors look at differentiation is tied to the product and is you know and is a benefit to consumers but if you're in a world with search friction and often the buy box distinguishes between purely homogeneous products consumers might actually benefit by only having to look at one product if they're purely homogeneous so that's sort of another consideration that's not really including this model you know also in the marketplace often there are many sellers you know it's not a setting where you have two or three sellers like the experimental investigation there's a wide range of prices for these sellers they have diverse pricing strategies you know so if i think about two or three sellers using you know a particular symmetric learning algorithms you know it it i'm just not sure if that's exactly what's going on on the buy box so it's and it's also not really the typical setting you would think of for collusion so that's that's just sort of a comment on like the specific you know motivating example here but i mean i think this is what they're studying here is quite generally applicable and you know even even to some extent like think about the typical retailer choice of whether or not to stock coke or Pepsi you know at the retail location that's a product where you've you know you have you have two different brands and some differentiation potential collusion there and they're deciding you know whether or not to include one of those products so i think this is a quite general problem but i would encourage you know maybe thinking a little bit or just wondering a little bit about thinking you know am i is there am i missing something sort of with the marketplace link there again maybe there's just future research to be done there the two other specific questions one is just i thought it was interesting that there was non-monotonicity with the algorithm prices with respect to gamma so i was wondering if you had some intuition as to why that might be coming up because i think that was a little different from what you might expect from the theory and then the third specific question was on you know you do this exercise you didn't get to on the critical growth elasticity but basically asking from the platform's perspective how much benefit do you have to give the consumers to to generate excess profits and so i was sort of wondering if you thought about other ways of doing that in particular looking at just if i get one additional consumer how much more profit do i have to get from that consumer from other products or down the road and if that sort of gives us intuitive results but overall i thought this is a really excellent paper very well done and i'm looking forward to hearing the discussion after this thank you thank you alex so uh so now let's uh let's move to the to to q&a and uh i at this point i think it's uh it's best if people unmute themselves and ask questions but i would propose that we start first with the questions that have already been asked and i postponed so uh jpil had had a question j do you want to um do you want to ask ask it to yourself or should i read it from the chat okay so i will ask the question so i'm wondering rather than showing one product to to everybody so what if the platform has some kind of information about consumer preferences and do individualized showing so that in that case i think that the variety problem can be also mitigating for consumers um yeah so i agree that would be a good point i mean in the theory the theory part is obviously very stark but in the simulations we do allow for some consumers to see everything and i guess if the platform had some information about consumers's matches with products they could probably do better matching between who gets shown this limited section selection who gets shown everything to perhaps mitigate the variety loss a little bit so i agree yeah that's a good point and then uh andray and jack had a similar question i don't know which one of you want to ask it i'm happy to i'm happy to follow up actually there's the follow up on jpil's question it made me think that um basically you can think of the platform as having multiple measures or multiple design choices so the ones you look at are mainly design choices that are uh whose effect will be to essentially increase competition in lower prices what jpil's asking is that so for example showing uh consumers uh showing personalized offers would basically go in the opposite direction so it might lead to a higher equilibrium crisis so and then the question the natural question is how should we think about the incentives of the platform like in general it's not clear where the platform would want equilibrium prices to be higher or lower i mean i guess it depends where it gets transaction fees from the prices depends if you're also factoring consumer participation decisions on the platform and so on so how should we think about that um should i maybe go with this second point first yeah so that's a good point so we have a little bit in the paper uh where we also look at um platform profits so it's true that depends a little bit about how the platform um earns its fees if for example it earns per unit fees then it's very easy to come up both in theory and in the simulations um with situations where the platform actually benefits at the same time as it increases consumer surplus um if the platform gets per revenue sharing fees then you can also find that these interventions increase platform profits it turns out it is a bit more difficult um and so this is what by the way alex thanks thanks for the great discussion um so as alex mentioned the discussion we also then look at a critical growth elasticity so we say well sometimes these interventions might for example reduce um revenue and so that might seem to reduce platform profits but arguably if the intervention is increasing consumer surplus um by a fair bit then maybe that might pull more consumers to the platform and so we compute um how elastic the the size of the user base with respect to consumer surplus has to be in order for the platform to be made whole and we show that often that's or in my opinion the numbers are not very large in order to make that happen so it's a good point but i would argue that many of these interventions can simultaneously benefit consumers and also the platform so on gregg taylor um sure say uh you sell this as um sort of being about algorithmic pricing um it sort of seems what's going on is that um this learning algorithm is converging to something like an equilibrium and so i wondered um you know why do you think this is specifically about algorithmic price then why couldn't we apply it more broadly to any kind of situation where firms are commuting an equilibrium um and then another quick question if i may is um you said at the start of your talk that nobody really knows um how the amazon buy box works it seems like if um this was really about trying to influence firm's ability to collude they'd want to go out of their way to publicize you know particularly what the value of this advantage is and so i wondered if you could comment on that at all thank you um so maybe maybe let me go for the the second point first so that's yeah so the why does amazon not um publicize that i think that's a very good question i mean i guess on the one hand you might be tempted to say well if they gave i mean i'm sure it's a very complicated rule anyway but um they might open themselves up to problems of gaming um they might want to change it at some point i guess as well on the other hand there are studies that have scraped data and there are certain things you can learn so i guess as a trade-off you don't want to give too much information because you might open yourself up to gaming but if and it seems like increasingly says have access to quite complicated tools which can analyze how the buybox works they may get the essence of it anyway so i guess that would be my answer i'm not sure if that's a if that's a great answer to your question it's but the question is very well taken so uh what i will do now i will stop the recording uh but we still have