Sandro Shelegia: Impressing the Algorithm : Sales-Based Ranking, Learning, and Off-Platform Pricing

[music] Heat. Heat. [music] >> [music] >> Thanks to the organizers for for having me. I'm um excited to tell you about uh this paper. This is joint work with Hesky Bar Isaac. This is already our third uh third paper. Uh the first one was on uh showrooming. Then we did a paper on platform steering and then this paper is basically platform steering with showrooming. So there in a way there's some kind of uh this kind of ties a bow over the previous two papers. All right. So impressing the algorithm is the name. Uh that's the catchy part. And then there's a long description of what what is going on but I'll tell you about it anyway. Okay. Wait. So let's see. Right. Uh okay. Okay. So, uh the first thing that uh I probably don't have to defend too much with with the audience uh is uh the fact that uh ranking algorithms are um are key players in e-commerce and they affect who is visible and who sells and who doesn't. Um so I think that's something that is well understood especially by this audience. So the um uh obviously ranking algorithms would affect prices on the platform and the market structure on the platform and u this has been uh this has been a consistent um topic for for various recent papers. Uh a few people have have um contributed including ones uh ones in the audience. Now we we're going to actually not engage with on platform pricing at all almost by construction slash assumption. So instead we're going to be interested in um how an algorithm could be strategically designed in order to affect prices off the platform rather than on the platform. So the on the platform pricing we leave uh alone because of I'm going to explain why but uh or how and then uh we're going to focus on offplatform prices. Um so this is going to uh this kind of strategic design will run into two potential allocative distortions. uh one will be on the platform which is uh uh what product should the platform u feature so that consumers become aware and potentially buy it. So that will be one potential source of distortion because products will not be the same and the platform may because of strategic considerations distort its own allocation of uh consumers to consumers attention to to products. And then the second issue that will turn out to be important that that that's that's where offplatform prices come in is that um we're going to be asking where do consumers buy. Uh so here we're going to be um simplifying the world in such a way that there's a platform where consumers can buy and the same good would be purchased at the direct channel of the of the seller. And the question will be uh which of the sales channels uh will end up being um being used by by consumers indogenously indogenous to prices of the seller to the platform design etc. So this this relates to kind of showrooming/ leakage uh kind of literature. I already mentioned that uh Heskin and myself we have a paper on this uh the actually the closest paper to ours in terms of uh in terms of the setup is uh Andre's and Julian's paper from couple of years ago on leakage well so I mean showrooming leakage are can in this setting are basically interchangeable and then there's other papers like Andrew Andrew and co-author also have a related paper okay so Um, now there's lots of chatter out there that claims and there's some proper empirical evidence partially from academics, partially there's some evidence from from policy makers that uh onplatform rankings uh tend to sometimes depend on offplatform prices and uh this is done to deter showrooming. Okay. So the idea being that a platform may want to or does some platforms do punish uh punish quote unquote punish sellers whose offplatform prices are low. Okay. So they want to keep off platform prices high so that purchases happen on the platform rather than off the platform and kind of one way to to think about it is that this is a way for the platform to deter showrooming which is that consumers discover the product on the platform but then they buy the product off the platform at a lower price. So by uh conditioning on of offplatform prices um the the platforms are able to kind of move demand towards the platform or in the in the language of Andre and Julian's paper to minimize leakage to this to the direct channel. So uh DMA DMCC which is the British one um have some uh some restrictions on this. there there have been uh suggestions of doing algorithmic audits to find out this kind of behavior and potentially punish it. Um, and uh, the point we're going to be making with this model, one of the points we're going to be making with this model is that actually an algorithm does not necessarily have to directly condition on offplatform prices um, but can reproduce very similar uh, outcome by simply conditioning on on platform sales. You can think of it as as the following. On platform sales are kind of an echo of what is going on with prices off the platform. If offplatform prices are low, on platform sales are low because more people are leaking to the to the direct channel. So the the the platform that observes on platform sales can basically proxy the the offplatform prices with them and then uh basically indirectly punish the same thing without ever explicitly explicitly touching the um touching the the offplatform prices as such. So u with these ideas in mind so the question we're going to be asking are um uh are are the following. So the maybe a narrower version of the question would be the following. If you have a platform optimal algorithm that conditions on prices of the platform as opposed to the one that doesn't what changes to uh what changes in terms of offplatform prices as I said on platform prices will be assumed to be or the model is set up in such a way that on platform prices will not move either way. So the question will not be what happens to onplatform prices they will stay the same but offplatform prices can be affected. uh then uh we're going to be interested in who gets featured by the algorithm and that's where uh a distortion that I I preempted will uh will live and eventually this will all lead to some platform profits, welfare and consumer surplus con comparisons between algorithms that can or cannot condition of platform prices. Now, uh another kind of side question we're going to be asking is what happens if you if uh this world is augmented by um contractual agreements such as price parity clauses. So this would be a combination of some kind of algorithm operating on the platform, but there's also a a legal contract that was signed um that uh restricts prices to be um to be lower. Uh and there we're going to have hope hopefully some interesting results for you. Um yeah so uh one thing that uh we're going to be uh we're going to be modeling is the fact that sellers uh understand that ranking algorithms uh uh are important for them and they try try to manipulate these ranking algorithms because ranking al algorithms tend to learn things um uh and based on what they learn uh they um they change things. So in the in the old days of internet this was called search engine optimization because the the kind of the the conduit was uh was Google search but now a lot of the purchases happen through dedicated u market places such as Amazon booking etc. So kind of the the goalposts would slightly these things now are called algorithms not search engines but you know roughly the same kind of issues are at play now. Um I mean you know we are two theorists so this this is the most anecdotal claim uh ever in history. So if you look around the internet and you try to see what what do um what are um kind of individual sellers such as hotels or sellers of goods on Amazon what you know what are they thinking when they are interacting with these algorithms and one thing that comes up is that uh they're um uh they are advised by an a sizable industry which is advising sellers how to kind of manipulate algorithms. is to direct a lot of their traffic internal or external to the Amazon for example in this case Amazon listing. Okay. So the idea here would be that uh if you have some independent traffic let's say coming to your um direct channel you try to direct it to the to the Amazon listing uh because um uh because you um you generate more sales on the platform. the platform sees sales, thinks, okay, this is a good seller. Maybe I should keep showing this seller to consumers. And that that buys you um that buys you exposure. So, um in this paper, we're going to be instead of uh this kind of direct manipulation of sales via somehow channeling them through to the platform, what we're going to be thinking about is um is more uh in line with uh with just looking at pricing off the platform. And the idea is extremely simple. Uh to the extent that uh you know there's consumers uh will only buy on the direct channel if the price is uh low. The the lower you make it, the more consumers will not buy on the platform. The higher you make it, fewer consumers will buy on the platform. This will change uh the the fraction of sales that happen on the platform. And then this will uh this will in the model will will be used by the seller to strategically manipulate the the the learning that that the platform will be doing. So uh if uh I mean some of you uh if you haven't seen this paper you may have nevertheless recognized that this looks like career concerns. So the platform will have some expectation of what price the the seller sets on the direct channel. If the platform does not observe this price and that the seller let's say deviates and charges actually a higher price what's going to happen is that compared to the expectation of the platform on average there will be more sales on the platform because of platform direct price is higher. this will uh force the the platform's learning um learning structure to overreact. It will have to attribute this to uh to the type of the seller rather than the the price increase of the seller of the platform. And this creates something that is very similar to career concerns uh structure that we're familiar with um from from earlier literature starting from Holstrom and etc. Now uh this this kind of career concern structure will be there just by the virtue of the platform um learning but on top of this the platform which has a commitment power and that's the kind of platform we're going to be studying will actually be able to distort these uh promotion uh criteria even further to reinforce career concerns. So there will be career concerns regardless. But the platform by shaping its algorithm can make the career concerns even uh even stronger. Uh and uh why would it do so? Um by by doing so it would it would achieve even higher prices platform therefore even more sales on the platform and that's where the platform makes the revenue. Uh and then what we're going to show is that um if you do not allow an algorithm to condition on offplatform prices, the welfare can actually be lower because what you are doing is that you are forcing the algorithm to use so sorry the platform to use the algorithm in a distortive manner in order to achieve a goal that had it been allowed to condition directly on off off platform prices it would have to it could do without any distortion. So that's kind of uh the idea and uh our another uh important result is that once you start looking at uh contractual agreements such as PPC they at least in our model and I'm going to comment on how in a way our model turns out to be a best case scenario for PPC to shine. PPC can uh actually achieve first best welfare sometimes when neither of the other regimes that we consider is able to. and I'll I'll explain why PPC turns out to be such a magical silver bullet in this setting. Any questions so far before I move on to the model >> and there are no questions in the chat. >> Very good. Let uh I'll take it as um it was all clear but or nobody was paying attention but anyway. So the model baseline model so we have a monopoly platform. The important thing is that consumers can only discover the seller on the platform and only if the seller is featured by the platform. So that's very important. So this is a complete bottleneck. There's no way for consumers to reach the seller outside of the platform which is I mean it's not crazy for Booking.com, Amazon with smaller sellers. Nobody's going to find them directly, you know, they have to be found through through these big websites. So the platform monetizes through a um a fee adwell or fee f although in this setting whether it's adval or more unit is going to be the same. So we're going to have one seller whose type theta is uncertain. So it's not certain it's not known neither to the seller nor to the platform. That's that's an important consideration although we relax it and then actually results are quite similar although they change slightly. Um, so the seller can sell on the platform or off the platform and the production costs are uh zero. I going to comment on uh what the type means and what this selling on and off means on the on the next slide. Um, so there's also a short-lived short-lived uh per period specific seller whose type alpha is between 0 and 1/2 and this seller will act as a outside option for the platform. So uh consumers have unit demand for the good valuation is one and on platform price is fixed at one. We can derive this as a result that the platform uh the platform algorithm induces the seller to set price equal to one. Here it's kind of a little bit turns out it's not completely trivial but the the baseline idea is quite sim simple. the platform is making a fee on um on the on the revenue on the platform. So it wants to increase the price as much as possible to make a as as high of a fee as uh as possible. So basically valuation for the good on the platform equals one. Price on the platform equals one. So consumer surplus on the platform will be zero. And then once this price is fixed, we're going to be talking about um we're going to be talking about offplatform discount capital delta t which will be in an interval that I'm going to explain. Okay. So basically the way to think about pricing is very simple. The platform price is one and the offplatform price is discounted off of one by by capital delta. there's two periods um and the period two algorithm can condition on period one on platform sales S1 okay so the the algorithm in the second period can condition who is featured on what sales were observed in period one because the the the reserve seller the outside option is short-lived this kind of dynamic considerations will play no role for for that seller okay so consumers we have unit mass of consumer s uh in period one in period two mass beta arrives and beta basically measures how important the postarning period the second period is. So now theta and alpha come back theta and alpha are basically fraction of consumers who actually find the product appealing. If they don't find the product appealing they don't buy it at all. So theta and alpha which is which are the types of the seller and the reserve seller are basically fraction of consumers that like the product. So higher type means this this seller is better at uh at satisfying demand. Now importantly uh for our consumers we're going to assume and this is exactly what Andre and Julian do in their paper. We're going to assume that [clears throat] when this consumer so we know that their valuation if they like the product is one on the platform and then they're going to suffer a um this utility of buying from the direct channel which is little delta and little delta is going to be between uh delta underscore and one and the underscore can be negative which means that some consumers actually may strictly prefer at equal prices to buy on the direct channel because of some extra perks that the direct channel uh gives consumers. So uh basically this the little little delta will be the one that decides uh which which consumers go to the direct channel and which don't and the idea uh is very simple. If little delta is bigger than the price difference the discount uh that means that this utility of the direct channel is big and these consumers will buy on the platform and the rest of consumers will go to the direct channel. Um as I mentioned uh we we in principle allow that um that some consumers have negative this utility meaning that they strictly prefer the direct channel to the to the platform and uh this gives us some richness that u that is useful later. So the market is the way this was constructed because the price uh on the platform is one willingness to pay is one. Uh so consumers are assured to get uh zero utility at least and that means that the market is covered. Okay. So the timing is the following. Before period one, the platform commits to an algorithm. The seller observes uh what what the algorithm is. Um the algorithm is mapping from everything that the platform knows into which seller is uh is promoted to be seen by consumers. I I should have mentioned that uh consumers can only see one seller. It can be the reserve seller or it can be the the main seller but it cannot be both. So therefore basically uh the platform has uh so each consumer has this attention of one unit and this attention has to be allocated to one of them and the and the the algorithm basically decides where the where the where the attention goes. Um then so the the platform uh the sellers ch the seller um the the seller and the period specific reserve seller choose off platform discounts in each period. Uh the platform basically executes the algorithm and uh according to the algorithm gives um the the chosen seller uh the market basically uh consumers observe the the discount. So if the seller is featured consumers observe the seller they immediately observe the discount that this seller gives on the direct channel. They know their this utility from the direct channel and they they choose where to shop. The market is covered. So they they will buy for sure. uh the the important twist is that after period one the platform observes what sales have occurred on the platform and therefore the algorithm uh um can condition on them but the platform does not observe sales that are outside of the platform. So uh that's that's an important consideration that's what career concerns will be based on. So we're going to have um three types of algorithm to think of. There's a baseline algorithm which is our kind of main uh main protagonist. That's our baseline model. This algorithm can see um well because all platform prices are fixed at one this algorithm can only see one thing and that thing is sales that occurred in period one and use them in order to decide who is featured in period 2. So then we have OP algorithm. OP stands for offplatform price algorithm. This one in addition to observing the sales also observes uh kind of simultaneous uh prices of the off the platform. So this this algorithm observes everything. It observes exactly what the seller did. So if this algorithm because there's commitment if this algorithm does not like what the seller did off the platform the algorithm can can be committed not to show the seller. So this one has a lot of power in terms of um dictating what the seller does off the platform. And then finally there's kind of a in between algorithm we call PPC algorithm which is like the baseline algorithm in terms of information it has. So it can only condition on sales of the first period but it has a contractual obligation that has to be fulfilled which is that the the seller cannot give positive discount. So the seller is allowed to charge a higher price um higher price on its own direct channel but is not allowed to charge a lower price. So the discount is not allowed to be positive. Uh okay. So um all right. So how am I doing with time? Uh so um let me walk you through very fast through the kind of static benchmark. So this this is a benchmark that applies to the reserve seller who is shortlived. So doesn't have any strategic considerations. Also applies to the to the seller who is not shortlived in the second period because the second period if if the seller is promoted in the second period that there's no future. So that's basically a static analysis. So you can write down the profit per consumer who is actually willing to buy from the seller which is fraction theta or alpha depending um as a function of the discount that is given in the second period. uh like so. So the uh 1 minus f is how much money you make if you sell on the platform because you price is one but you have to pay the fee of f. Uh and then the uh the um what you see as a second term is the fraction of is the fraction of consumers that will buy based on the discount that is observed in the um in the direct channel in which case the seller is able to recover the fee F which is a good part but is forced to give a discount. Therefore, some of this uh fee recovery is wasted through the discount. And uh this also shows you that the discount will never exceed the fee because the fee is what is what drives the discount. Well, you can easily maximize this and you find the the optimal discount which is um f plus underbar delta over two because underbar delta can be negative um the the discount actually can be negative as well. Okay. Okay, so the higher the fee, the bigger the discount the the seller gives, which makes sense, right? So the the higher the fee I have to pay on the platform, the bigger offplatform discount I'm willing to tolerate in order to move consumers away from the platform to my direct channel where there's no fee. Now the op algorithm here is very simple because it basically conditions the visibility of the seller on the discount and therefore can dictate the discount and forces the discount to be as low as possible which means that nobody buys on the direct channel and then PPC algorithm is not so powerful. It basically cannot it will not interfere with negative discounts. So it will not touch uh delta 2 star if it's negative. So if the if the seller is willing to set a higher price on the direct channel but it can force uh price uh on the direct channel not to be lower. So the discount will be kept at uh zero. All right. So that's um okay. So let me mention one thing here that uh given the the way the the model is set up the socially optimal discount is zero. Okay, remember this is a covered market and the only reason why consumers are choosing the direct channel or the platform is because of this dutility parameter. It's socially optimal to make the prices equal because cost everything is uh everything else on the supply side is equal between the platform and the direct channel. So you don't want to distort consumers decisions between the channels. You want to let them govern this decision to be governed by the little delta there this utility. So therefore, socially optimal discount is zero. And as a side note, if some consumers actually prefer the direct channel, it may may well be the case that the a positive platform fee is socially optimal. So this is something is kind of a let's say a minor result that we find, but something that I don't think is in the literature and we think that is something to highlight. A positive platform fee fights the the the sellers's desire to extract rents from the fact that some consumers actually prefer its channel to the to the platform. And these two may kind of uh end up with socially optimal uh price even though from the looks of it you would think that having a positive fee is bad for welfare but not so in this model. Okay. So uh so now let me get to I have whatever a bit more than 10 minutes left. So let me get into the meat of the of the problem which is the dynamic um dynamic uh story. Okay. So now let's think about um the um the whole problem. So we have a platform who does not know the type of the seller. Theta is unknown. The platform has to decide well. So let's say that the seller was featured in the in the first period. So the sales of the first period will be observed and the platform has to decide how to promote the seller based on these um observed first period sales. Now one thing that we show in the paper uh is that a threshold rule is optimal. So we don't have to worry about any other rule but the threshold rule. So let's say capital T is the threshold that was imposed by the by the optimal algorithm or any algorithm let's say in period uh uh sorry this should be period one sales threshold this is a typo so what this means is the following sales in the first period which are equal to what they are equal to the type of the seller which is multiplicative to um to its pricing decision times Q of delta 1 which is simply the fraction of demand that the seller left on the on the platform. So the the bigger the discount, the smaller is Q. If this number exceeds the threshold, then the uh then the algorithm will retain the seller, which is the same as to say that if the type of the seller is sufficiently big compared to the discount that the seller charges and the um and the threshold t that was imposed. Now the tricky part of course here is that uh the baseline algorithm does not observe delta 1. So the platform will have to make a guess about equilibrium delta 1 which is uh in the next line is delta 1 star. uh and for for a given threshold and optimal discount for that threshold we can figure out a little towel which is the for that for that sales threshold the type threshold that will clear the the sales threshold. Okay. So in equilibrium given a sales threshold and the incentives of the seller there will be some types that will clear the threshold and some types that won't. Um and the the whole game uh as as I proceed from here will be what equilibrium threshold type does the platform want to target for itself. Now one thing that I should mention is that for efficiency the equilibrium threshold toao should be equal to alpha which is the outside option is this reserve seller period reserve seller. Why is that? Well if the seller turns out to have higher probability of attracting consumers than the outside option that should be the seller that's retained. If it has lower then u it should be the other way around. So the towel the equilibrium threshold should be equal to the outside option alpha. But as we're going to see this is not always going to be the case. Now the first thing uh we need to understand is um how the the seller faced with a threshold capital T decides on what discount to uh to set. Now the the first period profit is easy to understand. This is similar to the to the static problem. the seller sets a discount. Uh some consumers buy on the platform has to pay a fee. Some people buy on direct channel doesn't have to pay a fee. There's a tradeoff. Uh and uh it's multiplied by 1/2 because um average type theta is 1/2 and the the seller doesn't know his own type in the beginning. So if only period one profit was to be maximized, it would be maximized at the at the static optimal discount that we already derived. But then that's not the full problem because the seller understands that in the second period if it's featured mass beta of consumers will arrive. It will make static prof equilibrium profit per these consumers because it will do static optimal pricing and the algorithm cannot affect it. And then the integral shows you for which type realizations the seller actually ends up being promoted. And the key issue is that the the lower bound of the integral actually depends on the actual choice of the of the seller in terms of discount. And the idea here is very simple. for a given um sales threshold. The smaller the discount that the seller gives on the direct channel, the more likely it is to exceed the threshold because even for lower realizations of its type uh it will be able to to deliver the sales that the threshold demands and that's what the career concerns effect is uh is going to do. Basically instead of just maximizing period one profits, the seller will be understanding that it wants to distort its pricing um uh upwards uh in terms of the the levels downwards in terms of the discount. It wants to offer a lower discount on the direct channel compared to the static optimum because it allows um it to retain its own position on the platform by manipulating basically what theta the the platform believes the the seller has. Okay. So that's what basically that the next line um tells us. uh and then I mean because we are dealing with um with the uniform world we can actually derive the the optimal um dynamic uh discount in the first period which is uh the static uh the static optimum minus uh a positive number. So the discount is smaller always. So because of career concerns, the seller will always distort its offplatform price upwards because it's trying to impress a um impress the algorithm which is using a which is using a threshold rule. Okay. Um so that's kind of the the first lesson. The first lesson is for any threshold algorithm the seller will distort its pricing meaning and this is going to be good for the platform because the seller is trying to impress it. But notice that in equilibrium the platform correctly anticipates delta one star. So it will not be impressed. It will actually end up knowing exactly what the type is. It's just on the margin the seller wants to impress it and therefore delivers rants to the to the platform. So that's the first um thing. Now the next thing that we do in the last five minutes I have is uh so this is the kind of the core um core of the paper is to understand what is the optimal um uh algorithm that the platform wants to implement and here the trade-off uh is uh also relatively straightforward. So the the platform profit is feat times a fraction of sales that happen on the platform in the first period and in the second period. The first period sales depend on the uh on the algorithm because uh the algorithm affects what discount the the seller gives and therefore what fraction of consumers buy on the platform. And here we are uh we are pretending that the platform as if chooses the the the threshold type towel although in the background it chooses the the the sales threshold t but think about uh it choosing directly the uh the the threshold type. So if I change the threshold type I change what discount um the seller wants to give in the first period. Roughly speaking, if I make it harder for the seller to be retained in the second period, this will uh force the seller to give even smaller discount on the direct channel, therefore bring even more sales to the platform. So that's uh that's one thing that uh that comes uh across. Now in the second period uh the platform is going to retain the seller or the reserve seller but both of them are acting myopically. So the quantity they're going to deliver is the same. So the only issue that matters is the is the big brackets here which is uh below uh theta. So if theta the type of the seller realizes to be below toao then the uh seller is dropped and therefore uh reserve sellers type alpha is in play and above to theta is in play and um so if this if the platform wanted to set a uh optimal um optimal threshold type toao without the considerations of the first period it would just set alpha equal to da. So, if I want to maximize second period profits, what do I want to do? I want to retain the the seller when he's better than the reserve seller and drop him when he's worse. But there's another effect which is that by making it harder for the seller to be retained, I actually encourage him to bring sales in the first period and that effect will always be there and therefore uh may therefore the uh the sales threshold may be distorted. Uh so uh let me um let me walk you through the the sales threshold um situation. the the sales threshold depends on the outside option. Turns out that if the outside option is large to begin with, I can just set the sales threshold the the type threshold exactly at the outside option and that will already encourage the the platform sorry the the seller to give such a low discount that he closes down the the the direct channel. So basically the the the optimal threshold achieves complete closure of the direct channel in the first period. Nothing to worry about. If the um if the outside option is intermediate then actually the the platform wants to push the threshold all the way to the to the corner solution where the direct channel is nevertheless closed but now there's a distortion to the to the threshold. So the threshold is too high. uh and then eventually if the outside option is quite small the threshold is still too high to our star exceeds alpha meaning that the outside option is sometimes retained when it's worse than the seller who is dropped and the discount is bigger than it uh the discount is such that there's some uh direct channel sales okay so I I have very little time so let me uh let me basically mention the following what ends up happening is that um so that the the dotted line is the outside option. What ends up happening is that for intermediate levels of outside option, the algorithm drops the more efficient seller a lot of the time and that's a big inefficiency that comes into the picture. So the the algorithm wants to encourage the seller to give lots of sales in the first period and is willing to distort the retaining threshold to a massive degree. In this uniform case, you can see it can be much higher than the than the outside option. Uh what that means is that the the algorithm creates uh a big inefficiency uh in terms of who is promoted. An algorithm that can directly condition on on offplatform sales does not have to do any of this. an algorithm that can check what the prices are on the on the direct channel can tell the seller look if you misbehave on the direct channel you are not going to be seen. So the seller is forced to to give no discounts on the direct channel and basically close it down. Once this is achieved the um the platform can promote uh promote the seller efficiently. So basically the I mean the point we are making in uh in uh in pictures that I don't have much time to uh to show you is that uh because uh because of this uh basically situation where that we are in the third best in the second best the third best which is allowing the the platform to condition on off platform prices can be actually better than uh than the second best and then uh let me finish with uh I have I don't know 10 seconds let's say let me finish with mentioning uh one of our headline results which I I was hoping to have more time to discuss which is that price parity close can can achieve uh first best I mean it's I'm not going to try to explain this picture but let's say for for low outside options price parity close achieves first best because it has the following beautiful property by construction when it binds it means that prices are equal on the direct channel and uh and uh on the on the platform I already mentioned this is efficient. So a price parity loss that binds in both periods achieves efficiency in terms of which channel sales channel allocation but we are able to show that when it binds in both periods it also does not distort the allocation of uh correct seller to the second period and therefore it achieves everything that needs to be achieved. Now is this some lesson that we can take to any bank and cash it? No. because we have a covered market. PPC does not have any welfare implications in terms of uh dead weight losses etc etc but we we think that we're highlighting an important uh propc um channel that has not been uh has not been discussed in the literature. We do bunch of variations of the model and uh we believe that uh what we're saying is quite robust to various uh things that are uh are to be are to be examined in this kind of framework. Anyway, so I um I leave you with the literature slide and I stop here. >> Uh Sandre, thanks very much. Um now we'll have a discussion from Marcus. Well, first of all, I'm great. Thanks a lot for the presentation, Sandro. And thanks from my side also to the organizer, uh, Andre, Julian, and Chuck for asking me to discuss the paper. So, my job is very easy in terms of I didn't have to prepare slides and I don't need to give a summary. So, it's only about five minutes and some comments to perhaps stimulate the discussion. Um, so first of all, I think it's a very nice paper. Um, I really enjoyed reading it. Um so it takes um the the way kind of how the algorithms are structured and what can be done or probably cannot be an algorithm very serious and I think it's the the first paper doing this um and also this trade-off between um kind of short-term benefits on the platforms to um increase sales on the platform but kind of maybe long-term losses in terms of the wrong salaries then promoted I think is very clearly spelled out and um I haven't seen this before. So overall I think it's very done model very nicely done in models very elegant. So very many nice things to say about the paper. Um so in terms of um stuff that comes to my mind um when when reading the paper um so Hesky and Sandra do a lot of extensions as well. So one thing which I found a little bit underdeveloped there was the exogenity of the transaction fee F. Um so basically um um f is taken as exogenous here which I think is perfectly fine for the purpose of kind of um having the onplatform price constant because um all consumers have a valuation of one and basically there is rectangular demand. So this price basically doesn't change anything on the on platform price but I think it can have interesting effects on the off um platform price. So for instance, if F would be higher, then as a seller I make lower profits on the platform and because of this I have the incentive for example to give a higher discount to consumers. And so I think um first of all there could be interesting interaction effects between um um the size or the value of the transaction fees that the platform charges and the the price um that the the sellers char um charges offline. And so in some sense in a bit of a one one step further I think it would be interesting um to see how kind of the optimal algorithms that the platform is doing can be combined with the with the fee that the platform is charging. Um so for instance um do I want to charge a higher fee in a more basic algorithm or maybe in a let's say more sophisticated algorithm as the the OP algorithm in in the paper and I think it could be an interesting um thing to study. I cannot tell from kind of my my reading of the paper whether the framework allows for this. Um but perhaps it could be interesting um to discuss this. So this was the first point that came to my mind. A second one which I not suggest to do within this framework but in general. So what we have in the model is basically that there is competition between the um re reserve seller or kind of the outside option and the the main seller. So the one who behaves strategically for getting the preferred spot but but if I get the preferred spot as a seller then I kind of basically make all the sales I can make dependent on the prices I'm charging. But in some sense there is no price competition. Um so so once kind of the the optimal spot is decided um this seller is making the sales and particular the the second one doesn't get anything. Now in some sense when I'm thinking how I usually search for hotels or authors. So of course if a seller is ranked or hotel is ranked at number 10 usually this is out of the picture probably for most um um consumers. But let's say the first two to three or often how many do fit on the first page um um dependent on your laptop or the the mobile with which you're searching are usually taken into account. And so one question is um just as a speculation how would in your model kind of not only competition for the preferred spot if I might call it for the extensive margin but also competition kind of via prices so for the intensive margin. So kind of some consumers might buy from one seller others from the other seller but there is let's say a benefit them for the first spot as compared to the second spot. how would probably this change the the predictions or would this kind of um speak towards the favor of one or the other algorithm. So I think within the the framework these were the the main two thoughts that came to my mind a little bit kind of two smaller comments I I had outside the framework um is well so I think it's great um um that the platform sorry that the paper is looking at the algorithm in in a lot of detail. Now one thing which one could think of is well in general is the algorithm the preferred things that the platform could do. Um for instance some platforms might auction off their slots and so is it could it be interesting to compare whether kind of an an algorithm um one of the three or probably the OP algorithm can do better than auctioned offer is some equivalent between different selling mechanisms and the platforms are usually doing. Um so when kind of not only focusing on the algorithm so again this is not a comment I think um that should be addressed in this paper or should be analyzed in detail but if there is something interesting to say on this I I thought it would be interesting to say kind of how do not only different types of algorithm fare against each other but how do algorithms in general um fare against other types of selling mechanisms. And so a very last point which I kind of um um were thinking of in reading the introduction. So in some sense the the main mechanism how a seller can can kind of um affect whether it is in the first spot or not here is the pricing um um in the offline sorry in the offplatform channel. And so I was thinking whether there are also some other ways how in some sense a seller um can affect of being promoted within the platform ranking or even getting to the first spot. So kind of um is the main point here all about prices or can it for for instance be also that I put a link um um to the platform I or I delete the link um to the private website. So I'm not sure whether these are realistic examples um but kind of a a minor thought I had towards the start when I was reading the introduction is kind of pricing the main point how I can get promoted on the platform or can there be other stuff that the seller can do. So overall I guess these were my my main points. Um again thanks a lot umandro for the paper and the presentation.