Daniele Condorelli (University of Warwick) - Buyer-Optimal Platform Design

Intro [Music] um so uh so what this is about uh the paper is called buyer optimal platform design so let me explain the main idea uh behind this so uh uh we want to think about the platform as matching platform here so and uh uh when you look around how uh a number of these internet players have developed you can see that a big chunk of what they are doing is a form of matching in fact alaran even famously said that Google is a matching platform now what does it mean it means that the platform is going to essentially when you um a platform such as Google you make a search for I don't know an electrician and is going to put you in contact with some electrician or you go on rbnb and you want to find an apartment in tus and uh the the the platform is going to only reveal you a subset of these results now what we are contending here is that this subset is stored okay it's not just an informational matter it is a matching matter so if I match you with a certain room then and you occupy the room then someone else cannot be matched with the room and so on so I think what I tried probably not very well to say is that we are thinking of of matching markets this is not just a platform giving information about the available options to um to its users but is the platform attempting a form of matching of course there is also information being revealed here in this matching and this is exactly uh where we where we come from so so so this is the first point the second point is that I mean I think we all know that these internet platforms we are talking about have enormous amount of data um on their users and I mean so probably this has been said many times so I won't elaborate on this point much but Google Itself by uh tracking your location in your phone it does it every seven second it can it can generate quite a good picture of your wealth and your willingness to pay on a number of um products let's say okay so so this is the second observation and this uh the information that the platform has is is way more than the information that individual agents have on the platform uh when it comes to information about the other parties in the platform okay so Google knows more about me than this electrician I'm going to click on and call uh does okay so this is the second observation and now the third observation is that now if if the matching performed by the platform is does in fact depend on the information that the platform AC about you which is conceivable then uh there will be a feedback effect uh with the respect uh to the other party in the transaction so um so if I'm I'm renting my house on rbnb in fact I have a beautiful house in Sicily if you're interested in vend Reserve let me advertise so when I when I when I put my uh house on rbnb then uh uh I mean I I get to see maybe um good the clients and I don't know maybe uh wealthy people and so this justifies the high price that I'm charging I shouldn't say this but I am charging a high price so the fact that Google matches that the platform matches me with the um with the clients that have high willingness to pay let's say reinforces my uh High pricing of the house okay so there is some equilibrium feedback of uh the pool of agent with whom you are matched to and the price that you are um that you are asking okay now this only happens because we are thinking of a platform where the transaction that takes place between this agent is not completely and this is the last element is not completely regulated by the platform but it is it happens by a bargaining between the two agents okay so this is not the case of uber for instance that matches you to a driver and at the same time it indicates the price at which the transaction takes place we are thinking more of platform perhaps such more such as Airbnb well there is an element of bargaining where there is some price posting uh that uh one um one side is able to do toward the other okay so so these are the kind of elements and and what we are going to study here is how to design this platform in a way that countervail the bargaining power that one party one side uh may have in this this transaction that takes place post matching okay so this is essentially what we uh I'll be trying uh to formalize and and what we are going to suggest is the distortion that you will have to impose will be substantial this is what what I will try to formalize now this is not we think uh Match discrimination something that just our mind taught there seems to be evidence of this uh of this of two things both of this um in a sense this what we call match discrimination so that the fact that who you are matching match to may depend on the information that the platform has about you and the fact that uh uh in fact there might be um there might be uh an effect on pricing of this so so this is just to present this quote which was Wall Street Journal inquiry or are founded thatle user spend as much as 20% more on an night on Hotel so the online TR side is starting to show them different and sometimes cost their option now again I'm I'm not I don't want to say suggested I know the reason for why this happened I want to suggest that this phenomenon we are talking about is not just a theoretical phenomenon okay good so let me let me move into the model which it will be Matching model quite simple of so we are building this uh uh with a unit mass of sellers which are vertically differentiated uh and they uh each have a measure of good of unit um sorry of quality Q okay and quality is going to be distributed in Q lower bar and Q uper bar and let's call F this distribution of values of quality and then we will have bias and we have again a unit mass of bias and Biers distinguish theel by their valuation now for the sake of this talk and also for the sake of the paper we uh uh we say to two valuation I will Comm if someone will ask later U why the case with multiple values is way more complicated and uh let's call the fraction of bias with I value mu and uh this is an important assumption the well they all are actually but the value of a buyer is only known to such buyer and the platform okay so essentially here is the platform that comes with Superior information about the buyer and the seller in particular not the seller in this case because we assume that the value is no quality but this is not as important good so what what game do the uh what game is being play here so the platform matches bias and seller one to one possibly run the matching rule is observed but not the matching okay so essentially the platform decide I'm going to match a high type with all the high type with quality above Q mu and all the low type equ equality below Q mu okay so this is a potential matching now this matching is deterministic so all the matches are known but if their matching was random then you would the agent would learn their the rule they would form posterior about who they matched with but they will not observe that directly now after the match takes place the seller makes a take it or leave it offer to the match buyer and as I mentioned this may upen under symmetric information and this is exactly the point where one of the party has bargaining power over the other okay and the buyer accept to reject so essentially this is actually a simple matching model where the matching is not determined by rules of stability by chosen by a platform and what happens after the match is not again determined by stability but is by is determined by the matching by the by the bargaining between the Matched parties and what we are doing here the main thing that we are going to do is to look at what is the welfare optimal matching and compare it with the matching that instead it is buyer optimal and let me I will justify this assumption uh if needed but um I mean um so so one one obvious this is this is of interest because the buyer is the party that doesn't have the bargaining power so there is uh there is a reason why a platform might want to uh shift the rent from one side or the other or so there might be because they wants to incentivize buyer participation or because perhaps he can only charge buyers for some reason or because yes in general one side is uh already in the platform and the other is being attracted to it okay so um let me move on to the details so matching is just a couple of Matching function that determines essentially the probability that yeah go ahead sorry just to to be sure so you you not modeling the the way the platform makes uh money right so it's just somewhere in the background that the platform charges buyer so there's no commissions there's no no I'm not I'm not doing that so the platform here is either maximizing seller Surplus or is maximizing buyer Surplus or it's maximizing welfare and yes you may think that the platform uh is uh if it is maximizing by a surplus it is perhaps because it can extract a fraction of that surle if not all so but we are not uh modeling how the platform would balance participation on both side in that sense this is not what we are doing here so uh the matching so so we can think about the matching as these two function essentially for each of the seller I'm going to tell you with which probability match to a high type and which probability is match to a low type and um as usual I matching is going to be feasible if of course I'm matching no sellers to more than one uh um to no no seller to more than one buyers that I'm assigning uh a measure of I value buyer that is consistent with the initial measure of it and the same for low value bias okay so I mean what do you want to really to think about if uh if everybody is matched with probability one so the only uh function that really matters is this pH of Q which tells how do I assign a share of I type to each of our seller okay and in fact this function also determines the posterior that each Posterior of the seller has over uh the value of the buyer okay because if I'm a seller and the matching rule tells me that I've been assigned a high value with probability 23 and the low value with probability 13 so that will be a my posterior here after being matched okay and this is this m p of Q now why is this this posterior is important because this posterior is going to determine price and in the two types case and this is just Monopoly pricing in the two types case it takes a very simple form so if my posterior is below the r between the low and I value I'm going to uh charge the low price which in this case is L * q and if and then I will sell to every body and otherwise if my posterior is high so I'm confident that the buyer is high value then in this case I prefer to charge the price LH and only sorry qh and only sell to the high D okay so this is really basic uh bargaining between a buyer and to seller when the buyer has two values okay there's nothing new and then we can compute our object or interest which is this buer cus so essentially we scan through a cross all seller and uh you need to note that buyers is are only going to make a rent if they receive the low price okay so of course the low the low value buyer is never going to make a rent so the only rent is going to ACR to the high value buyer and this going to ACR when is going to be charge the low price okay and so uh this rent amounts to Q * H minus L it only accur to the I type so it goes to pH and it only happens when the price being set is low so this is essenti and I mean the key the key Point here is look I low types are always going to make zero profit in B gaining the only one who is going to make some rent in bargaining of the buyer sites is are the high values but the high values are only made only going to make a profit when they are charged low price so essentially what the platform wants to do through the matching is uh sort of influence both how these buyers are allocating to seller and at the same time persuade sellers to charge low price if the attempt is to uh uh is to uh maximize by a cus okay so let's start though with Welfare welfare maximizing marching okay this is uh shouldn't be too surprising so suppose I want to maximize welfare okay now what is welfare here essentially is going to be uh the sum of the value of each individual transaction that I can perform now the first observation that one wants to make is that any deterministic matching is going to include complete information it's going to induce complete information so if I know as a cell that I match here to I or a low type and I know the type I match to I'm going to extract the entire Surplus from this transaction so in general a deterministic matching is going to induce complete information under complete information there's not going to be any breakdown in negotiation at the moment of trading between buyers and seller and so all the gains from trade among matched agents is going to be realized which leaves us that if I can order the trades in such a way that high value buyers are matched with high quality sell then I'm going to maximize welfare and I'm and and I'm going to maximize welfare for a class argument since I mean Lawrence and Becker that there there are complementarities in value and quality okay and so the the the positive assortative matching is the welfare optimal matching I take all the high value buyers and I match with the top quality Sellers and I take all the low value highers and they match them with the low quality s and of course one consequence of this in this uh quite stylized model here is that sellers are obtaining all the Surplus okay and so there's no uh conflict here between maximizing welfare and maximize Supply surus which is because it's a result of them having a full bargaining power in this world okay so uh after this we move to the Bier optimal match so so this is essentially Optimal Matching uh the thing that I mean again I wouldn't call it new but it's the our result and uh maybe it's better to just go to this figure here to explain it and so and uh let's start uh um by the panel on the right so when you look at the panel on the right you are going to get there depicted the matching okay so we are going to depict this pH function from Q lower bar to Q upper bar and we are going to depict here the optimal matching now how does this optimal matching work as I said we can obtain Surplus only by uh matching I uh value buyers to sellers that charge low prices but how do we induce a seller to charge low price well we can induce a seller to charge low price only by persuading the sell that is not matched with very high quality high value buyers so what we do we create a bin of of high value and low value buyers that makes the sellers just indifferent between charging the high and low price and we create being of this sort as large as possible now in this case we are going to exhaust P the low type buers because the we mu is larger than L over H so we have a lot of I values and now once we have exhausted all the all the low types we are going to be left with another Bean only composed by high type now we have these two bin of consumers and how do we match them well if we want to create the maximum surf plus we are going to create we are going to match uh the the pot that mixes low and die value to all the higher quality Sellers and then we will be left with a bunch of high value buyers and we will match them with low quality sellers okay so and this is where uh the matching becomes uh in a stochastic sense negative assortative it becomes negative assortative because low quality uh sellers receives on average expect on average to be matched with higher value consumers then uh than the high quality do and of course this raises question of stability of the of the platform and and issues of competition what if this platform was competing with another platform in fact which we don't uh which we don't address here but um I mean except in maybe in the cheeky way of saying okay but if they were doing ber they would do the same but that's yeah I don't want to I don't want to I don't want to go there so so I want to make this remark that in fact the matching is stochastic assort negative assort so it is introducing Distortion and it is introducing Distortion at the level in terms of pure sorting that is above the one that we would get if we were just to ignore information okay so because of course the natural policy question would be here okay but let's get rid of much discrimination alog together so if we get rid of much discrimination then of course uh everybody is going to be matched not based on on their characteristic SS but randomly now when I when I do this random matching the Distortion in terms of uh welfare of the of the couples that I'm producing is going to be less than the one I do when I'm trying to maximize buyer Surplus okay so this is I think one uh key message that that we want to give the Distortion that are being imposed are are of course this is in one case in the other case instead uh the buyer optimal matching is a force toward more sorting so it is a force toward more welfare so when mu is is less than L over H instead what I'm run out first I run out of I type when I create my bean where I keep the seller IND different and so now I'll be left with low type and this low type I'm going to match with the low quality sers so in this case I'm not going to introduce sorting Distortion in fact in this case pushing to buyer optimal will uh improve uh sorting it will not be as good as when I do positive assortative but it will be better than random matching and this is um um I don't know what I'm doing here so by this okay well I said this okay so and this brings us to some uh some welfare consideration okay so I mean the first one is obvious Byer op matching gives higher buer suprus than P but lower profit and Welfare and buer optimal matching is of course given Higher by this the random matching however when the seller is charging the low price all the time is going to give equal profit and higher welfare and because the profit Remains the Same but the welfare is higher because of this now uh more sorting that takes place that is welfare announcing however uh the ranking is unclear when um when there are a lot of ey types in this case uh the profit is going to be uh uh lower but the welf ranking now is not clear because of this addition sorted Distortion in fact it can be proved that um um it can be proved that welfare can decrease over the round of mat now the last point I want to make on this slide and I mean there is a figure of I mean I I should comment on it but so but essentially over there I would like to draw the parto Frontier right because we are looking we know what is the seller optimal matching which is the positive assortative and definitely the SEL optimal matching is the maximum that can be achieved in this economy in terms of rents that are being created and then uh we have our buyer optimal matching that is over there now the point that I wanted to make is that the parto Frontier is not the straight line that connects pal to bomb so we can not just okay let's randomize between the buyer optimal and the seller optimal when we want to find the par Frontier and this is an open question in a sense you are going to have to play with the matching in some way there's going to be an element of distortion of the matching and so this is going to be some convex set that goes above um uh this straight line I mean I say this in case someone uh is interested this is I think an interesting problem more in the mathematics of matching maybe than the the economics but is interesting okay so good so let me uh mention the literature and of course if Literature you want to send me an email I may omited your paper or not uh and um so please do so so let me spend a couple of minutes to uh put this in relation what we think is the relation with the l so an important relation with matching because in matching uh matching is essentially I mean all this literature has sort of impos conditions on how everybody Bargains with everybody else and how this bargaining is going to generate the matching and these are all condensed uh by the notion of stability okay now of course this is uh this presumes that there is no gaining post match so how would this uh matching platform work when there is gaining post match so this is a question that we think is um is important and in fact uh one of the laws with I mean the national Residency program which is the classic example of the twoed market matching has undergone a law s by doctor that they were claiming that uh the fact that there was no bargaining and that that uh price were posted exante would uh represent a loss for them so anyway here there are consideration of postmatch b g okay but I don't have too much time so I won't spend a lot I think I want to say because this is the Right audience the ideas that we are elaborating on in this clean setup have been before there is a paper by Alexandra there is a paper by and R and by um Ario and Julian so and and and and I think in in in this last one there's been even uh um visible the feedback effect of uh of matching or establishing of a consideration set prices so let me give credit to this literature um to for the uh some of the underlying ideas um this is um this is also a platform model yeah told me to tell you when you have 10 minutes left so perfect perfect so this is also plat so there have been a lot of platform model what differentiate our paper from this list um I think is I mean not from the last two I guess but from the from the other ones is that they are more interested in the mechanism designed question of how a platform would elicit uh values by uh playing with the match so the match as a as an allocation in a mechanism designed problem and how to manipulate this matching to induce Revelation if possible and then there are the paper of Alexandro here and Matt and others that I think are more in the spirit not of the matching problem but the information problem so who should I uh introduce you to although there is the consideration there of potential competition between the people that I introduce you uh to but yeah let know I don't remember now this paper so good so I won't say more and I did study them but uh I mean my memory nowadays goes fast and and finally this I think and this is how we started it it relates to the to the literature and information design and in particular the connection is pretty strong with the paper by Bergan Brook and Morris beautiful paper if you haven't read but hopefully you did basically this paper solves the problem of uh price discrimination in full and so you may ask yourself okay let's if the monopolis can be ended with some information about consumer what kind of outcome can we achieve can we achieve and and and the authors give like a very complete and St C essentially anything that gives the cell that is feasible and give the Cell at least the Monopoly price now our model is going to get down to there if we assume that uh quality is constant so in a sense what what we are doing is generalizing their model by allowing for all the seller to be different once this seller become different then the matching becomes relevant and uh well uh I I I have something to say here but maybe we can postpone to the discussion if something is interesting interested okay so let me move on from the Extensions literature okay here is some extensions um what of unnown quality I don't think this is very interesting to me so what is a bit more interesting is this other setup okay so you can imagine okay but I told you a story that uh basically there was uh these terms that negotiated Expos but you may think of setup in which things are posting prices and the platform then chooses a price dependent matching okay and matches then takes place and buyers buy or not okay so this would be more like maybe the rbnb uh case you could imagine in which the platform can uh if you're putting a certain price uh push you up or push you down in the ranking now uh what we show here is that essentially once we do this uh then there is going to be an equilibrium uh uh when the platform implements p and um so I mean I won't go into um details of this um but um so essentially is the idea that there's going to be uh there's going to be price competition there's going to be more competition because now these sellers are the moment they are deciding the price they are going to think that they're competing to each other for the best matching but on the other hand the platform loses uh losing steering power because it cannot influence prices as much as it was doing before okay because now prices are set before the platform even uh chooses a match but the the the theory point that comes out of this is that postmatch bargaining is really essential for the optimality of sorting Distortion so and I think this is goes back to the main point that that we probably want to make if there is this platform that matches buyers and seller and bargaining takes place Expos I mean I think of another platform you can think of dating for instance where where there is some matching taking place but of course the the true bar gaining and the allocation of Brands happens happens after and this outside the control of the platform and what we are saying is that maybe platform that are designed to improve uh the welfare of the party who doesn't have bargaining power in this postmatch bargaining are going to have to do this at the expense of substantial distortions and yeah and this assumption is really Partial Inform Platform crucial uh I mean we can do this with a partial inform platform now in a sense the platform only receive a signal about the uh the buyer and then essentially it's going to match based on Signal as opposed to match on perfect information Discussion okay and uh well I mean I think we can leave this uh for discussion I'm going to end soon so maybe if you then have question about what you'd like to discuss more we can we can do that I mean this is interesting I think for those that are into this literature on price discrimination um how to extend this to multiple values Conclusion okay so let me conclude so we studed the model where seller price after being matched with private inform buyas and the matching is done by a platform that uh is in forms and so inevitably when he condition the matching on information must reveal information and um we are we are making the point that the platform that c about buy supp will distort the matching away from the ficient and the Distortion uh can be severe sometimes the efficient matching is positive assorted and the buyer optimal is negative assort the buyer optimal matching may be less efficient than ROM matching I think this is another key point because of course you can tell me well I mean it's obvious that if all deterministic matching are going to uh generate are going to be Ware optimal then yeah of course you need to increase by higher Surplus by random matching but how much you need to increase that and in fact bring it to a point where Distortion are above the fully random matching is perhaps an observation which is no and I mean this inside extend to multiple value parti partially inform seller and also the same logic and I think there is I think the not the J Market paper but another paper but wheni it was on the market this year is about horizontally differentiated seller there's a similar flavor in a sense because now I can match you to your favorite and I can match Alexandro to to his favorite too but then both firms are going to fully exploit their uh their knowledge and EXT fully extract the rent from both of us and so might be better off by by sometimes being mismatched but uh uh keeping uh the plat keeping the sells in the dark about our time and this is I think the current team in price discrimination now a possible implication uh I I didn't dare put policy implication but a possible implication is that I mean maybe uh uh when we are thinking about regulating this platform uh there's more to do perhaps with uh what we can do about bargaining power than tampering with the matching algorithm so for instance when uh uh Price Line emerged as a platform in which uh buyers would post their price and and seller would compete uh uh for the buyers and so perhaps this was an attempt precisely to reverse bargaining power and and and now the same does eBay that for consenting sellers allow them to give some bargaining power to Consumer by allowing consumer to uh uh make price price requests and so again this might be uh have been done by the platform in an attempt to rebalance uh bargaining power that as we have seen is going to balance rents on the two sides U of the platform without having to uh manipulate the matching thank you and please write me if you have comments and stuff even if you don't like it I'd be interested to know thank you Danielle thank you now we have a discussion by Alexandro so I stop sharing yes My thoughts well yeah thank you um Alexander for inviting me and thank you Daniel for engaging in super clear presentation um in the spirit of the instructions that I was given I'm just going to talk about you know what I my thoughts are on the paper it's said no slides and I and I jumped on that opportunity um the um I think this is a super timely and uh very elegant and um and very nicely done paper um of course I related work and of course it reminded me of um uh current practices in digital markets and advertising markets which are uh manage campaigns and so what I mostly took away from this paper is a um is a very simple and and and convincing framework to distinguish uh between two types of uh mechanisms for uh matching buyers and sellers or allocating advertising space um of course you know the model is is stripped down so uh so it's not married to one platform or one application uh and what are these two well you know they didn't have equal shares in in Daniel's time but um there's a version of the model where first a matching happens and then and then the prices are uh matches announced and then and then the prices are set uh and the one with the reverse timing and and really each one of those maps to a um widely used mechanism in in digital markets you know the first one essentially said says um my the platform talks to the to the merchant and says my dear sellers uh give me your budget and um based on the features of your product uh I will assign you and show you to the following populations you don't need to bid for a keyword I have all the data I know where to find your buyers that's the first one that's the base model that's what we we saw for most of the time um the other version is also realistic and if anything is it's probably closer to where where the future is going which say something like and and I have you some of my talks I have quotes from um meta and and Google description of their algorithms and Van I can send them to you um it's where the the phrasing is different is please upload your product catalog which you think might include the prices of the products that you want to advertise um and then having sort of received the the website the the page the entire set of products and somebody wants to advertise then I will go I am the platform I will go and I will find um uh the buyers that are most interested in your product okay so both both types of managed campaigns or auto bidding or whatever you want to call them um both of them exist and and what I found super useful from this paper is a way to systematically think about the different implications of uh different mechanisms for um uh for welfare for prices uh for course for the creation and the distribution um of Sur plus um so at a at a high level I I I think this is this is a very nice contribution um as we are um you know as I get a little bit closer into the um uh the details of the model I had a first reaction that was very similar to uh to Alex's question during the talk um which is okay the matching here is is announced up front and and and how does it happen um and you know how do we microfile the the platform preferences um so I think that can be a useful prompt uh for for for a group discussion I'm not going to take a lot more time um this question of um you know what is the platform doing you know what how do we micr find this choice of of um of matching is intimately related to the Assumption of onetoone matching and so I think talking about it and and and and the talk or or after the talk I I think would be helpful um Let me let me go in in three steps um one question here is um you know there are many uh each each person can only go into one room uh but each um each hotel has many rooms right then again there are also many similar hotels so so let's start with the with the first one um in the Baseline model I think it's probably worth mentioning that um there is a totally equivalent interpretation where there's a single representative uh seller this seller has a menu of products is one product of each you know distribution of products of exogenous quality CU okay this seller shows up to the platform and the platform tells them um this is what I'm going to do for you I'm going to advertise each of your products to a given demographic say to a given consumer with a given profile and um and so you know who's going to be in front of each product and then and then you decide the prices um you can pay me for this service in my little toy model the um the seller would pay all of their all of their profit now if the platform maximizes a weighted sum of consumer surplus and producer Surplus depending on the weight on these two they're going to go either for the for the one that know that makes them charge the most to the seller that would be the assort the positive assorted the matching or to the possibly more interesting one that U that Daniel showed us and then depending on the distribution it can take different um different values that already sort teaches us a lot right there was the case in which the the matching is um stochastically negatively assorted matching and um you know in that case you would have some high types who are paying some very high prices for some relatively bad products who could you know in principle buy a better product at a lower price because it needs to be price for the uh for the bucket um and of course that's not a concern to the platform because those people will never see that product and so that's that's part of the of where the Distortion is coming from um so I think that's a nice interpretation the um the the the deal with competition in one to one comes if you follow this line of thought it says Okay um why not invest and give everybody and improve the distribution of quality uh there's no cost obviously here in the model but you could give a better distribution of quality to all of these buyers um and you're like okay maybe scarcity at the at the individual seller level maybe investing is too costly okay um but then maybe there are more sellers um so so I I think One Direction with with the you might want to go with the paper is to think about how um the long and the short of the market here would um would impact the results as I I'm going to wrap it up in one minute as I was going you know through my train of thought I was like okay maybe there's more sellers but the platform is smart they're going to take basically the um selection of products from all these sellers that are of equal measure is the measure of buyers so so that's just they're just Cosmetics on the paper um and they're going to ignore the other you know products that they just won't get matched that's fine um I think that's fine until we get to the uh the matching on prices because then um if there's more products than than uh than buyers then then at that point you know the platform can uh can engage them in some competition and so I think tracing and I'll conclude with this and then send some somewhat smaller comments to to Danielle and balash but um I think tracing the implications of you know where is one to one and equal measures of products and and buyers where is it basically without loss and and where would it change something I think that would um I think that would strengthen the message okay and um well thanks for having me and I welcome more comments from the for