Redistributive Allocation Mechanisms with Scott Duke Kominers | a16z crypto research talks

Transcript

so um let's get started one um thanks for coming last a16 research uh crypto research seminar of the week we've got our very own uh scout commoners who will be telling us about redistributed allocation and mechanisms before you get started let me just mention that muhammad park who is his first co-author he'll actually be visiting us i believe it's the week after next so he'll be hanging out here so that's that's another thing to look forward to so scott oyoz excellent thanks so much um thrilled to be you know back here presenting a second time this week very different format of talk you know no no audio at the beginning or anything this is uh this is a formal research talk um but you know as with the other like you know i love participation and comments and

questions and stuff so feel free to like you know just ask questions or you know shout them out raise your hand type them in the chat oh you know i'll be monitoring all of these things at once um you know and economists are very used to having lots of questions during their talks so please please do discuss um and then let me also shout out you know uh muhammad akbar who tim just mentioned is going to be visiting the group and pyotr dwarjak these guys are both totally extraordinary um and you know while our names are in certified random order in some shapley value sense you should apportion more than two-thirds of the credit for this agenda to the two of them because it could never have happened without either of them but it could have happened without me so if you take the you know the marginal

contributions of all the sub coalitions like when you compute the shapley value you know sort of you know more of the the density falls on their subcoalitions in any event um so this is a paper that i uh you know started writing gosh four maybe years ago like a long long time ago in in you know especially relative to typical timelines in cs um and it didn't start as a crypto paper um in fact it was a time when i like wasn't aware of like a lot of sort of the the modern consumer crypto applications that i studied these days but as we'll talk about you know sort of throughout and especially at the end it actually turns out to be like highly germane for uh you know for a couple of crypto applications you know the the starting observation is

that many goods and services are allocated using non-market mechanisms even though monetary transfers are available so like we we frequently do non-market allocation um this comes up in housing markets and healthcare uh you know so food think about in-kind food transfers like food stamps um commercial applications include event tickets i guess park permits are not exactly a commercial application but sort of more commercial than those other three uh because they're definitely not essential goods in some sense um like unlike housing healthcare and food but like event tickets you know we we see artists selling tickets to concerts at much lower than what would be market clearing prices and we all just saw this play out

worldwide with vaccines as well so like you know despite the fact that some people would have had exceedingly high willingness to pay to get vaccinated early against covet 19 in practice the u.s and virtually every other country in the world used some uh you know sort of priority system where they you know sort of allocated early vaccines to health care workers other sorts of frontline workers like people in grocery stores and also people who are at especially high risks of the elderly immunocompromised and so forth um and that's despite the fact that you know you you could in principle have used a market allocation and some people would have had very very high willingness to pay so these are all contexts where we see non-market mechanisms being used

um this also crops up in our crypto world we see it frequently with nft it's where assets are sold typically at far below market clearing prices um you know and and sometimes you know sort of sometimes via constrained sale mechanisms via waitlist and sometimes just in public sales at below market clearing prices and we see gas wars and and other sorts of uh you know competition to gain access as a result um and this is divorce this last bullet point is a little bit more speculative because i don't know of an example of it although we have talked about doing such a thing in diem uh you could imagine that if you have a semi-permission network you actually care a lot about say the geographic distribution of your your validators

right for some sort of like physical robustness to different forms of disaster or attack uh and so you might in fact be willing to um you know offer more attractive terms to someone who's willing to run a node in a location that would otherwise not be part of your system uh or you know inside of a non-profit institution or something of the sort and so once again you know you you could imagine a situation where the the organizer of the market would prefer to use a non-market allocation to do distribution or at least a partially non-market allocation you might have you know different market clearing prices depending on some of the characteristics the participants or you might just sort of like you know sort of sell sell units at different prices depending on sort of

you know you're sort of like an early sale a late sale with different probabilities of getting the good [Music] but so looking at this as an economist you know we sort of left scratching our heads right like you know these are all high value goods or at least some nfts are high value goods um why not use a market mechanism which at least in principle should lead to more efficient outcomes at least as measured by you know people's willingness to pay and one answer that we see often and that we see in all of these contexts you know phrased slightly differently is redistributive concerns right we um you know we have in-kind transfers of housing and health care and food because we think these are essential goods and and often people's low willingness to pay for them is not a

you know signal of low demand but rather a signal of low ability to pay we think it's important for them to have access even though they don't necessarily have the ability to pay for them in the context of event tickets the highest willingness to pay agents you know again it might be driven by ability to pay as well as value and those might not be the ones that have the sort of greatest positive externalities for the you know for the concert so for example um you know a friend of mine told me about an instance in which you know sort of effectively an entire pitbull concert was filled with mckinsey consultants uh you know as a kinsey event and while like mckinsey has a you know very high willingness to pay for pitbull tickets uh you know this this turned out to be like

a pretty low energy pitbull concert because you fill an entire uh i think people are like zoom filters laughter but i think some people might be laughing that's good um the uh you know it turns out to be a pretty low energy pit bull concert if you fill the room full of mckinsey consultants you don't have any like you know sort of uh you know um well we won't characterize why perhaps you know this sort of wasn't optimal but but artists often try and keep prices low as a way of getting your sort of their true high energy fans into the room um please so can you clarify what you mean by non-market like what's the difference between like free market market with quotas and tariffs versus non-market

yeah so we'll make this very we'll make this very precise in a few slides but in this context we're going to be talking about pricing that's sort of like not you know that doesn't result in assortative um you know matching on uh you know on willingness to pay so so some sort of like price constraint with rationing or randomization um we often in these contexts also see you know sort of totally unpriced allocation right so some so you might allocate like event tickets you know buy sort of a full lottery at price zero or something that's sort of a special case in in of the price zero you know we're gonna have transfers that's sort of like fixing the price at zero but like we're not talking about very complex uh zero price prioritization schemes like you might

see in the context of a of a two-sided or of a you know a matching based you know sort of allocation without money model um but there again i think the core intuition is the same the decision about like do you want to use a non-market mechanism comes from some redistributive preference you you care a lot about the types of people who receive the good and here we're going to be thinking about doing that redistribution through a through a pricing system with potentially with rationing but you can also do that via you know various forms of prayer direct priority scheme does that help awesome further questions all right um so the model today is actually going to be

a one-sided model because it's going to make the dynamics we're talking about clearer but let me just quickly like present some intuition that um at least for me is really helpful in thinking about what's going on and we have we have another paper called redistribution through markets which matches this supply demand curve i'm about to show you a little bit better and with apologies i'm like going back to econ 101 but like this is a little wacky i'm going to show you an econ 101 picture and and point out something that was always been in this picture but i myself had never noticed until i started working on this agenda with with muhammad and peter um but it's sort of like very essential in how we think about the use of market clearing mechanisms so here's a classic supply and demand curve uh i am terrible

at pictures this is true so i have to remind myself what the heck it says so supply curve slopes up demand curve slopes down good um you can think about every point on the supply curve it's representing an agent right so this is somebody who's like you know value you know opportunity cause or cost of selling is is is that point and up here it's you know it's a higher cost we've like got somebody else who has a higher cost of selling buyers similarly up here this is someone who values the good at this number this is somebody who values the good at this number and why do we pick the market clearing price well oops sorry it maximizes the area of this trial right if we push the price above market declaring instead we introduce two inefficiencies one of them is this triangle here it's

called the deadweight loss triangle these are trades that the market would bear but that don't happen right here's a person with willingness to pay above that seller's cost of selling and we don't have them trade because the price is too high the second inefficiency which isn't sort of as visually clean is this dashed line there's more people who want to sell at this price than what to buy and so we have to do some rationing we don't necessarily pick the most efficient sellers so those are the two allocative distortions the nice thing about market clearing pricing sorry is it you know saves us from both of those distortions right we get rid of the daily loss triangle and supply and demand clear perfectly so we don't have to do any rationing [Music] but note also in this picture is that

blue box right so there's also a transfer from buyer surplus to seller surplus right here it's red here it's blue and if for some reason we thought the people in our market the sellers in our market were high social welfare value relative to buyers right if we cared about getting money to the sellers enough we might be happy with this allocative distortion in exchange for an improvement in equity right and improve for like the transfer value of the market and getting some value from the buyers who buy to the sellers who sell and again as i say we're gonna be talking about you know one-sided markets today but like

this is the core idea that like somehow we're gonna we're gonna be more okay with market distortions that distort away from allocative efficiency when they serve a really strong welfare purpose but of course if we just knew precisely who we were trying to target and could target them you know then we don't need to use you know market forces quite as much to figure out like you know who we're who we want to uh target but some information you know especially you know think how the more anonymous your participants are the less information you have about them the more you actually might need to use people's behavior as a way of screening their level of need and even if you do know who they are their behavior might screen some levels

can i identify some levels of need that you might not be able to observe like particularly easily um so like think back to the start of the pandemic at the start of the pandemic became much more dangerous to drive for ride share companies uh in some abstract a hard to understand way right like respiratory pandemic clearly having a bunch of people coming in out of your car is a dangerous thing to do we don't quite know how dangerous but like rideshare got more dangerous more or less overnight and yet a bunch of people started driving for rideshare for the very first time and the way to think about what was going on there is presumably not that these people were risk seeking it like hoping to catch covet as early as possible

but rather that you know rideshare is a market with free entry and at that precise moment they had an idiosyncratic cash need that meant being able to enter into this market was was valuable to them right and that might be that like you know they were just furloughed from their job or you know they had a family member who got ill so they needed extra cash in the short run um and so in that sense you know ride share markets by you're sort of like the at the start of the pandemic especially we're selecting for sellers through their behavior who were higher need on average and so distorting the price you know sort of bumping in that case you know bumping up the price a little bit would effect a pretty high social welfare transfer

from buyers to sellers especially because buyers are pretty price inelastic so the size of that deadweight loss triangle isn't actually that big um you know and so through the market you can sort of identify you know agents you know where where the transfer role of the market is actually sort of a powerful social welfare tool and again maybe some of those things the market you know the sorry the government or so whoever the you know the tax authority is could eventually pick up right eventually you know that someone's been furloughed from their job but the market could sort of like respond immediately in a way that uh you know that a government allocation can't necessarily and then again this like you know you have a sick family member thing is maybe information the market can learn about you that you can never like sort of

credibly communicate to a to a government scott i have a question this example you're you're fixing the you're distorting the price right is it does the picture look different if you distort the quantity instead if you say like only x transfers can happen but the price could be freely set or is it the same picture uh it's probably about the same picture right like if you uh i guess it depends a little bit on the way in which the market adjusts following a change in quantity but if you like you know fixing price so that this is the market clearing quantity and fixing the quantity to equal this market clearing quantity should lead to that being the

market clearing price um modulo like general equilibrium adjustment so i i think it's effectively the same there um we're gonna see that that in-kind redistribution is not always the most efficient way to redistribute you might find that you actually want to raise a lot of revenue in the market and then just redistribute that as like a lump sum transfer uh and so there are there are various types of distortions you might want and they don't all look like ones that could be implemented through sort of redistribution through the quantity lever but like in this case i think they're basically equivalent further thoughts or questions great questions all right

so what do we need to do today uh so as i mentioned you know that that two-sided example is sort of for framing intuition uh we have another paper that sort of like matches that a little bit more directly it's called redistribution through markets uh today we're going to be looking at a one-sided allocation framework with redistributive concerns and importantly as i've already hinted we're gonna be taking this market design perspective so this is not public finance this is we control only a single market we're either a regulator who oversees that market or we're just the market designer you know we run the marketplace platform or something of the sort and we're going to be allocating goods of heterogeneous quality uh differing in observed and unobserved agents rather differing and observed and unobserved

characteristics and so we're going to have like a a curve of qualities um and which can also i guess be interpreted as like a probability of receiving the good um and the agents are going to be sort of have some observable labels and then some unobserved characteristics both like a you know an unobserved willingness to pay and an unobserved social welfare way we're going to solve the optimal mechanism design problem under incentive and individual rationality constraints uh and crucially those welfare weights are going to enter into our objective function so we're going to be doing optimal allocation with respect to what we can learn about the welfare rates because voters are unobserved um

as you'll see we're actually going to have to be drawing inferences from agents types and their behavior as to what those welfare weights actually are [Music] and what you know the the main takeaway from the paper is a framework for thinking about when you want to use some degree of redistributive allocation versus not and the key factors that drive this turn out to be the interaction between the social preferences as reflected in those welfare weights and agents observe you know the agent's observable characteristics um the role of revenue generated by the mechanism so like how much you care about revenue versus versus improving welfare through the mechanism directly um so no so for example if you can make really efficient lump sum transfers right if i can if there's some set of agents i really really care about but i

can raise like you know money from the mechanism and then buy them some really really useful good public good then maybe i still don't want to do a redistributed allocation because i want to raise as much money as possible and then use that revenue to improve welfare and then last it'll turn out a little bit to depend on sort of properties of the good itself so it only makes sense to use a good for in-kind transfers when that good is sort of universally desirable this is like you know if i have um i don't know what's it got to be really careful what's it good that's not universally desirable um you know pick your pick your favorite really really ugly sweater you know it doesn't make sense to give people in-kind transfers of super ugly sweaters because that may not actually be

valuable to them in a way that like causes the you know sort of that that causes us to be able to um you know sort of shift welfare by by lowering price um but that's a that's a different story we'll talk about it a little bit later every question that's where we're going yes the heterogeneous quality is i mean that different people care about different um items like different amounts or like everybody agrees that like each item is like what its value is that everyone is going to have a personal ind like an individual specific willingness to pay for quality and then the qual the quality levels are agreed upon by everybody so there might be like uh you know a um you know a good healthcare program

and you know like a really really power like sort of strong healthcare system and a medium healthcare system and a weaker healthcare system um you might have a different shadow value of healthcare quality but everyone agrees that the really good one is really good they ever increase the medium owner's medium and they just put different weights on it and indeed your willingness to pay is going to interact linearly that will actually be important for our machinery although i think not important for the messages okay not to belabor related literature too much but let me just quickly flag first of all um you know there's a lot of it but uh but first of all like you know there's a sort of folk theorem in economic theory that every idea in economic theory is an echo of a

classical result from the golden era of theory uh and indeed this is this is true of this entire research agenda as well marty weitzman had this beautiful paper back in the 70s that posed the idea that you might want to use rationing instead of market clearing pricing when you're concerned about equity in addition to efficiency right you have some agents with less ability to pay um you know fully market clearance you know market clearing pricing you know competitive equilibrium might not be welfare maximizing um you know this is as i mentioned also the uh sort of the tune we pick up in our other paper redistribution through markets and then you know sort of methodologically what we're talking about today sort of under the hood is building a lot on you know sort of like

really leaning heavily on these ideas by condorelli uh from 2013. um and then you know sort of the the story around why we want in-kind transfers in this context is sort of going to be very you know sort of like a like a mechanism design flavor of a story that we see in public finance as well that basically you know sometimes um you know sometimes we can screen people they call it self-targeting it's also called that in the economic development literature sometimes we can use people's behavior to screen how much we welfare we we put on them in a market uh oh and then footnote this also like you know we're gonna see mechanisms that look very similar to what you see in frameworks with budget constrained

bidders uh slightly different reason but there's a there's a sense in which there's a relationship because these budget constraints are sort of like a you know an infinite shadow value on cache past a certain point all right so without further ado let's let's set up a model we're going to be allocating a unit mass of objects to a unit mass of agents as i mentioned each object could have equality and this this was a precise answer question so the qualities are just this you know sort of distribution of qualities uh and agent types are you know have comprise a label a willingness to pay for quality and an unobserved social welfare weight so the designer knows the type distribution but crucially does not

observe the social welfare weights for the individual agents and note that if an agent of ir lambda type ir lambda receives a good with quality q and pays t then uh her utility is going to be qr minus t so that's that's how quality interacts with williams to pay so you have like a linear fixed willingness to pay for quality and your contribution to social welfare is that value but map multiplied by lambda everyone okay so far so scott can you talk about like sure it looks like i should not think if t is a transfer in the traditional sense is that right uh no

t is a transfer in the traditional sense um we just have a a welfare function that has weighted utility by by lambda but t is part of your utility so you receive the transfer in your in your puzzle than your utility function but the the social planner puts shadow value of that transfer lambda okay so transfers i guess need not cancel out in the overall revolution ah we are going to require a full budget balance so so the transfers in t are going to cancel out but indeed is what you're saying sort of the net value of a transfer can be positive right so i can take a dollar from somebody super wealthy and give it to somebody who's very impoverished and that has a net positive return to social welfare whereas like under a normal

model it would be neutral i'm not sure i completely understand why utility is like hugh times r when you're not paying anything it's q times r when you're not paying anything uh oh well it's if you receive a good of quality q and pay t so if you receive the good for free you of quality q then then you get q times r and then pay zero but in in general the allocation's gonna involve you paying something for for the good of quality queue so so it's it's not that your value is qr always it's like you've got the object of quality q and you're willing to pay for quality is far okay by the way that you can implement like people not getting the good just by

having some objects of quality actually zero right this is this is a closed interval yeah i just think of r is like a amount to pay per quality per unit quality exactly that's a willingness to pay per unit quality and as i say like i don't actually think any of the chord qualitative dynamics i'm talking about are going to change if you instead they made that concave but they would just sort of get compressed um and and machinery wise it's actually like we're leaning on the linearity to to be able to like find to sharply characterize the optimal mechanism cool all right and then again quick reminder the i is the observable so this might be like the neighborhood you live in or like you're holding is of a certain nft it's like whatever we can expect it

might be your income if we're the government it's whatever we can observe and verify about you unobserved willingness to pay is like your your sort of individual private value for quality and then lambda again is the thing that actually affects the welfare function but we can't observe it directly so we have to infer it from i and r uh so we have access to arbitrary direct allocation mechanisms we insist on you know sort of pardon the lots of notation i figure it's good for the video to actually give the the formalism but these are all stan the standard constraints as you expect them you know feasibility we have to like allocate the qualities we have you know instead of compatibility um you know we have to elicit values truthfully ir we can't make people worse off by

putting them in the mechanism and non-negative transfers so we're gonna sort of insist that we not run a deficit um one interesting footnote here because lambda influences the sorry and objective the designer's gonna maximize a weighted sum of revenue and utility so alpha times the sort of net transfer plus lambda times you know sort of dotted with this utility vector across all the different agents um one important note is because lambda affects the designer's utility but not the individuals if we try to elicit lambda directly people would just tell us what we wanted to hear right if we asked them like you know are you the person who's high you know sort of social welfare weight they

would say of course i am you know obviously um if in fact we were going to use that in the mechanism so essentially we're limited to eliciting r and imputing lambda uh under incentive compatibility and so indeed without loss of optimality we can make the allocation and transfers depend only on r and i but not on lambda directly and so instead of like just directly eliciting lambda and plugging into the welfare function because like again you know people will just will tell us whatever lambda they think we actually want to hear because that'll get because it gets them a better outcome and doesn't affect their utility um the uh the designer is going to have to

work with the expected social welfare weight given i and r so economically what we're really doing is we're estimating the need of agents given what we can see about them and what we can listen about them and so the optimal mechanism is going to declare and really the optimal allocation is going to depend on the degree of correlation between the labels and the willingness to pay with the unobserved welfare rates so so what if the labors were just done would this just be like a straightforward problem sorry if the labels were just what the lambdas were published oh yeah so if the lambda uh so we still might we still might ask like how do we do the allocation given

the lambdas and there's a there's a i guess a greedy algorithm or something you would use to do it um but it definitely gets easier so for example like lambda equal to i right so if every i like perfectly identified your lambda um then we might still decide we'd still be deciding within group um in fact actually how far am i from ha let me let me explain this slide and then i'll answer your question because like i want to reference the thing here so the way we find the optimal mechanism which i'm not going to belabor uh you know in the talk today but the details are cool and as i mentioned like you know major shout outs to conderelli for a lot of machinery um but there's sort of two steps so there's like a an allocation across and within groups

um the cross group allocation is basically going to be a greedy algorithm conditioning on what the within group allocation is and the degree algorithm is going to sort of be like allocating each marginal unit of quality to where it has the highest sort of expected social return and then the within group is going to be sort of optimal allocation given that label and we might find whether we want to sort people and willingness to pay we might find that we want to do fully random allocation we might find we want to do something in the middle uh but it's it's whatever sort of like you know welfare optimal within that group if the lambdas were sort of completely known from the group allocation that actually gets very easy right it turns out that

like a lot of the allocation questions depend on the average the average social welfare weight we basically um you know be we'd still be doing a version of this type of allocation right like it's possible that we might have really really high lambdas within a group but some agents with really low value for the good and so we might still give some units to one lambda and some units to another lambda and go back and forth but it's true we would like we'd have much less than we need to to actually elicit right we could sort of you know sort everybody by lambda and then just decide sort of cutoffs in each group for each pricing scheme or something like that could you go back just pause on the models the previous slide this one or two back this one um and you i think i missed this on the

very first flight i refers to a single player or i is like a demographic i is a demographic so an agent is an ir lambda sorry that's that's fine and then yeah great that's actually like kind of clunky notations i had not thought of previously um although it has the advantage you can say like you know ir lambda like ir baboon for anybody who watched that old cartoon but um the uh it's a crypto talk i have to make at least one totally random reference um so uh but yeah so so the i is actually like your your demographic type and it could be a very rich demographic type it could be your neighborhood your income your like i don't know uh your employer your

profession like you know in the context of vaccine allocation we think of this as encoding your profession your like general risk factor your age all of that stuff and then and then also just make sure so for non-negative transfers it actually means you can't you're not allowed to just say like i land the people uh you're going to get money from the people this is the net transfer so we can we can do some amount of uh we can do some amount of that but but it's manifested through alpha here right so we can raise money so if alpha is like higher than that than the the average pareto the average um lambda in some group uh or the yeah the average pareto weight

in some group um we can sort of raise money through a transfer and then like alpha sort of reflects giving that to you know giving that away as like a public good or something like that um but this is stopping us from just like this i guess plus the ir constraint or stopping us from just like taking a ton of money from people and giving them nothing in return um yeah and in some sense not only are we tying our hands to only one market like we're only sort of designing a single market we're also turning off just sort of like redistributive taxation power to the extent that we're doing something you know redistributive with cash it has to be cash earned through the mechanism by selling the good which again in a lot of these contexts

we're thinking about seems reasonable right like the national park service doesn't have the ability to look at go and tax people randomly nor does the typical nft meet and then can you go one forward again went forward yup or maybe two sorry where you settled here so then um how how are things possibly going to be valid so when you say allocate within group group refers to just by yeah right and then so when you say allocate within group you just mean that's based on um r because that's correct you can possibly use besides i

yep okay okay sorry so this is not this is not like obvious that you can do these two separate or is this like it's not obvious that you should be able to do that you should be able to break it down like this correct yeah this this is this is not obvious um i mean is it obvious that this is like something you could do and the only remaining question is optimality or is it yeah so it's um sure i mean because for any distribution of qualities to a group you can solve the optimal allocation problem right it's some mixture of like you know

assortative matching at some pricing and rationing right so for any allocation of qualities to groups i give you i give you i can tell you the optimal way to distribute those qualities within each group and so then it just it turns out that you can that that sort of gives rise to this like sort of uh um expected social return of giving the margin unit to a given group because you know for each unit if you think i just like peeling off the quality distribution um we know from i don't know more or less like simpler mechanism design like how who's going to get that unit if we give it to each group and so we know the expected social return of giving it to each given group and so we can just now greedily allocate on the basis of that see

sorry so then okay so maybe something maybe obvious is too strong of a word but you could say whatever allocation you eventually use that's projected onto each group whatever you do projected onto each group better be optimal within that group correct and so now if since that has more structure just write that down and optimize over that directly yeah that's a nice way of framing it actually indeed there's this sort of like dual question of like could you do it in like could you do it sort of in reverse like basically like you know price the quality is like sort of per label or something but uh but indeed like

uh you basically then have to keep you you basically end up doing this again just sort of you know in in in some inverted like coordinate space because you have to like keep track of a different available price for each label as you as you move through the quality distribution cool [Music] all right but so the the really important question is actually sort of like what does this the shape of the mechanism look like um and so the fact that the optimal mechanism has this like really simple structure means we can actually ask of the of these solutions sort of when you want to use each uh you know when you want to use in-kind versus market allocation so when you use in-kind redistribution which will mean in this context random allocation at some range of a same range

of quality levels at a below market clearing price and the answer is going to be you roughly want to do this when you have some way of uncovering inequality in the unobserved welfare ways and there are two ways that this could happen one of them is what we call label-revealed inequalities this is when you just know that like in a given group you actually want to you know sort of transfer more utility to everyone in that group so when the average pareto weight on group i so that's that like average um uh expected lambda uh exceeds the weight on revenue it's optimal to do at least some kind redistribution to that group for the context for the case of universally desirable goods these are

goods for which even the the lowest type wants the good uh special case of that is essential goods so like food stamps or public housing um here like you know you you have some eligible group um and you know we it makes sense to get do in-kind redistribution because we care about sort of transferring value to that group um i'll show you the formal statement about that in a second but it it's it's not so much in this context about giving them the good you know giving them utility by way of giving them the good but by you know doing like pooling some units of the good at the bottom we can actually lower price to the entire group the second reason you might want to do

in-kind redistribution is when there's what we call willingness to pay revealed inequalities this is when the welfare weights are strongly and negatively correlated with willingness to pay so think here healthcare this is like you know that uh you know someone is only willing to pay you know sort of 500 for some super important medical treatment the inference there is not that they don't want the super important medical treatment but they like you know probably have very little ability to pay for it um so low willingness to pay for essential health care um leads us to infer that you actually probably have high social welfare weight you're probably like you're sort of impoverished or otherwise in high need and so there again we might want in kind redistribution because it's a way of transferring to those agents who we infer through their behavior are

actually high need isn't that scott i mean wouldn't that be vulnerable to manipulation though because like anybody can manipulate their willingness to pay down as you know this is what you're doing yeah so so it has to be done in a way that is incentive compatible which is actually very important right so we're pooling some quality levels um so you're gonna get lower quality at this lower price um and so but the the pooling and the pricing has to work out precisely so that like really high types don't want to mimic the low type so so yes exactly so like and this is in fact a problem with lots of public housing programs so there are a lot of places like amsterdam for example where the public housing has historically been

so good that even the very wealthy people would like to have it if they can and so as a result um you end up with sort of the wrong people claiming the you know the the transfer um and so indeed you actually like you know within group are gonna get like you know sort of these willingness to pay revealed inequality people are gonna get access to higher quality goods than they they would get at the market clearing price but lower quality than others you know for for incentive concerned reasons or lower yeah lower lower expected quality because it's random allocation okay so just formally like what what does this look like so label revealed

inequality as i mentioned is that the average per weight in a group is strictly larger than the weight on revenue alpha and the good is universally desirable so lowest type place you know has positive willingness to pay um then there's some cutoffs so that we want a random allocation at a price of zero for all types below that cut off now one intuition for this could be that we're just like giving the you know sort of those agents welfare by giving them stuff for free but that's actually like like not what's going on here um what's really driving this you know because remember in this group we want to we want everybody to do better right this is the average period of weight for the entire group we care about giving welfare to everyone rather than just the people with low

willingness to pay uh here it's that a random allocation for free lets us lower prices for everybody right by like pooling a bunch of prices you know sort of objects at a lower average fault you know sort of by you know at the bottom you know we're sort of pricing at the the average quality in that pool rather than the top on the margin and that means we can lower the price that everybody else faces sort of to the extent that we have an assortative allocation at the top um meanwhile there's this willingness to pay revealed inequality as well this is the one where where we care about the people with a really low willingness to pay in particular um and you know you can write out the exact condition it's gonna look actually pretty familiar you know has has a has a virtual value

component in it uh just with these you know sort of uh compared to these uh these sort of social welfare rates for the transfer um assorted matching is going to turn out to be sub-optimal of willingness to pay is strongly negatively correlated with welfare rates as i said so the converse question is when do we want to use market mechanisms so when instead do we want assorted matching at market clearing prices and this sounds almost tautological but let me then try and convince you with two bullet points it's actually not as tautological as it sounds you know roughly this wants to happen when the revenue and efficiency motives dominate versus redistributive concerns when somehow we care more about alpha and or overall efficiency than than redistribution but the question is when

does that happen so there are two contexts one of them is about revenue maximization so this is just when when alpha is high and remember this doesn't necessarily mean we're a for-profit entity it might mean that we just like can do something really socially valuable with that alpha that's sort of effectively a transfer to everyone so if the weight on revenue is above the average pareto weight on some group we want at least some assorted matching um and that's gonna that's gonna happen when you're your buyers are sort of like low low pareto weight in the first place i think corporations or as i said when lump sum transfers are feasible sorry the other context is efficiency maximization again this sounds almost tautological

but like we can say something precise about what it means here which is kind of interesting like when is efficiency maximization optimal in this framework it's when the welfare rates do not correlate with willingness to pay when we're not like you're within it within a group but we're not inferring anything from people's willingness to pay that tells us about welfare so that's when there's either a small dispersion in welfare weights to begin with so just like everyone in the group is equal or or like you know we don't care we have sort of uniform welfare rates over the population but also it could be that they're a large dispersion of welfare weight so there's big differences in people's like you know ability to pay or like their income or their level of need but it isn't correlated with willingness to pay so i think this is like bottles

of milk right like if somebody's not willing to pay a dollar for a bottle of milk or inference is typically not that they're super impoverished but rather they just don't like milk um and so you know mark you know in many ordinary scale markets we actually even if we wanted to do redistributive allocation we couldn't because we're not learning anything about the welfare weights from people's willingness to pay right we could subsidize milk for populations where we can see in observables we want to subsidize them but we can't sort of like do redistributive pricing within a group because the willingness to pay just tells us people's tastes yes you didn't include the case where there is very strong positive correlation between willingness to pay

and wait is that because that's obvious for this because it's not true uh no no that one's that one's straightforward so there's really strong positive correlation between welfare rates and willingness to pay both of these push in the direction of uh you know it's good for revenue to do market pricing and it's good for welfare to do market pricing you might yeah mod you know up to the average for raider weight so that's within group you might still have some amount of you know sort of redistributed by allocation across the group somehow [Music] cool um okay just the interest of time this is this is the statement of the assorted matching at the top um

yeah i mean this is this is pretty close to that statement you know basically if the revenue maximization motive dominates for high enough types that of course you want some amount of assortative matching um same thing if the efficiency maximization motive dominates for high enough types but then you know sort of we've talked a lot now about the within group distribution um let me quickly say something about the the cross distribution um so here's something that's a little bit uh that i would not have sort of like i was surprised about as we were working on um but mechanism design concerns actually make sort of totally clear exposed so let's imagine now that we have two groups and then group one we're doing assorted of matching and in group two we're doing fully random

matching so like there's one group that's like all market pricing in one group that's sort of like all-in-kind transfer you can ask the question of like which units do you want to send to which groups and the answer is a little bit uh you know surprising so like the natural conjecture and often what we do in practice is we send the lowest quality objects to the group that gets you know the the in-kind transfer but in fact from a mechanism design perspective what you'd really like to do is take more revenue out of group one and the way to do that is to have higher dispersion in quality within that group so you actually want to send like middle quality objects to the as the in-kind transfer and use the top and bottom

quality objects uh you know sort of for the assorted matching group one quick question please i don't remember if i missed an assumption on lambda but i think if i remember correctly you said lambda also multiplies how much you suffer from payments how much the welfare metric suffers from your payment once the welfare metric suffers from payments yep is it possible that even when you're doing the assortative matching you don't want to raise a lot of revenue because the welfare metric gets destroyed by people with super high lambda even though i care about adding revenue yeah probably

um you may be limited in how you may be limited in your ability to collect not that much welfare in assorted matching because the incentive constraint forces you to have a price gradient that's kind of back to this case i guess right it's like how does your weight on revenue compare to your average pareto weight in in a given group oh i see okay so i think there's actually a lot big into that which is that you would never be in a situation where that happened and you were doing the sort the um ultra maximizing matching okay do you think that there's a lot that goes into that aside from just intuition you put at the bottom uh correct and indeed like so this is and you might still have some degree of assorted matching at the top um

but you know because all this result tells us is that we want some amount of random allocation at the bottom the reason we want the random allocation at the bottom is precisely because it lets us lower prices to everybody while maintaining incentive compatibility that's actually like a more precise it's a very nice it's a very precise intuition for why you actually use the random allocation to lower prices for everyone because you couldn't even if you wanted to lower prices to everyone at the top you can't just do that because you lose the incentive constraint in the last couple of minutes i just want to say a little bit about policy i'm gonna talk about you know uh government policy for a second and then then talk about nft mint policy um so looking at the world with this sort of

logic changes the way we think about a lot of sort of non-market versus market allocation mechanisms so an early case uh you know another early pandemic example something that happened in in march 2020 was a bunch of people went to dollar stores bought all the hand sanitizer and then started selling it on amazon and ebay for you know 400 x markups uh 40 to 400x i guess markups um and this was you know so people were very upset they referred to this as price gouging these some of these people have since been prosecuted um but like to an economist at first blush that sounds sort of strange it's like well you know people's willingness to pay was very high you know they were able to sell these things for forty dollars a bottle when they bought them for a dollar like that's that's markets working isn't it

so in the frame of this paper you can sort of realize that that's like a really regressive allocation right like at the start of the pandemic everyone thought they needed a lot of hand sanitizer and you know it started out pretty evenly distributed across the country and if anything buying it from from dollar stores which are often in lower income areas and you know selling it to people with high ability to pay right you know sort of willingness to pay a 40 was not 40 was not reflective necessarily of like you know especially high demand relative to others but just like a greater ability and access to pay large amounts for it on an internet platform and if anything the need was probably greater in those low-income communities where people were

more often having to go in person to jobs take public transit and so forth and so this is like a really regressive reallocation of the goods um meanwhile food stamps which are you know sort of people have criticized for you know sort of providing in-kind transfers to individuals you know actually food stamps are really really hard to get access to right it's a really really small benefit and so there's a sense in which like the the process of going through you know sort of becoming um you know sort of gaining certification to receive food stamps it's sort of almost its own means test it's a little bit outside of this

model but it's like you know it's like a queuing or like some sort of like very very strong like active uh you know sort of work to gain access and it's like the people who show up and like pay that cost to participate are signaling their need again through their behavior uh and indeed right like you know the shadow value of transferring some you know so some welfare to them uh or some surplus to them rather is probably such high in welfare terms that we could actually make food stamps programs much larger um this also has bearing and how we think about sort of inequality on on marketplace platforms uh and then you know as as promised this like it was shaped in a lot by thinking about you know nft mints and other sorts of like you know

community building um processes in in the crypto world uh indeed it's shaped so much that we're we're now working on a paper that uses a lot of the same machinery and logic here to try and understand for site you know you know precisely what i'm gonna i'm about to say in more detail um also by the way that cueing thing so jointly with shangri-li we're also trying to understand that so so when you have a world where some people have you know high value for money and other people have high value for time you can use queuing as a way of screening the people with with high value for the good high value for money but low value for time and so that now the cross-correlation between the value for money and value for time becomes relevant but so um you know very non-random example uh you

know sort of uh jenkins of la is having their bored and dangerous mint next week uh this is extremely non-random example i'm i'm very good friends with the people who who run this project we have a bunch of joint projects in progress uh and moreover they're an a16z portfolio companies this is emphatically not a random example it is also not investment advice i'm only here to talk about their uh their auction mechanism so uh they're running a you know market clearing dutch auction which is actually sort of like a you know also pretty interesting they're beautiful and like very sophisticated contract doing a you know a full clearing price auction with automatic refunds there's also some interesting stuff there but

like many projects they also have a you know a you know like a white list in this case the right list where they're selling the goods at a discount and this is going to several different sets of individuals these are people who you know own their original nft collection who were involved in the production of the book board and dangerous or who you know sort of engaged in in puzzle and other competitions inside of their community sort of show you know sort of showing effort and interest in engagement and in fact there's actually sort of three phases there's a public sale the rightless sale and then a free claim for all you know sort of a price zero for all of their original nft series holders um

and this setup you know it's a little bit abstracted from from the the world of the model of course but it's actually very much the same sort of idea right like here you know we have different individuals like this is this is label revealed in equality we have individuals with different welfare weights that we place on having them in the sort of remain in the community and get access to the new good right like the highest rank is the community of people who are the writers room and sort of contributed to writing the book uh next are you know people who are either actively engaged in the community or who were involved in licensing and sort of contributing intellectual property to the book and then there's the public where we have sort of no ability to screen other than on price and you've got the prices exactly sort of

structured um you know in the way that the the model would would predict that you should under the optimal mechanism that you sort of you know you're essentially giving a discount to the agents that you have special welfare reasons to want to include and and thus care about their welfare [Music] uh willingness to pay revealed inequality actually does happen in these contexts as well although i haven't i've looked around i couldn't find a specific instance that had actually been used although i've seen there there are a number of projects that had talked about doing a mechanism that's actually very close to the um the the middle type goods where they basically have a clearing price auction at the start so there's like assorted matching on price uh clearing price or or um pay as bid

descending auction at the start so you know assorted matching on price with probability of getting the good equal to one then like a a mint for their their community at some reduced price and then an open mint at an even lower price of all the remaining objects and so you have precisely the price gradient that would be sort of set up by that last um example i showed you you can mint with certainty at some clearing price you can mint uh you know if you're in the the group of active and engaged community members at some lower price you know sort of like middle quality if you will uh and then you know there's a there's a sort of a frenzy at the end at some low but market clearing price where you sort of know you're getting rationed [Music]

all right so that is our story for today uh we've proposed a model of optimal allocation under general redistributive concerns we've sort of saw the correlation between the welfare weights and the elicitable and observable information is what drives like whether you want to do redistributive allocation and it also matters very much how revenue used you sort of collected by the mechanism that's used like to what extent does revenue substitute for doing redistribution through the specific market excuse me and again in here and this is i think very general and extremely not limited to this particular market design context the key dynamic is that we're using the the observables and even more importantly agents behavior like what

they reveal about their welfare weight from their behavior in the market you know again we scratch the surface and how this ties into crypto applications specifically but but i do think there's a real sense in which in markets where participants are mostly pseudonymous this is a particularly important thing to be able to do we really do actually want to be using all the information we can get from people's behavior to try and understand you know sort of what their contribution to social welfare to our community to you know to an open source product whatever it is is worth all right qed and happy to chat a little bit more with questions thanks so much so maybe just to connect the dots a little bit more the mapping between sort of your model

and results in that teammate examples um so like for the jenkins example was that a case where like lambda in effect was known it was that he's even almost like defined by the by the design yeah so lambda lambda is mostly defined by the group so like yeah so i would think of you know they've they've assigned or they haven't they have an average yeah it's maybe yes and maybe no i think of them as thinking they know the average lambda which is an assumption of the model right that we can we can compute lambda bar uh you know for each group like you don't know precisely who in your your community of people who license intellectual property are the ones you're most excited about bringing into your your azerbaija world but you can infer that those are like more

likely on the margin to be people who have high social contribution um and so i think of them as knowing the averages but but not necessarily the individuals lambdas so that's what that's actually like precisely how we set it up in the model that makes sense that makes sense and then probably they're just being like slow with a change of variable here but so the um trying to connect like what you said about the partitioning quality space and the like three intervals and yeah and then versus sort of like some of the examples in a teammate where you have stages and like reduced prices yeah is that just like a change yeah so queue here i would think of it an nft men so you could actually do it where you sell different qualities right so i've seen a few projects proposed but

nobody actually do a process where if you mint earlier in the auction process you have a higher probability of getting a rare or something of the sort um but uh when i'm thinking of this here q is more like your probability of being able to buy successfully or like maybe the number of units you have access to or something like that um and so uh so in the case of jenkins like q is one you know sort of like or you you buy with certainty each time you buy in the auction you also actually get to buy with certainty in that middle category but then like if there were a cleanup step um that would be like you're buying with some probability below one because everyone's trying to buy at the same time okay this makes sense so basically i mean you always right so you actually think like stage

two and stage three both are kind of like over demanded like many more people sort of like exactly right right so then the point is it's just going to be the third stage it'll be a lower price would be a larger population will be a smaller probability of of being a winner and so that's the that's the exact thing excellent excellent questions like entertainment's like in these cases are all i can see just two and three of less quality doesn't like gas fees like raise the price to what would be in stage one and kind of mess things up a bit yeah it's true i i i very sneakily the very last minute changed a word in this uh in this slide to make to exactly avoid that concern so the way you would really want to do this

is a descending auction with a fixed price lottery at the end rather than a you know a fixed price sale at an instant um i agree so like the uh you know something that is totally outside of this model at the moment is anything resembling a gas fee um and and we've seen repeatedly that that uh you know probability you know probabilistic mints at far you know with rationing at far below market clearing prices have found market clearing prices and gas fees instead um but i think you you could do this in practice if you did it via via a lottery that people just have like a long term sign up you know you sort of at the end of round two announced okay this is the number of units available you have two days to sign our lottery list and then we're just going to draw

the randomness for you you might and indeed you're just like generally good lottery etiquette for people who are a good on-chain lottery etiquette for people who are uh you know watching this in the future uh you're gonna probably wanna cause people to escrow so that they can't create you know infinitely many lottery accounts and so that you have you know you you know that you have the the value in place to call in exchange for the mint questions for scott awesome thank you scott thank you so much