***Please note that this is an automatically generated transcript and will contain errors.***

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Well, first a disclaimer, this is very much progress. So, this is joint work with, joint work in progress with command. Quintus and Christophe was underway somewhere, by a, it's labs down. The other, I don't mean this is I have, like, a hard stop at 530, which have been pushed at the end of my thought, but I do need to run out and become something right after that.

So, apologies in advance for being that. So. Okay, so this is, the limit out to, just just write down a basic model and try to understand inside this or decentralization. Okay. So what if, our basic part is the following, which is there is some valuable object that is being, allocated. And the value of that object is not known to the people who are bidding for it.

Okay. So one example could be you're just bidding for the rights to on a block. And then, you don't know what is the value of the next. It could be, you don't know what the price is. It could be like, as, you know, me in front of us, in front of us, comparing notes and what we're going to talk about in one version could be you're bidding on, some sort of ETF.

And that ETF consists of stocks in Japan and stocks in New York. But unless you're physically in New York, in Japan, at the same time, you don't know the value of, you know, your ETF, where you choose to put yourself determines how much information you have, how well you can bid, and what, kind of, what, what what outcomes might be.
So I'll tell you where we go. I'll tell you what model, I'll tell you about these two, and then I'll run out and, I will answer all the questions. Here. Okay, so here's our story. There's there's going to be a dinosaur going to be continuous. Time starts at time zero. And there's going to be some period.

That period t is the period at which the value of this object matters to everyone. Okay. There's a bunch of information sources. You can think of them, in the paper, which will, inshallah exist someday in the future. It'll live on some general metric space, but for now, just think about it. There are two spots. Okay? That's like New York and those Tokyo.
Oh, that's two information sources. Okay. And what's going to happen is now that we got clock involved in this, there's going to be information coming as geometric Brownian motion okay. So as time evolves there's going to be two things. So if you're sitting right at New York you can see what is the evolution of a process in a value in New York.

And if you're sitting in Tokyo you can see what's happening there. So you have a process in Tokyo. The thing is that what really matters is what's happening at time T so what the value of the good at time t is what everyone cares about. And that is some function of
The, the instantaneous value of that process at Cafe in New York and the instantaneous value of that process. Okay. At that the in Tokyo. Okay.

That's the value process. Now I want us to, then we want to layer on top of this value process again, we want to layer on top of this value process is that there is some sort of auction happened. The bidding of this auction happens, period that the instantaneous, value or a bunch of bidders can choose where to put themselves in the space that defines New York and Tokyo.

So, for example, if we really just do a until, you know, this buys better three dimensional boards, we're just going to have a two dimensional board. You can choose to put yourself, for example, anywhere between New York and Tokyo. And then based on where you are in New York, in Tokyo, you're going to suffer some delay to, if this is point X, you're going to suffer some delay to.

In terms of what you see about Tokyo, you're going to I'm sorry, what you see in New York, and you're going to suffer some other delay. So what you see, with respect to top. Okay, based on that, what are you going to do? Well, you have you you're you're seeing you want to build a time t but of course, you only see what the value of the process was at.

The delays that you chose. Okay. So you want you want to make a bid based on this? You're only seeing this information, so you have some residual, you have some expected value for the goal, but you also have some residual variance for the. So if there's a single guy, for example, who's sitting here and they're choosing what they want to do, for instance, the auction might be you can buy this good for a price of L, some limited price.

Do you want to buy it or not? If you're sitting right here, your value is going to depend on both whether you should buy it or not. It's going to depend on your expected value. The expectation of v t, conditional on this, because it's you know, it's a drifty geometric Brownian motion does that. And another thing that will enter when you try to compute your expected value, because if you buy, you worry about what is valid.

Maybe right now, according to what I'm seeing, the expected value of the good is above my limit price. But the, but, there's a bunch of variance, so with some probability it falls below the limit price. And I eat the loss. So you also might care about or you actually do care about the variance of your value conditional on the information that you've seen.

So what does that mean. So for example the simplest proposition that we can show is if there's one guy and they have to choose whether to buy where to live. And let's suppose, for example, the value of the object is just the sum of these two signals. And these two processes are sigma one. So there's variance associated with process one.

And there's a variance associated with process two. They're going to choose the barycentric medium. So they're going to choose roughly to equalize the two variances. That's that's what a single person is going to do in this very simple model okay. That's a tells us that at least if you have one guy there's you'll find this and those binaries, they're not going to fall okay.
With Coinbase or Binance. They're going to pick the point that minimizes the residual variance, given that what they care about is the sum or some information okay. So now what happens with an auction. And that's where a lot of things start to happen. And we get stuff. But we'll tell you where we like stuff okay. So one problem with regular Brownian motions is that they're going negative.

And having the prices go negative is no fun in an auction or having values going negative. So instead, we change to geometric mean motions and do products instead. Okay. And because, there's an economist involved, economists can do lots of things, but, they get stuck with two people. So they're going to be two people. This okay.

So there's going to be x and x comma. And they're going to choose me for that. Okay. What's the structure of the game. We're looking at the structure of the game we're looking at is each of us is going to independently choose where to sit, where to live on this line or potentially off this line. Then we're going to be in the solution.

Gonna we're going to learn about each of us, the settings off that we choose. I learn that I'm not chosen over here to learn that I choose. I chose to set over here, and then I will, bid in this auction. Now, what happens when you do something like this is that the auction actually becomes kind of complex from.

It's not a private value auction. It's an interdependent value auction. So what does that mean? That means that because I'm sitting here, I know we both understand that the value of the object is going to be the product of the value at New York, and the value is Tokyo. But because I'm sitting over here, I know, I know more about, I know more about the New York value.

I know what she knows about, the New York value. I know, because I've seen the whole evolution. I know like, I know that come up saw, in more delayed. This will be sort of, now this will become Delta one of XM and, Delta one of ABC and the two of XY so seem like it's going to so, so each of us is going to understand some part of the other person's information.

Each of us is going to understand that the other person knows more about something other than the, like so I also understand that she knows more about what happened in Tokyo than I have. So I face adverse selection from Cinemark in terms of what the Tokyo value is. And then we both understand that because of the nature of the place we both live, we both also have problems, that neither of us knows perfectly what's happening in Tokyo.
And that actually happened. So what can we show in this model? We can show a few things. So first we can show that in in sort of not an equilibrium for anyone. If there are two sort of sources of information, it's not an equilibrium for anyone, for both people to sit in the same place. That's kind of dumb.

You're going to make zero money because you both know the same things, and then you just build up to the same value. It's worth it to get information from somewhere else. What else can you show? Well, that that starts to depend on the auction. So we where we start as we went down a rabbit hole of trying to solve the second price auction, because the second price auction is easier to solve in analytical form and in analytical first form, we can, calculate what happens.

But, so we, we can show that, one of the problematic things about the second price auction is suppose you even go to the limit. Suppose like finance means, and Binance has all the information. And the New York information is basically a constant. For example, there's really no variance in the New York information. We can show or we we were very surprised to show and spent a lot of time going back and forth that, even if I sit in New York and see a sitting all the way Tokyo, your intuition would has all the information Malaysia is sitting.
You know, we call it New York, but Timbuctoo with no relevant information. And indeed, even then, I will earn positive rents in the second price auction, which is kind of done and suggested to us that something bad is happening in the second price auction. We figured out that something bad is. But, it's, related to a, it's related to a pathology of the second price auction, which is the CMA sometimes means less than is expected value for the good in an interdependent values auction.

So these positive rates on the table sometimes, so that is problematic. So we then switch to the first price auction. And now the problem with the first price auction is that there is no, easy to describe analytical platform of what our, of of what our equilibrium strategies are. We believe that the equilibrium in the first price ought.

Or let me not say that, we believe that we can solve it with numerical simulations. We've somewhat convinced ourselves that it doesn't have the pathologies that we described in the second price auction. And that's why we are so hoping to do, I said this is a progress report, not a paper. So, what we're hoping to do next is understanding, is it indeed the case that, for example, the equilibrium is, in this second price auction is the growth in sits all the way in Tokyo and I equals it all the way in New York.

Is that the equilibrium that you get sort of geographic decentralization to at least the places that are producing the relevant information. So you want to co-locate, and then once we if we can, get it there, then we can do other fun stuff. But that's kind of where we are. I'll stop here, take questions and run.

Yeah. Are you modeling latency to the option here or. That's like, so do. So that is, that is so right now the way we're doing it is regardless of where you are in this network, you, you bid exactly at that date. So, there's no, like, additional latency to the auctioneer. Be super interested. That is,
So. Yeah. So we know how to do that. Oh, we need to solve this first before we can do that next. But the next step is going to say something like also your that depending on where you picked you don't get the British coffee. Your deadline is endogenous like two thirds of the other proposals which would be the natural sort of proposal time.

Right. You want to you can push it right until you can get enough, at the station for your B and that's sort of next on the. Yeah. This is kind of a model if you're the testers or uniform in the space. So it doesn't matter where you are. But it's easy to change. Yeah. That that part.

Yeah. Does the model allow for one participant to have multiple, brassicas across the, well, you'd have to define what that means in terms of you put on multiple replicas. But then what does that mean in terms of my bet? If I paid based on like I don't break the speed of like and like you'll get my information from New York to Tokyo if I submit two bids, assuming that New York and Tokyo moving zero random pattern like, depending on like your bidding is going to be different where you are because, like, it could be.

Exactly. You'd be differently based on where you are based on the information you'd see. So maybe like, you know, if you think of it as like the value of an ETF that's been, say, stocks in New York and stocks and Tokyo maybe the New York stocks right up in the Tokyo stocks. Right. Yeah. So but when you go to Tokyo, stocks go down.

You understand that when, Oakmark understands that when he's being outbid by me, you being outbid? Probably because the New York stocks went up. And you want to take that into account when you're bidding. So that's sort of the underlying technical work. But solving for.

The same I think if you the more understandable or Quintus or Christophe will give you the more understandable versions of this, if I can understand it, so can you. Is it okay? A quick question. I know that this is just not my field, so I may just not be understanding something fundamental, but like what? Why would it not converge to just New York and Tokyo?
Because that would mean that you at least getting the best possible time. Not for one source of information. Always. Yeah, that was our intuition. But in the second part. So imagine the world where Sigma is at Tokyo and Tokyo has all the information in the second price auction, the structures, the second price auction, the structure of the equilibrium of the second price auction, or the structure of the second price auctions are multiple equilibria.

Okay. For example, there's an equilibrium where I've been $1 million regardless. And you say, well, okay. Yeah. So that those that now it's not that kind of the equilibrium that's driving a problem, but the equilibrium that, is the natural equilibrium that has been studied for this says that you be sort of in number and the that number can only depend on what, you know, obviously.

Right. So you have to draw some interpretation of what the other person knows and the cutoff value, the imputation of what you put off, what the other person knows means that sometimes you're bidding less than your expected value for the good. That's bad news. Like if you're sometimes bidding less than your expected value for the good, it means you're not sitting in Tokyo who has all the information, but his bidding luster is expected value for the good.

I have no information. I can pick the expected value for the good and make some money. But that's dumb, right? But because then there's also somebody who could do it, that somebody is sitting in like, you know, tell you you could do it. Yeah. And typically when you say it's dumb, you mean that the model probably doesn't reflect reality, I guess.
Yeah. It doesn't it doesn't reflect our considered intuitions as fine economists, but it's the whole the whole game in economics is like, you see where the arrow landed, and then you draw the concentric circles around it and say, all right, so that's up. Thank you. All right. And I that's.