 Also from the CryptoEcon lab, we have Tom Mellon, who comes to CryptoEcon lab from a background in theoretical physics and computational chemistry. He spent the last couple of years modeling infectious disease. And now he will be talking to us about fair prices for perpetual storage. Take it away, Tom. Cheers. Thanks very much, Carla. Yeah. So I'm gonna talk about a fair price for perpetual utility. So what does this mean? So I'm just gonna change my screen because we seem to be sharing the present review. No problem. Give me one second. Okay, there we are. No problem. Okay, so a fair price for perpetual utility. What does this mean? Okay, so utility, first of all, from the user perspective, this is the expectation of access to a service now or at some time in the future. From the perspective of the storage provider or what you might think of as a miner and other networks, utility, block rewards essentially are one in proportion to the utility provided. So utility, what we're thinking about here on the Filecoin L1 is data storage, which gives a decentralized and robust and efficient foundation for humanities information, but elsewhere it could be other things. So it could be off-chain compute, it could be networking, it could be tension. But focus here is on data storage. Okay, so perpetual, what do I mean by this? So perpetual is a pretty high target. I mean, keep things in context. I mean, I think it was like in the 50s, when Shockley got the Nobel Prize for the transistor, progress has been absolutely massive. So who knows where we'll be in 50 years, but as an absolutely serious target, we do need reliable long-term storage. I mean, you can see the kind of motivation from this in terms of societal value. I mean, if you wanna store important information, election results, humanitarian data, environmental records, you need to do this in a long-term way. And this kind of relies on securing a chain of evidence, relies on immutability, and it relies to be able to store on a scale of decades to ideally hundreds of years. Okay, so price. Price, we're gonna talk about a little bit. I'm gonna skip over this slide for now, but there are different things to think about there. I think an interesting aspect of this is what we think of as the fair price. So, okay, sure, you can just say the fair price. This is kind of the market equilibrium between supply and demand. But I think we can do a bit better than that. I mean, in order to come up with a fair price, you have to be able to give some assessment of what the underlying factors are that determine the price and what this is likely to be in the future. And that's not simple at all. So in order to come up with a fair price, I think we have to be informed and we have to have sufficient models and information to do this. So there's fairness in this aspect, but there's also kind of a wider point as well. So fairness generally has not been the domain of economics as pointed out here by Kahneman and Taylor. But I think to make it kind of wider point, we have an opportunity to do something different here. In general, web two economies have been based on this kind of principle of information asymmetry. You don't really know how your information is being used. Take for example AWS for one example. I mean, it's easy to get your data in there, very low cost, but getting your data out can a different story. And this same story is seen across web two, but I think with web three, we have a chance to do something completely different. Everything is written in code in a transparent way and the incentives are laid down in a completely transparent way. It's much more equitable to the different parties involved. So I think there is really an opportunity to have a much fairer take on long-term storage and other things in web three generally. Okay, so that's kind of the background. Some of the things that we can think about whenever we try to examine long-term storage are sure there's a mission. This is both motivating us. We wanna have long-term storage for humanity's most important data and to an extent, the principles with which we will develop this is motivated by fairness and encoded in the crypto economic incentives, in the carrots and in the stick, in the collateral and how this is slashed and the block rewards that are earned. But some other aspects that we have to kind of drill into if we want to price something like perpetual storage, fundamentally, you're relying on people, having hardware, having disks, buying bandwidth, having physical facilities. So that is something we have to consider if we're gonna think about price as well as other things like redundancy and how we might use some DeFi ideas or funding ideas to structure how the long-term storage is paid for. Okay, so first of all, the basics of the crypto economic incentives, storage providers, block rewards, in order for storing information, but if they don't store it reliably, their collateral can be slashed. So you can see here that if we examine the chain, you can see how effective these incentives are. So, okay, sure, anybody can have a fault, even good miners, a hard disk can fail or electricity can be cut. But you can see here the incentives are effective because, for example, for this miner sector that's shown, I don't know if you can see it well, but for this miner sector that's shown, okay, there's a fault, but then that fault is recovered the next day. And then, okay, there's another fault, but it's recovered again. So the incentives are incredibly effective. They're virtually always fixed, but there's also sufficient slackness in the system that good miners, if something breaks, they don't get penalized straight away. So this is kind of basics of crypto-economic incentives and determining these parameters and how big the faults fee should be and what the delays are. This is something we try to determine through simulation, but I'm not gonna go into that today. I just wanted to set out the basics of the incentives. Okay, so how do these incentives actually affect the price? So one aspect of this is hardware costs. And this is kind of an interesting little problem that came up whenever I was in Las Vegas last week talking to some of the storage miners. One of the things they were telling me about is, okay, we've got these hard drives and these hard drives fail sometimes and they have a warranty and the warranty is three years. And so there's different kind of options they can take, they can have a strategy where, okay, they replace it with a warranty or they just wait as long as possible and let the disk fail or, but there's a kind of different outcome from each of these strategies because if the disk fails, then it takes some time to replace and then you're open to A, losing block rewards and B, getting your collateral slashed. So it's kind of like under these kind of different trade-offs, if you buy a new disk too early, then you gotta pay more. If you wait too long, of course you gotta pay less for disks, but you got more chance of having an unplanned failure and getting slashed. So under this kind of situation, what's the optimal strategy? So one way, so part of what I'm doing here is I'm not gonna give you a price that is $10 for storing something forever, but I'm gonna set out some of the methodologies to think about this. So one way you can approach this, this kind of optimal strategy problem is to treat it as a renewal reward process. So as time goes on, disks can fail after a random amount of time and they can fail with different, they can stop working via different mode so they can fail or they can be retired. And whenever this happens, there's different ways that you can realize costs. It can be through having to buy a new disk or the slashing or block rewards. So to make progress in this, we can use the renewal reward theorem, which is given here. And okay, so yeah, we can use this renewal reward theorem, which states that the expectation of this process is given in terms of the expectation of the costs divided by the expectation of the disk lifetime. So good, but expectation over what? Expectation over some distribution. So we can model this distribution as the kind of classic failure distribution from reliability modeling, which is this kind of bathtub shaped curve as you see here. Now to actually model it, we can model it as a stretch dot beta distribution. Okay, fine, we can do that. So now our optimization problem is we want to optimize this functional. How can we do this? So we can't do it straight away because we don't know what the expected cost is and we don't know what the expected lifetime is, but if we break it up into the different modes in which the expected lifetime can be realized, then we can work these things out. So if we kind of expand that expected cost into the different ways that it can occur and we expand the expected lifetime into the different ways that that can occur as well, then we've got something that we can easily evaluate. And if we do this, we can find this optimization problem, plug in some numbers, okay, warranties, two years, three years, whatever, and find an optimal replacement policy for that disk. So this kind of feeds into knowing how long you should keep your disks for, informing miners, and of course it can feed into cost models. So another approach we can take to think about factors that affect price over a long period of time, again, is hardware. And so for hardware, physical media, we have price information. So we have this kind of Moore's Law-esque time series data. I mean, as you can see here over the past 20 years on this log scale, it's effectively linear. No, will this continue? I don't know, but you have to assume something. You always have to have assumptions in models. And if we have this assumption, can we somehow use it to inform what the price of the Filecoin Deals might be in the future? So Filecoin Deals, I mean, they've only been around for about a year. So it's kind of difficult to imagine how they might go in the future, but of course hardware is an underlying factor. So can we use this historical data to inform what the price might look like in the future? And yeah, sure you can. So we can make it like a simple generalized linear model. And if we do this, and we have some partial pooling of the coefficients in the model, so we can say, okay, we're gonna let the slopes of the historical data for disk drives inform what the deal prices might look like, then we can come up with some kind of trend for the future. Yeah, thanks. So we can do this, and of course we get a distribution. If we integrate these forecasts in the future, over all of the different realizations from the MCMC inference, then we can work at a distribution for costs of storage in the future. But of course, this is kind of limited because this is not the only factor that affects deal prices. There's so many other things. You gotta think about electricity, you gotta think about bandwidth, as well as just a market perception of what the demand might be. Okay, so let's one factor. Mostly what I'm doing here is kind of setting out some tools and frameworks for ways that we might think about this. So slight change of direction. Another factor is trying to consider how we might fund this. So one way to fund it is in terms of a yield bearing token or some kind of bond. So how does this work? This works, so instead of paying for the price of the storage fully upfront, is there some way that we can distribute the payments into the future using the interest from a bond, for example. So it's gonna be something that's very stable that produces a yield every year and that can continuously be drawn from. So if we invest in a bond, we expect to get something like this where the value of that grows over time as stated here. Now, this kind of growth satisfies the simple differential equation, but what if we don't just let the bond grow and instead we deplete it over time by using it the interest to pay storage providers. So instead, we get this kind of little differential equation like at the bottom. So now the kind of question becomes, okay, so if the client who wants to store data buys this bond and uses the interest on it to pay the storage provider, what does this look like? So how much do you need to put up for the initial bond in order to pay for the storage? So this effectively comes down to saying something like, okay, can you solve this equation under conditions, for example, like what I want is the bond to pay for the storage and for this to be completely depleted over the lifetime of the storage, for example, 100 years. So we can solve this, we can solve it, but only if we make a lot of assumptions. So we still need some kind of model for what the storage is gonna look like in the future for what the deal prices are gonna be. But if we assume that the storage price goes down very slowly, then we're kind of got this scenario. Yeah, so if we do make assumptions that it goes down very slowly, then we're in this kind of regime where, okay, you've got to pay a lot. If you have low interest rates or if you've got a very high interest rate, you can pay less and you can work out what these curves are and where you sit on it. But fundamentally, we have a kind of tricky problem in that A, we don't exactly know what the risk-free rate of return should be and B, we don't precisely know what the fundamental costs that feed in to determining the price of storage in the future are gonna be. So these are all things that are assumed, but sure, we can come up with a model that changes the funding and how the cost is distributed over time, but there's more to it than that. I guess that's what I'm saying. Yeah, so I think those are the kind of key points that I wanted to make today. If you wanna think about very long-term storage, for sure, we should absolutely do this. It's completely critical and very important and there's a lot of fundamental things we have to think about in terms of hardware prices and bandwidth and electricity that go into determining this and we can make a lot of progress on this and we can make a lot of progress on the funding side as well, but I think there's still some way to go, but yeah, we're going in the right direction. So I'll finish it with that. Thank you. Thanks a lot for that time, for that nice reflection on the difficulties and complexities inherent in modeling this sort of perpetual storage, these sorts of long-term questions. Speaking of long-term questions, do we have any questions to the speaker? Yes, I wanna be. Thanks so much. That was super, super interesting. I'm curious, I mean, I think some of these things where you're like, oh, there's a ton of assumptions to consider and it's just very hard to do. I think insurances do it all the time. They're like model very uncertain events and then there's still some price that they set to determine that this is what I'm willing to accept as a price and then sometimes they make wrong wets. And then are we fixed, right? And they have, I think, articulated some price, that like you pay for the first 200 years with 30% of whatever you put down and then the rest goes into an endowment that I guess is similar to what you're describing that then yield some interest and assume some price decline for other things. What's your take on how they're approaching the pricing? I know it's like a different model in that there's like only probabilistic guarantees for storage still being around versus in fact, I don't think we're deterministic but this curious, like Rweave has kind of tried to address that and has come up with some kind of mechanism to price it. So curious what do you take is there? Yeah, so it's kind of an interesting question. I mean, I think there's two ways to think about this in general. I think there's a research aspect and looking into all of these details and you can go into definitely a lot more detail than is in the Rweave paper which is kind of a relatively simple model makes quite hardcore assumptions and trying to look into some of the sort of sub-problems and sub-details is what I'm doing here and that's kind of more of a research question and then there's kind of a more of a business side which is like, okay, we've got this idea we're gonna release it. There is gonna be some risk associated with it. It might work, it might not. Yeah, so it's kind of like two sides. I don't know if that answers your question exactly but that's kind of what I feel you can jump into doing it but it's 100% not gonna be guaranteed. There is gonna be a little bit of risk associated with it. Yeah. Right, so I think a lot of this we're thinking having a proof of storage every day, right? But some of these older data they really probably don't require that necessarily. So what are the requirements if you wanna really put it in a glacier type storage environment, you know? Hmm, yeah. So I mean, I guess that's kind of an interesting question that maybe touches on some of the kind of deeper protocol level aspects that we might wanna think about in the future. So currently we have proofs of storage that go every 24 hours. Maybe for very long term storage that's not even something we necessarily have to have. You could have proofs that are only submitted once a week or something like that. Which might change the cost as well. So I mean, I think that kind of touches on quite an interesting idea for sure. Well, thanks again Tom for a great talk and for giving us again that long term perspective.