 It's such a great pleasure to be here. I would very much want to organize the, or I would like to thank the organizers, in particular for accommodating this hybrid model. I think it's for the first time for me that I participate in this really hybrid model, so not purely in person, not purely virtual. So it's really great. So thank you so very much for that. So today, what I'm going to present is joint work with Rod Garrett from UCSB. My name is Martin Van Oort. I work at the Bank of Canada, and the views that I expressed today, they do not necessarily reflect official positions of the Bank of Canada. And the paper that I'm going to present is Why Fixed Cost Matter for Proof of Work-Based Cryptocurrencies. And basically just zooming in on one question that the people sometimes ask is, well, Bitcoin, is it viable in the long run, or is it doomed to fail due to double-spending attacks? So one of the things, like there's these miners which basically, that keep the blockchain intact and they are incentivized by on one end block rewards. So newly issued Bitcoins. And on the other end, the transaction fees. But we know that as Bitcoin slowly grows to its limits of 21 million Bitcoins, that the number of newly issued Bitcoins per block declines. So people have been wondering, and it's really close to the question that Itai Abram asked this morning. Basically, are miners in the future sufficiently incentivized to do the right thing? And, well, there are people doubting about that. So there's, for example, this paper by Rafa Lauer. It's a BIS working paper. And it's actually a really nice paper to read, especially in the context of the question was asked earlier in the keynote. So basically what the paper asks is when are miners incentivized to do the right thing? And basically from this analysis, the conclusion in this working paper is that simple calculations suggest that once block rewards are zero, it could take months before a Bitcoin payment is final, unless new technologies are deployed to speed up payment finality. So, and then one might ask, well, are these double-spending attacks just a theoretical possibility? Well, we know they don't. They do happen in practice. So for example, there was this Bitcoin spin-off, Bitcoin gold that started as an as a side chain of the Bitcoin network in October 28. And they got attacked in a 51% attack in May 2018. And since then, there have been many double-spending attacks. So let's just zoom in for a moment into Bitcoin gold. So Bitcoin gold, it was born as a hard fork of the Bitcoin blockchain in October, 2017. It used a proof-of-work protocol that basically disabled the use of specialized equipment, ASICs for mining operations. And it did so by using a mining algorithm that was believed to be, or that was memory-proof. So basically you could no longer use these ASIC chips that were used to mine Bitcoin to mine Bitcoin gold because they didn't have that amount of memory. So, and the goal of this idea was to achieve a higher level of resilience through decentralized mining, to more decentralized mining structure because we have seen with Bitcoin that the mining structure has become more and more centralized. Now, only half a year later in May 2018, basically there were several 51% attacks on Bitcoin gold. And the attacker double-spent an estimated $18 million worth of Bitcoin gold. And how did that happen? Basically the narrative is as follows. So the attackers, they sent Bitcoin gold to exchanges. They exchanged the Bitcoin gold for other cryptocurrencies which they withdrew from the exchange. And then after that, they basically erased the initial transactions where they sent Bitcoin gold to the exchanges they replaced them by other transactions. So now they held both these cryptocurrencies that they bought on the exchanges and also the initial Bitcoin gold. And basically that was a loss to the exchanges. And then of course that led to loss of confidence in Bitcoin gold and a decline in the exchange rate. So currently, or at the moment when we wrote this, basically the exchange rate was only one sixth of what it had been at the time of the attack. And the number of Bitcoin gold transactions of Bitcoin gold transactions declined to less than a third what it was at the time of the attack. So basically here there's this chart with the Bitcoin gold exchange rate and you observe that it declined after the attack which is here on the horizontal axis at zero both in terms of Bitcoins and in terms of US dollars. So one key question is why was Bitcoin gold subject to a successful 51% attack? Well, Bitcoin has not been. And kind of a standard answer that people have in the back of their mind when you ask this question is often, well, nothing has as much computational power as the Bitcoin network. So that's really the fastest to do these computations that you need to do to mine Bitcoin or there's really nothing that can beat it. But what this answer is kind of ignoring is that the Bitcoin network is not one big thing in the sense that there are many different small actors within the Bitcoin network and they can make their own decision. So one of the things that we're wondering about in this paper is why does there not happen an attack from within the Bitcoin network? So why is there not a coalition of miners that together do a 51% attack on the Bitcoin network for financial gain? And basically we're asking under which conditions would it be profitable for them to do so? And it will turn out that the role fixed cost in cryptocurrency mining is going to be crucial to answer this question. So it turns out that actually the fixed cost of cryptocurrency mining cost that it takes to set up mining operations and to buy the hardware and the fact that you cannot really use this mining hardware for anything else that that actually provides a protection against double spending attacks. Now, of course, there's a quickly growing literature on Bitcoin mining and double spending and most of those papers they consider per period flow cost of mining, but not a fixed cost. So they only look at, for example, what you could consider as kind of the electricity cost of mining, but there are two notable examples. So there's exceptions on this rule. So the first exception is that Eric Boudich in his paper that was issued in 2018, he provides a verbal discussion of what would happen in his model when you would introduce fixed cost and it turns out that if you actually formally model the fixed cost and the alternative use value of mining equipment that the results are actually really close to his intuition. And secondly, there's a paper by Julien Prott. I think he's in the audience today and Walter and basically they discuss the entry, they model the entry decision by miners in the presence of fixed cost. They don't model the implications for double spending attacks, but their estimates, the estimates in their model, they suggest that fixed costs, they are substantial. So they estimate them to be about two thirds of the total cost of mining. So in terms of the total cost picture, fixed costs are really important. So what we do in this paper, compared to the rest of the literature is basically we'll incorporate fixed cost, the fixed cost of setting up mining operation basically in the question whether in the rich conditions, a double spending attack could occur or would be profitable. And basically, let me give you a quick summary of some of the theoretical results. So let us first look here at the column of where you only have variable cost. So there's this very quick economic result that if there are only variable cost that basically miners earn zero income in equilibrium. And why is that the case? Well, in equilibrium, since there's free entry, anybody can join for free. In the end, like quickly, basically, what will happen is that the marginal benefits should equal the marginal cost. And when there are only these variable costs, basically what will happen is that all the miners, they will earn zero income in equilibrium. So what is the implication of that? Well, suppose now there's a drop in the exchange rate. Well, for miners, that's not a big issue because they were earning zero income in the first place. And for that reason, they had very little to lose. So they don't lose a lot of money as soon as the exchange rate dropped. Okay, for now the mining rewards, there will be less than the cost of running mining operations. So some people will quit mining. Some miners will stop mining, but they don't lose anything in terms of monetary value. And then the third implication is basically, if there are only variable costs, basically what will happen and there's this really quick theoretical result is that the total amount of mining power will be proportional to the level of the exchange rate. So if the exchange rate drops by 1%, basically mining power will drop by 1%. And then Fort, well, if you're a miner, if you don't lose anything, if the exchange rate drops, so then you care less about the future of the coin. So you care less whether the exchange rate will drop, for example, as a consequence of a double spending attack. You will not lose a lot. So the cost of participating in a double spending attack are really low to you. So there's in principle a high willingness to join a double spending attack, higher at least than in the case where there are fixed costs. So if you look at the second column, well, if there are fixed costs, if you have to buy these equipment, if this costly to set up actually these mining operations, then miners don't earn zero income in equilibrium. Basically in equilibrium, it will turn out that new miners will join until the rewards that you get, the income that you earn is no longer enough to cover the cost of capital or the cost to replace your hardware. So in equilibrium, you will be earning a positive income, like economists would say there would be zero economic profits, but you're earning a positive income in the sense that you're still earning the cost of capital. And so when the exchange rate drops, you're basically losing because now you're no longer able to make good on your investment because now the exchange rate is lower and that's why the monetary rewards are going to be lower. And as when you are a miner, if there's this negative shock to the exchange rate, you will have an incentive to continue mining because you still want, because perhaps your income drop, but it dropped by a little bit, which will still make this positive margin which incentivizes you to continue mining. Of course, not when there's a really big drop in the exchange rate before smaller drops in the exchange rate. And well, since miners lose when the exchange rate drops, that's why miners have an incentive. That's why they don't like double spending attacks which can lead to drops in the exchange rate. So double spending attacks are really costly in the presence of fixed costs to the miners. And for that reason, it's less likely that the double spending attack is profitable to the miners. So we also do in the paper, but not in this presentation extension with cryptocurrency groups with transferable mining power. So in practice, you can mine different cryptocurrencies with the same mining hardware. And it turns out the results would be very similar if exchange rates could move perfectly, but of course they don't. And if they don't, but then that's in particular a problem for tiny currencies. So tiny currencies that have a low exchange rate correlation with their larger peers in that in such a situation, basically a transferability in mining power can eliminate the protection that fixed costs provide. And basically the intuition behind the result as well, there's all, even if the small cryptocurrencies, if exchange rate would drop to zero, well, the miners, they still have this option to mine this bigger cryptocurrency. So the loss to them is not that big. And empirical results, they provide supportive evidence for theoretical results. So in this presentation, I'm not going to go through the entire automata, but I just wanna show you a few pictures. So here in this picture, you see on the vertical axis, the mining power, the equilibrium level of mining power. And on the horizontal axis, you observe a percentage drop in the exchange rate. So when the drop in the exchange rate is zero, the mining power is 100% of the equilibrium value. If the percentage drop in the exchange rate is 100%, then nobody has incentives to mine, regardless of what type of hardware you're using. So the mining power will be zero in equilibrium. But then there's this threshold, which basically depends on the hardware. And this threshold equals the difference between the fixed cost of installing your hardware and its alternative use value and as a fraction of the total cost of using that hardware over the entire lifetime. So if you think about, for example, a situation where you use general purpose hardware, where these are just cloud service that you can use for any purpose, in that situation, you can think about this alternative use value as being really close to the fixed cost. So say it is close to zero. In that case, we are at the purple dashed line and basically whenever any drop in the exchange rate, when the exchange rate goes down by 50%, mining power will theoretically drop by 50% as well. But in a situation where you use different types of hardware, so for example, take an extreme case, take the SHA-256-A6, in that situation, you cannot really use them for anything else than mining Bitcoin. So you can think about this alternative use value as being really close to zero. So there will be this threshold value where basically for small changes up to this threshold, for small drops in the exchange rate up to this threshold, basically it will have no negative impact on the level of mining power. But if it drops by more than the mining power, we'll start to respond. So we can quickly check this in an empirical model. So of course, there's this time series of the mining power, so the Q. So here we are estimating changes in mining power. And on the right-hand side here, we have the change in the exchange rate. And you can think about the change in the exchange rate, like in a variable cost model where you just have the only thing that should matter for the mining power today is the exchange rate today. And the rest should not matter. But we also included here the historical peak in the exchange rate, so changes in the historical peak. So there's basically two ways that you can think about this model. One is, well, if you only have variable cost, then the only thing that should matter is the exchange rate today. So then only beta one should be relevant and there should be no time dependence. There should not, sorry, there should not be any pot dependence. So it should not matter what the exchange rate was say a year ago. That's one way to think about this model. It's a second way to think about this model. It's basically, well, we're allowing here the mining power to respond to changes in the exchange rate, but we allow it to respond more to increases in the exchange rate beyond the historical peak because then that's when you might expect a larger adjustment in mining power. And basically, under the situation where fixed costs are irrelevant, you would expect coefficient beta two to be insignificant. Now we can run that for several of the larger proof-of-work cryptocurrencies. And basically what you observe is that this coefficient beta two for the change in the look peak level, it's actually quite significant for many of the cryptocurrencies, which consistent with a story for fixed costs. Then, well, of course, then of course a drop in the exchange rate still has an impact on miners. So when they continue mining when they're with ASICS, but there's a reduction in the present value of continuing mining so you can calculate like how much would they earn over the rest of the lifetime of their hardware if there's a large shock to the exchange rate. And that's what this picture is showing. Well, if your alternative use value is really close to your fixed costs, basically what you will do, if there's a really big drop in the exchange rate, you do something else with your hardware, but that has almost the same value as mining. So that's not really a big thing. That's not a big problem. You can still get your return on your investment. But suppose you're mining with ASICS that you cannot really use for anything else. Basically what you will observe is that the present value of mining will drop considerably when there's a drop in the exchange rate and eventually will reach zero if the drop in the exchange rate is sufficiently large. And basically in this region, basically the value of continuing mining just matches your operating cost of the operation, say your electricity. So basically if we then move to double spending attacks, well, if you think about the double spending attack, there are two costs to the attackers. The first one is the coins mined during the attack, they are sold against the lower exchange rate because you expect or you can expect that the exchange rate will drop when a double spending attack is revealed. And secondly, there is this potential lower present value after an attack of continuing mining. So there's this lower present value of the mining hardware, which in particularly large for say ASICS. So basically what you can calculate is you can, from the theory you can calculate from a formula like how many coins do you need to be able to double spend in order for an attack to be profitable. And in this table we do it for a given set of parameters and actually in the paper we provide a table where people can look in their own numbers and then it gives you the number of coins that you would need to double spend for the attack to be profitable because you don't like our parameterization. But just for the parameterization that we've chosen in our paper, basically you observe here, so let's take a look at PEN OA. So suppose you would have a 100% alternative use value so that you could use this hardware for any purpose without losing value in any alternative purpose. And then suppose you would look at the drop in the exchange rate. Suppose you would expect that the exchange rate of Bitcoin would drop 30% after a successful double spending attack. Basically in that situation the attack would be profitable if you were able to double spend more than 146 bitcoins. So that's a really low number. But now if you take into account the potential fixed cost basically you observe that this number increases quickly so you easily get to a number that is more than 1,000 times larger if you take into account the fact that you cannot really use Bitcoin mining hardware for other purposes than Bitcoin mining. So because in equilibrium these Bitcoin miners make a positive profit and they will lose if there's a significant drop in the exchange rate that is why they would need to double spend far more coins in order for an attack to be profitable. So it is less likely for a profitable attack to be feasible. Now this is more the current situation so there's kind of block rewards plus transaction fees of about slightly more than 6.5 bitcoins per block. But suppose we would go to a future where there's only 0.42 bitcoins per block. So suppose where there's only transaction fees so basically this kind of has been the average transaction fees so for three quarters in 2019. Well in that case if you look at the numbers in the table they drop considerably. So this is kind of what people are worried about like this future scenario where there are only transaction fees and will this be enough to incentivize Bitcoin miners to do the right thing. Well if there would be if there would be a 100% alternative use value or alternative if there were no fixed costs basically they would need to double spend a few coins. So this is basically what the paper of Raffle Hour is warning for scenario and basically saying look you would only need to double spend if the exchange rate were to drop 30% you would only need to double spend 9 bitcoins in order for the attack to be profitable. But it turns out that if you actually take into account that you can only use the Bitcoin mining or hardware basically to mine Bitcoin so the alternative use value is 0 in that scenario that number gets closer to 20,000 and suppose you would expect a higher drop in the exchange rate of course we don't know how much the exchange rate would drop but if you would look at a scenario where you expect the exchange rate to drop by 60% that number would be even higher so you would be thinking about double spend 33,000 bitcoins and leave it to your imagination whether that's feasible or not. Now in the paper we also discuss we also give discuss a transferable mining power I'm not going to go into that during this presentation but basically what you get is you give miners this option to mine other cryptocurrencies as well and this is in particular an issue in situations where there is where one of the cryptocurrencies is tiny compared to the other. So concluding remarks accounting for fixed costs and alternative use value is crucial to understanding mining behavior and double spending attacks Second, there is this basic truth ASIC mining which involves fixed costs and a low alternative use value it reduces the profitability of double spending attacks of course that doesn't mean that it doesn't have any other problems there are issues that were raised earlier today for example decentralization but it reduces the profitability and therefore the feasibility of double spending attacks Third, the investment in special hardware weakens doomsday predictions regarding the fiability of bitcoin it seems that double spending attacks are less likely to be profitable if you take into account the specialized hardware that is used in practice for mining for example bitcoin and fourth but for that I refer more to the paper cryptocurrencies they may be less protected when they don't rely on specialized hardware when they are tiny compared to peers that rely on the same hardware and this is where I would like to thank you for the opportunity to present and also for everybody looking at this presentation thank you