Re: [Bitcoin-development] death by halving
On 26 October 2014 00:10, Ross Nicoll wrote: > I'd suggest looking at how Dogecoin's mining schedule has worked out, for > how halvings tend to actually affect the market. Part of Dogecoin's design > was that it would halve very quickly (around every 75 days, in fact), so > it's essentially illustrating worst case scenario. > Yes that is an interesting data point, but it's really hard to find comparables to doge, and most of its hashing is now merge mined with litecoin. Comparing doge to btc may be a case of apples and oranges. > > > Firstly, miners do not all move/shut down as a batch. Some will stay out > of loyalty/apathy/optimism, so there's a jolt to hashrate when the rewards > drop, and then a drift towards a steady-state. In most cases, the hardware > costs vastly exceed the running costs, so while they may never see ROI due > to the reward change, there's no benefit in stopping mining either. > > On the other side, mining hardware update cycles are extremely aggressive, > and newer hardware runs much faster. Further, those with newer hardware are > likely to have the best hashrate to power ratio, and be less likely to turn > off or rent out their hardware. > > So, in theory there may be an uncomfortable period where the hashrate > drops, but I would expect that drop to be much less than 50%, that most > hardware that's turned off is not cost-effective to rent out, and that > newer hardware being launched would push the hashrate back up again within > a sensible timeframe. > > Ross > > > > On 25/10/2014 19:06, Alex Mizrahi wrote: > > # Death by halving > > ## Summary > > If miner's income margin are less than 50% (which is a healthy situation > when mining hardware is readily available), we might experience > catastrophic loss of hashpower (and, more importantly, catastrophic loss of > security) after reward halving. > > ## A simple model > > Let's define miner's income margin as `MIM = (R-C_e)/R`, where R is the > total revenue miner receives over a period of time, and C_e is the cost of > electricity spent on mining over the same period of time. (Note that for > the sake of simplicity we do not take into account equipment costs, > amortization and other costs mining might incur.) > > Also we will assume that transaction fees collected by miner are > negligible as compared to the subsidy. > > Theorem 1. If for a certain miner MIM is less than 0.5 before subsidy > halving and bitcoin and electricity prices stay the same, then mining is no > longer profitable after the halving. > > Indeed, suppose the revenue after the halving is R' = R/2. >MIM = (R-C_e)/R < 0.5 >R/2 < C_e. > > R' = R/2 < C_e. > > If revenue after halving R' doesn't cover electricity cost, a rational > miner should stop mining, as it's cheaper to acquire bitcoins from the > market. > > ~~~ > > Under these assumptions, if the majority of miners have MIM less than > 0.5, Bitcoin is going to experience a significant loss of hashing power. > But are these assumptions reasonable? We need a study a more complex model > which takes into account changes in bitcoin price and difficulty changes > over time. > But, first, let's analyze significance of 'loss of hashpower'. > > ## Catastrophic loss of hashpower > > Bitcoin security model relies on assumption that a malicious actor > cannot acquire more than 50% of network's current hashpower. > E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based Double > Spending_ paper which shows that as long as the malicious actor controls > only a small fraction of total hashpower, attacks have well-define costs. > But if the attacker-controlled hashrate is higher than 50%, attacks become > virtually costless, as the attacker receives double-spending revenue on top > of his mining revenue, and his risk is close to zero. > > Note that the simple model described in the aforementioned paper doesn't > take into account attack's effect on the bitcoin price and the price of the > Bitcoin mining equipment. I hope that one day we'll see more elaborate > attack models, but in the meantime, we'll have to resort to hand-waving. > > Consider a situation where almost all available hashpower is available > for a lease to the highest bidder on the open market. In this case someone > who owns sufficient capital could easily pull off an attack. > > But why is hashpower not available on the market? Quite likely equipment > owners are aware of the fact that such an attack would make Bitcoin > useless, and thus worthless, which would also make their equipment > worthless. Thus they prefer to do mining for a known mining pools with good > track record. > (Although hashpower marketplaces exist: https://nicehash.com/ they aren't > particularly popular.) > > Now let's consider a situation where mining bitcoins is no longer > profitable and the majority of hashpower became dormant, i.e. miners turned > off their equipment or went to mine something else. In this case equipment > is alrea
Re: [Bitcoin-development] death by halving
I'd suggest looking at how Dogecoin's mining schedule has worked out, for how halvings tend to actually affect the market. Part of Dogecoin's design was that it would halve very quickly (around every 75 days, in fact), so it's essentially illustrating worst case scenario. Firstly, miners do not all move/shut down as a batch. Some will stay out of loyalty/apathy/optimism, so there's a jolt to hashrate when the rewards drop, and then a drift towards a steady-state. In most cases, the hardware costs vastly exceed the running costs, so while they may never see ROI due to the reward change, there's no benefit in stopping mining either. On the other side, mining hardware update cycles are extremely aggressive, and newer hardware runs much faster. Further, those with newer hardware are likely to have the best hashrate to power ratio, and be less likely to turn off or rent out their hardware. So, in theory there may be an uncomfortable period where the hashrate drops, but I would expect that drop to be much less than 50%, that most hardware that's turned off is not cost-effective to rent out, and that newer hardware being launched would push the hashrate back up again within a sensible timeframe. Ross On 25/10/2014 19:06, Alex Mizrahi wrote: # Death by halving ## Summary If miner's income margin are less than 50% (which is a healthy situation when mining hardware is readily available), we might experience catastrophic loss of hashpower (and, more importantly, catastrophic loss of security) after reward halving. ## A simple model Let's define miner's income margin as `MIM = (R-C_e)/R`, where R is the total revenue miner receives over a period of time, and C_e is the cost of electricity spent on mining over the same period of time. (Note that for the sake of simplicity we do not take into account equipment costs, amortization and other costs mining might incur.) Also we will assume that transaction fees collected by miner are negligible as compared to the subsidy. Theorem 1. If for a certain miner MIM is less than 0.5 before subsidy halving and bitcoin and electricity prices stay the same, then mining is no longer profitable after the halving. Indeed, suppose the revenue after the halving is R' = R/2. MIM = (R-C_e)/R < 0.5 R/2 < C_e. R' = R/2 < C_e. If revenue after halving R' doesn't cover electricity cost, a rational miner should stop mining, as it's cheaper to acquire bitcoins from the market. ~~~ Under these assumptions, if the majority of miners have MIM less than 0.5, Bitcoin is going to experience a significant loss of hashing power. But are these assumptions reasonable? We need a study a more complex model which takes into account changes in bitcoin price and difficulty changes over time. But, first, let's analyze significance of 'loss of hashpower'. ## Catastrophic loss of hashpower Bitcoin security model relies on assumption that a malicious actor cannot acquire more than 50% of network's current hashpower. E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based Double Spending_ paper which shows that as long as the malicious actor controls only a small fraction of total hashpower, attacks have well-define costs. But if the attacker-controlled hashrate is higher than 50%, attacks become virtually costless, as the attacker receives double-spending revenue on top of his mining revenue, and his risk is close to zero. Note that the simple model described in the aforementioned paper doesn't take into account attack's effect on the bitcoin price and the price of the Bitcoin mining equipment. I hope that one day we'll see more elaborate attack models, but in the meantime, we'll have to resort to hand-waving. Consider a situation where almost all available hashpower is available for a lease to the highest bidder on the open market. In this case someone who owns sufficient capital could easily pull off an attack. But why is hashpower not available on the market? Quite likely equipment owners are aware of the fact that such an attack would make Bitcoin useless, and thus worthless, which would also make their equipment worthless. Thus they prefer to do mining for a known mining pools with good track record. (Although hashpower marketplaces exist: https://nicehash.com/ they aren't particularly popular.) Now let's consider a situation where mining bitcoins is no longer profitable and the majority of hashpower became dormant, i.e. miners turned off their equipment or went to mine something else. In this case equipment is already nearly worthless, so people might as well lease it to the highest bidder, thus enabling aforementioned attacks. Alternatively, the attacker might buy obsolete mining equipment from people who are no longer interested in mining. ## Taking into account the Bitcoin price This is largely trivial, and thus is left as an exercise for the reader. Let's just note that the Bitcoin subsidy ha
Re: [Bitcoin-development] death by halving
Interesting analysis! I think there are a few important effects that aren't being considered. 1. When the block reward is halved, inflation is halved as well. Is this halving already priced in by the market or will it result in an upward pressure on the price? 2. It was acknowledged that the referenced analysis did not take into account the result of a double-spend attack on the bitcoin price. However, the effect of a detectable double-spend attack on the Bitcoin network is not isolated to Bitcoin markets. The price of altcoins often trend with the price of Bitcoin, so attacking Bitcoin may reduce the profitability of 'multipool' mining. Any alt-coin market vulnerable to the malicious hash-power would probably go into panic mode. -Alex Leishman On Sat Oct 25 2014 at 1:51:10 PM Alex Mizrahi wrote: > > >> For the sake of argument, lets assume that somehow (quite unlikely) > > > Why is it unlikely? Do you believe that the cost of electricity cannot be > higher than expected mining revenue? > Or do you expect miners to keep mining when it costs them money? > > >> half the mining equipment gets shut off. >> The amount of hashes/second is such that it is currently, lets just say, >> quite >> secure against any takeover. >> > > The equipment won't be simply turned off, it will be up for grabs. > > Please check this web sites: > > https://nicehash.com/ > https://www.multipool.us/ > > One can use them in the same way he uses normal mining pools, and they > switch between different chains. > Say, multipool.us can switch between BTC and PPC (Peercoin). > Mining BTC will be less profitable after a halving, so a miner who is > willing to maximize his profits might use multipool to auto-switch to > something more profitable. > Which might be attack-on-Bitcoin. > E.g. if 60% of bitcoin's total hashrate is available via "multipools", one > can try to pull of a double-spending attack. > > >> Your document makes a long series of assumptions about how this can turn >> out >> bad with each individually is implausible, together are just fiction. >> > > It sounds like you failed to grasp even basics. > > -- > ___ > Bitcoin-development mailing list > Bitcoin-development@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/bitcoin-development > -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
On 25 October 2014 21:53, Alex Mizrahi wrote: > > We had a halving, and it was a non-event. >> Is there some reason to believe next time will be different? >> > > Yes. > > When the market is rapidly growing, margins can be relatively high because > of limited amounts of capital being invested, or introduction of more > efficient technologies. > > However, we should expect market to become more mature with time, and a > mature market will result in lower margins. > The halving can do much more damage when margins are relatively small. > > Besides that, there is a difference in ecosystem maturity: > > 1. Back in 2012, miners weren't so focused on profits, as Bitcoin was > highly experimental: some were mining for the hell of it (it was a novelty > thing back then), others wanted to secure the network, others did it > because it was hard to obtain bitcoins by other means. But now miners are > mostly profit-motivated: they buy expensive dedicated mining equipment and > want to maximize profits. As you might know, at one point ghash.io > reached 50% hashrate, and miners didn't care about it enough to switch to a > different pool. > > 2. Back in 2012, we didn't have multipools. Multipools automatically > switches between mining different alt-chains to maximize miners' profits. > Miners who use multipools do not care how their hashrate is used as long as > they profit off it. > Particularly, check https://nicehash.com/ -- you can easily buy hashrate > to attack a smaller alt-coin, for example. > > If the halving will result in a significant hashrate drop (and we did > observe hashrate drop in 2012, although it wasn't that big), it might be > possible to buy enough hashpower to attack Bitcoin. > This is a good point, imho. Miner sophistication has increased drastically in 2 years. Sites like ( http://www.coinwarz.com/ ) can heavily influence mining, 1-2 orders of magnitude on significant levels of hashing. I think this is more prevalent with scrypt than sha256, litecoin is set to half reward in 9 months, and it will be interesting to observe what happens there. > > > > -- > > ___ > Bitcoin-development mailing list > Bitcoin-development@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/bitcoin-development > > -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
> For the sake of argument, lets assume that somehow (quite unlikely) Why is it unlikely? Do you believe that the cost of electricity cannot be higher than expected mining revenue? Or do you expect miners to keep mining when it costs them money? > half the mining equipment gets shut off. > The amount of hashes/second is such that it is currently, lets just say, > quite > secure against any takeover. > The equipment won't be simply turned off, it will be up for grabs. Please check this web sites: https://nicehash.com/ https://www.multipool.us/ One can use them in the same way he uses normal mining pools, and they switch between different chains. Say, multipool.us can switch between BTC and PPC (Peercoin). Mining BTC will be less profitable after a halving, so a miner who is willing to maximize his profits might use multipool to auto-switch to something more profitable. Which might be attack-on-Bitcoin. E.g. if 60% of bitcoin's total hashrate is available via "multipools", one can try to pull of a double-spending attack. > Your document makes a long series of assumptions about how this can turn > out > bad with each individually is implausible, together are just fiction. > It sounds like you failed to grasp even basics. -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
On Saturday 25. October 2014 13.27.30 Adam Back wrote: > - alternatively you might say why not 1/100th reward reduction per 2 > week period rather than 1/2 every 4 years, a difficulty retarget could > be a convenient point to do that. mining equipment has a much shorter lifetime than 4 years, so the halving makes it easy to base purchases on. Also, divide by two is the cleanest way to get to zero after a specific amount of divisions. -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
On Saturday 25. October 2014 21.06.32 Alex Mizrahi wrote: > If miner's income margin are less than 50% (which is a healthy situation > when mining hardware is readily available), we might experience > catastrophic loss of hashpower (and, more importantly, catastrophic loss of > security) after reward halving. For the sake of argument, lets assume that somehow (quite unlikely) half the mining equipment gets shut off. The amount of hashes/second is such that it is currently, lets just say, quite secure against any takeover. Your document makes a long series of assumptions about how this can turn out bad with each individually is implausible, together are just fiction. Your research didn't convince me about this being bad somehow. It also completely disregards the equilibriums reached by doing so. -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
Some thoughts about Alex's analysis: - bitcoin price may increase (though doubling immediately might be unlikely) after the halving (because the new coins are in short supply). Apparently there is some evidence of a feedback loop between number of freshly mined coins sold to cover electrical costs ongoing (which depends on halving also), in that there are claims that the btc price experiences some downwards pressure when margins are slim as miners sell almost all of them when the electrical cost takes most of the profit, and otherwise tend more to hold coins longer term. - that people who cant make money mining with 1/2 reward will resort to attacking the network rather than living with it for 2weeks until difficulty adjustment). actually it will be longer than two weeks if its going to result in a difficulty fall. - that the miners wont act in their own meta-interest to aim for the plausible new hashrate supported by the lower reward. mining equipment investment horizon being 3-6mo+ so it can easily make economic sense to subsidise it for a bit to smooth the transition. - fees might go up to unjam the network also, so the people benefitting from the transactions utility also help cover the transition costs. or maybe someone makes an assurance contract to pay the short fall and phase it out over a few months to smooth the shift. - there is a wide range of electrical efficiency, and some are much worse than others so there maybe a convenient equilibrium where there are enough left who can still profit. - alternatively you might say why not 1/100th reward reduction per 2 week period rather than 1/2 every 4 years, a difficulty retarget could be a convenient point to do that. Adam On 25 October 2014 11:06, Alex Mizrahi wrote: > # Death by halving > > ## Summary > > If miner's income margin are less than 50% (which is a healthy situation > when mining hardware is readily available), we might experience catastrophic > loss of hashpower (and, more importantly, catastrophic loss of security) > after reward halving. > > ## A simple model > > Let's define miner's income margin as `MIM = (R-C_e)/R`, where R is the > total revenue miner receives over a period of time, and C_e is the cost of > electricity spent on mining over the same period of time. (Note that for the > sake of simplicity we do not take into account equipment costs, amortization > and other costs mining might incur.) > > Also we will assume that transaction fees collected by miner are negligible > as compared to the subsidy. > > Theorem 1. If for a certain miner MIM is less than 0.5 before subsidy > halving and bitcoin and electricity prices stay the same, then mining is no > longer profitable after the halving. > > Indeed, suppose the revenue after the halving is R' = R/2. >MIM = (R-C_e)/R < 0.5 >R/2 < C_e. > >R' = R/2 < C_e. > > If revenue after halving R' doesn't cover electricity cost, a rational miner > should stop mining, as it's cheaper to acquire bitcoins from the market. > > ~~~ > > Under these assumptions, if the majority of miners have MIM less than 0.5, > Bitcoin is going to experience a significant loss of hashing power. > But are these assumptions reasonable? We need a study a more complex model > which takes into account changes in bitcoin price and difficulty changes > over time. > But, first, let's analyze significance of 'loss of hashpower'. > > ## Catastrophic loss of hashpower > > Bitcoin security model relies on assumption that a malicious actor cannot > acquire more than 50% of network's current hashpower. > E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based Double > Spending_ paper which shows that as long as the malicious actor controls > only a small fraction of total hashpower, attacks have well-define costs. > But if the attacker-controlled hashrate is higher than 50%, attacks become > virtually costless, as the attacker receives double-spending revenue on top > of his mining revenue, and his risk is close to zero. > > Note that the simple model described in the aforementioned paper doesn't > take into account attack's effect on the bitcoin price and the price of the > Bitcoin mining equipment. I hope that one day we'll see more elaborate > attack models, but in the meantime, we'll have to resort to hand-waving. > > Consider a situation where almost all available hashpower is available for a > lease to the highest bidder on the open market. In this case someone who > owns sufficient capital could easily pull off an attack. > > But why is hashpower not available on the market? Quite likely equipment > owners are aware of the fact that such an attack would make Bitcoin useless, > and thus worthless, which would also make their equipment worthless. Thus > they prefer to do mining for a known mining pools with good track record. > (Although hashpower marketplaces exist: https://nicehash.com/ they aren't > particularly popular.) > > Now let's consider a situation where mining bitcoins is no l
Re: [Bitcoin-development] death by halving
> We had a halving, and it was a non-event. > Is there some reason to believe next time will be different? > Yes. When the market is rapidly growing, margins can be relatively high because of limited amounts of capital being invested, or introduction of more efficient technologies. However, we should expect market to become more mature with time, and a mature market will result in lower margins. The halving can do much more damage when margins are relatively small. Besides that, there is a difference in ecosystem maturity: 1. Back in 2012, miners weren't so focused on profits, as Bitcoin was highly experimental: some were mining for the hell of it (it was a novelty thing back then), others wanted to secure the network, others did it because it was hard to obtain bitcoins by other means. But now miners are mostly profit-motivated: they buy expensive dedicated mining equipment and want to maximize profits. As you might know, at one point ghash.io reached 50% hashrate, and miners didn't care about it enough to switch to a different pool. 2. Back in 2012, we didn't have multipools. Multipools automatically switches between mining different alt-chains to maximize miners' profits. Miners who use multipools do not care how their hashrate is used as long as they profit off it. Particularly, check https://nicehash.com/ -- you can easily buy hashrate to attack a smaller alt-coin, for example. If the halving will result in a significant hashrate drop (and we did observe hashrate drop in 2012, although it wasn't that big), it might be possible to buy enough hashpower to attack Bitcoin. -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
We had a halving, and it was a non-event. Is there some reason to believe next time will be different? -- -- Gavin Andresen -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
> The hashpower market is maturing in the direction of > financial instruments, where the owner of the hashpower is not > necessarily the one receiving income. These are becoming tradeable instruments, Meni Rosenfeld issued tradeable mining bonds back in 2012: https://bitcointalk.org/index.php?topic=65569.0 So this is hardly new stuff. But it definitely won't help. The contract specifies how many bitcoins bondholder would get depending on difficulty and other factors. But, usually, bondholder doesn't care (and cannot check) where these bitcoins come from. Thus the owner of the mining equipment can temporarily turn off that equipment off, and instead buy them on the market, as he needs to spend less money than he would spend on electricity. Then he can pocket the difference. > Simplistic models cannot predict what hashpower does in the face of > business-to-business medium- and long-term contracts. > Ah, yes, let's forget game theory, business people know it better! -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
It is an overly-simplistic miner model to assume altruism is necessary. The hashpower market is maturing in the direction of financial instruments, where the owner of the hashpower is not necessarily the one receiving income. These are becoming tradeable instruments, and derivatives and hedging are built on top of that. Risk is hedged at each layer. Market players also forge agreements with miners, and receive -negative- value if hashpower is simply shut down. Simplistic models cannot predict what hashpower does in the face of business-to-business medium- and long-term contracts. On Sat, Oct 25, 2014 at 2:22 PM, Alex Mizrahi wrote: > >> >> "Flag day" herd behavior like this is unlikely for well informed and >> well prepared market participants. > > > It is simply rational to turn your mining device off until difficulty > adjusts. > Keeping mining for 2+ weeks when it costs you money is an altruistic > behavior, we shouldn't rely on this. > > -- > > ___ > Bitcoin-development mailing list > Bitcoin-development@lists.sourceforge.net > https://lists.sourceforge.net/lists/listinfo/bitcoin-development > -- Jeff Garzik Bitcoin core developer and open source evangelist BitPay, Inc. https://bitpay.com/ -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
> "Flag day" herd behavior like this is unlikely for well informed and > well prepared market participants. > It is simply rational to turn your mining device off until difficulty adjusts. Keeping mining for 2+ weeks when it costs you money is an altruistic behavior, we shouldn't rely on this. -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
Re: [Bitcoin-development] death by halving
On Sat, Oct 25, 2014 at 2:06 PM, Alex Mizrahi wrote: > Hashrate might drop by more than 50% immediately after the halving (and > before difficulty is updated), thus a combination of the halving and slow > difficulty update pose a real threat. "Flag day" herd behavior like this is unlikely for well informed and well prepared market participants. -- Jeff Garzik Bitcoin core developer and open source evangelist BitPay, Inc. https://bitpay.com/ -- ___ Bitcoin-development mailing list Bitcoin-development@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/bitcoin-development
[Bitcoin-development] death by halving
# Death by halving ## Summary If miner's income margin are less than 50% (which is a healthy situation when mining hardware is readily available), we might experience catastrophic loss of hashpower (and, more importantly, catastrophic loss of security) after reward halving. ## A simple model Let's define miner's income margin as `MIM = (R-C_e)/R`, where R is the total revenue miner receives over a period of time, and C_e is the cost of electricity spent on mining over the same period of time. (Note that for the sake of simplicity we do not take into account equipment costs, amortization and other costs mining might incur.) Also we will assume that transaction fees collected by miner are negligible as compared to the subsidy. Theorem 1. If for a certain miner MIM is less than 0.5 before subsidy halving and bitcoin and electricity prices stay the same, then mining is no longer profitable after the halving. Indeed, suppose the revenue after the halving is R' = R/2. MIM = (R-C_e)/R < 0.5 R/2 < C_e. R' = R/2 < C_e. If revenue after halving R' doesn't cover electricity cost, a rational miner should stop mining, as it's cheaper to acquire bitcoins from the market. ~~~ Under these assumptions, if the majority of miners have MIM less than 0.5, Bitcoin is going to experience a significant loss of hashing power. But are these assumptions reasonable? We need a study a more complex model which takes into account changes in bitcoin price and difficulty changes over time. But, first, let's analyze significance of 'loss of hashpower'. ## Catastrophic loss of hashpower Bitcoin security model relies on assumption that a malicious actor cannot acquire more than 50% of network's current hashpower. E.g. there is a table in Rosenfeld's _Analysis of Hashrate-Based Double Spending_ paper which shows that as long as the malicious actor controls only a small fraction of total hashpower, attacks have well-define costs. But if the attacker-controlled hashrate is higher than 50%, attacks become virtually costless, as the attacker receives double-spending revenue on top of his mining revenue, and his risk is close to zero. Note that the simple model described in the aforementioned paper doesn't take into account attack's effect on the bitcoin price and the price of the Bitcoin mining equipment. I hope that one day we'll see more elaborate attack models, but in the meantime, we'll have to resort to hand-waving. Consider a situation where almost all available hashpower is available for a lease to the highest bidder on the open market. In this case someone who owns sufficient capital could easily pull off an attack. But why is hashpower not available on the market? Quite likely equipment owners are aware of the fact that such an attack would make Bitcoin useless, and thus worthless, which would also make their equipment worthless. Thus they prefer to do mining for a known mining pools with good track record. (Although hashpower marketplaces exist: https://nicehash.com/ they aren't particularly popular.) Now let's consider a situation where mining bitcoins is no longer profitable and the majority of hashpower became dormant, i.e. miners turned off their equipment or went to mine something else. In this case equipment is already nearly worthless, so people might as well lease it to the highest bidder, thus enabling aforementioned attacks. Alternatively, the attacker might buy obsolete mining equipment from people who are no longer interested in mining. ## Taking into account the Bitcoin price This is largely trivial, and thus is left as an exercise for the reader. Let's just note that the Bitcoin subsidy halving is an event which is known to market participants in advance, and thus it shouldn't result in significant changes of the Bitcoin price, ## Changes in difficulty Different mining devices have different efficiency. After the reward halving mining on some of these devices becomes unprofitable, thus they will drop out, which will result in a drop of mining difficulty. We can greatly simplify calculations if we sum costs and rewards across all miners, thus calculating average MIM before the halving: `MIM = 1 - C_e/R`. Let's consider an equilibrium break-even situation where unprofitable mining devices were turned off, thus resulting in the change in electricity expenditures: `C_e' = r * C_e`. and average MIM after the halving `MIM' = 0`. In this case: r * C_e = R/2 C_e / R = 1/2r (1 - MIM) = 1/2r r = 1/(2*(1-MIM)) Let's evaluate this formulate for different before-halving MIM: 1. If `MIM = 0.5`, then `r = 1/(2*0.5) = 1`, that is, all miners can remain mining. 2. If `MIM = 0.25`, then `r = 1/(2*0.75) = 0.66`, the least efficient miners consuming 33% of total electricity costs will drop out. 3. If `MIM = 0.1`, then `r = 1/(2*0.9) = 0.55`, total electricity costs drop by 45%. We can note that for the before-halving MIM>0, r is higher than 1/2, thus less than half of total hashpower will d