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Date: Sat, 25 Oct 2014 13:27:30 -0700
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From: Adam Back <adam@cypherspace.org>
To: Alex Mizrahi <alex.mizrahi@gmail.com>
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Cc: Bitcoin Dev <bitcoin-development@lists.sourceforge.net>
Subject: Re: [Bitcoin-development] death by halving
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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 <alex.mizrahi@gmail.com> 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 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 drop out.
>
> The worst-case situation is when before-halving MIM is close to zero and
> mining devices, as well as cost of electricity in different places, are
> nearly identical, in that case approximately a half of all hashpower will
> drop out.
>
> ## MIM estimation
>
> OK, what MIM do we expect in the long run? Is it going to be less than 50%
> anyway?
>
> We can expect that people will keep buying mining devices as long as it is
> profitable.
>
> Break-even condition: `R - C_e - P = 0`, where P is the price of a mining
> device, R is the revenue it generates over its lifetime, and C_e is the
> total cost of required electricity over its lifetime. In this case, `R = C_e
> + P`, and thus:
>
>     MIM = 1 - C_e / (C_e + P)
>
> `f = C_e / P` is a ratio of the cost of electricity to the cost of hardware,
> `C_e = f * P`, and thus
>
>     MIM = 1 - f * P / (f * P + P) = 1 - f / (f + 1) = 1 / (1 + f)
>
> MIM is less than 0.5 when f > 1.
>
> Computing f is somewhat challenging even for a concrete device, as it's
> useful lifetime is unknown.
>
> Let's do some guesstimation:
>
> Spondoolies Tech's SP35 Yukon unit consumes 3.5 KW and costs $4000. If it's
> useful lifetime is more than 2 years and a cost of KWh is $0.1, the total
> expenditures on electricity will be at least $6135, thus for this device we
> have `f > 6135/4000 > 1.5`.
>
> If other devices which will be sold on the market will have similar specs,
> we will have MIM lower than 0.5. (Well, no shit.)
>
> ## Conclusions
>
> Reward halving is a deficiency in Bitcoin's design, but there is some hope
> it won't be critical: in the equilibrium break-even situation hashpower drop
> is less than 50%.
> 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.
>
> ------------------------------------------------------------------------------
>
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