Anthony Towns [ARCHIVE] on Nostr: 📅 Original date posted:2015-10-27 📝 Original message: Hi all, A question that's ...
📅 Original date posted:2015-10-27
📝 Original message:
Hi all,
A question that's been raised a few times in various places [0] is what
the impact of a fully armed and operational lightning network on miners
fees will be -- lightning depends on the security of the blockchain to
be functional, but the blockchain will eventually rely on transaction
fees to be secure, so lightning had better leave sufficient transactions
for the blockchain!
A trivial answer to this is "market forces will work it out" -- too many
lightning transactions reduces security, reduces lightning transactions,
so it will presumably stabilise at something sane, and everyone lives
happily every after.
But I think it's actually a tractable question, so we can probably
actually work out numbers!
Basic assumptions:
1. devs/miners limit the number of transactions per block
2. miners choose the transactions that pay the highest fees to fill
blocks
3. bitcoin watch what miners accept, and all settle on the smallest
per-transaction fee that will get them included in a block
4. some people would like to use bitcoin, but are priced out because
there are cheaper alternatives at the given per-transaction fee.
eg at 8c/tx, it might be cheaper to send 50c by paypal (at 5c+5%)
than the blockchain; whereas at 7c/tx bitcoin would be preferred.
If blocks were unlimited, miners would accept every transaction, no
matter how small the fee (2), which would set the per-tx fee to ~1
satoshi (3). Rational miners will thus limit the number of txs they
accept (1) to ensure fees don't go to zero.
Market assumptions:
5. the only thing preventing bitcoin from replacing credit card
transactions at point of sale is (a) adoption of bitcoin, and (b)
the transaction fees -- ie, if Visa/Mastercard is cheaper, people
will keep using it.
6. Visa does around $7e12 (7 trillion) in volume per year in the US;
and about 60e9 (60 billion) transactions [1]; on average that's 1900
tx/s, and about $117 per transaction.
7. The micropayments market is very small by comparison, with only
$1e10 (10 billion) in volume per year, counting anything under $12
as a "micropayment".
8. Imagine payments are distributed in a log-normal distribution,
then we can use the figures from (6) and (7) to get parameters
median=exp(mu)=77.669, sigma=0.9021.
9. Visa charges about 20c+2% per transaction
10. Lightning will charge 1% for a full transaction (eg, 8 hops,
0.125% per hop)
Basic conclusions:
A. First thing to note is that of the three alternatives, ie, Visa,
lightning and blockchain; that Visa and lightning get more expensive
as the transaction amount increases, but bitcoin doesn't.
Additionally, lightning is (by assumption) always chepaer than Visa.
B. Without lightning, then, the highest value N transactions will go
via the blockchain filling it up, at a fee equal to about 20c+2%
of the smallest transaction. (If the fee were any lower, smaller
transactions would be eligible for the blockchain, and higher value
transactions would bid higher fees to ensure they were included first)
So if the fee turned out to be 40c, transactions above $10 would be
in the blockchain, and smaller than that would be via Visa.
C. Without lightning, as bitcoin adoption increases, either fees rise,
or number of transactions per block increases proportionally. If
1% of people know about bitcoin, and use it whenever it's cheap;
then 2% of people knowing about bitcoin gives twice as many
transactions at any given price level. If blocks accepted 2000 txs,
and there were 1000 $20 tx/block and 1000 $10 tx/block, then
doubling adoption either means having 2000 $20 tx/block and a new
fee of about 60c (versus 40c), or doubling the block size and
keeping the fee.
D. Without lightning, fees increase rapidly with adoption: there are
1900 tx/s on Visa with an average value of $120, so there are probably
around 900 tx/s with a value greater than $100. With a 1MB block
allowing 2000 tx every 10 minutes, 0.4% adoption of bitcoin allows
everyone of those transactions to be worth over $100, which in turn
means the per transaction fee could be up to $2.20 (compared to
about 2c at present)
E. Without lightning, by this analysis, miners fees are mostly subject
to what the competition charges -- if Visa drops their rates from
20c+2% to 5c+1.5%, bitcoin transaction fees will drop
correspondingly.
F. With lightning, the only part of the above that changes is the
comparison to Visa -- instead of the only alternative to putting
your transaction in the blockchain being to pay 20c+2% to Visa; you
can pay 1% to lightning nodes to route your payment; so the outcome
to miners is exactly the same as if Visa dropped its rates to a
flat 1%. If the number of transactions per block stays constant,
the transactions actually selected will also be the same, but fees
paid to miners will reduce by about half (ie $2.20 to $1, 60c to 20c,
40c to 10c)
Numerical conclusions:
G. 60e9 transactions per year is 164M transactions per day or 1.13M
transactions every ten minutes. If each megabyte of block size allows
2000 transactions, then handling 1.13M transactions every 10 minutes
would require 565MB per block. However this would also drive fees down
to zero; so there is a smaller blocksize that induces optimal fees.
H. Given the log-normal distribution in (8), at 100% adoption and 100%
availability of lightning, this turns out to occur with a blocksize
of about 83MB, and a corresponding fee of about $2.02. This implies
a rate of 276 tx/second on the blockchain, and miner revenue of
about $335,000 in fees per block (compared to the inflation reward
of about $7500 per block, at 25 BTC and $300/BTC).
J. In such a scenario, lightning would be cheaper for any
transaction with a value under $202, by far the majority of
transactions. Lightning nodes would thus take the remaining 1624
tx/second, and earn what works out to be about $107M in fees per
day, or, for comparison purposes, about $750,000 in fees per block.
Collectively, lightning nodes would be handling 5.8 times as many
transactions for about 2.2 times as much in fees.
K. In the same scenario as above, but without lightning (and thus Visa
as the only alternative, pushing fees up), the optimal blocksize
works out to be 90MB, with a corresponding fee of about $4 per
transaction. That works out a rate of 300 tx/second, and miner
revenue of $720,000 in fees per block. Visa would handle the
remaining transactions, earning $232M per day, or for comparison
purposes about $1,615,000 per block.
L. If people adopt bitcoin and lightning independently of their
transaction amounts, and the log-normal model above is accurate,
those figures scale fairly simply: with lightning, $2.02 remains the
revenue-maximising per-transaction fee for miners; optimal blocksize
scales proportionally; ie with 10% adoption, an 16000 transactions per
block or about 8MB is optimal, and with 1% adoption, 1600 transactions
per block or about 800kB is optiomal.
M. Varying the fee lightning nodes charge in the scenario above has a
direct effect on the bitcoin fee, but does not change the optimal
block size for a given level of adoption. So halving the lightning
fee to 0.5% would result in the optimal fee also halving, with miners'
revenue halving to about $168,000 per block.
N. If lightning had fees at 0.22%, the optimal bitcoin fee would be
about 45c per transaction (with lightning still cheaper for
transactions below $200 in value); at 10% adoption, optimal blocksize
would be about 8MB or 16000 transactions per block, which would
result in about $7200 per block in fee to miners, which is about
24BTC per block given a price of $300/BTC. This might be a plausible
set of figures to target -- reasonable volume, reasonable profit,
still fairly cheap, and with wide but not completely crazy adoption?
Caveats:
Z. The log-normal distribution might not be reasonable. I've no idea of
anything better though. Also, the numbers from Visa might be
inaccurate or incomplete in the first place. They're also a couple
of years old, don't include Mastercard, Amex, etc.
Y. Visa, bitoin and lightning aren't exact subsititutes:
* Neither Visa nor Lightning can execute "smart contracts" like
bitcoin can; so the blockchain has additional demand on it beyond
Visa's current market.
* Visa is expensive or unsuitable for micropayments while lightning
is designed for them, so the potential demand may be larger than
estimated above (7).
* Unlike Visa, lightning and bitcoin do not naturally support
payments on credit or fraud protection for consumers, so some
proportion of Visa's market is probably not addressable by lightning
or bitcoin.
* Lightning payments are confirmed immediately, unlike bitcoin
transactions which take some time to be confirmed and can be
unconfirmed for a short period afterwards, and unlike Visa where
chargebacks are possible for month.
X. Increased adoption probably has some correlation to transaction
sizes rather than being completely independent; ie early adopters
probably have a different distribution of transaction amounts compared
to late adopters. No idea /how/ that's likely to differ though...
W. Current fees of up to ~2c/tx differs wildly from the above estimates
of $2 to $4 as the revenue maximising fees for miners above, given
alternative methods of payment take 1%-2% in fees. Maybe that just
means miners aren't maximising fee revenue at present (given low
adoption, and high inflation reward that's probably reasonable);
but maybe it means the distribution of payment sizes in bitcoin is
wildly different to the estimated distribution of Visa transactions
above (and skewed much lower). Alternatively, maybe it means that
miners aren't an effective cartel, and thus can't force fees to rise
to maximise revenue; that doesn't seem likely to me though...
Cheers,
aj
[0] https://www.reddit.com/r/Bitcoin/comments/3n89cu/lightning_network_onion_routing_proposal/cvlvskx
https://www.reddit.com/r/bitcoinxt/comments/3hf74y/lighting_network_ultimately_takes_fees_away_from/
http://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-October/011523.html
[1] http://investor.visa.com/files/doc_downloads/annual%20meeting/Visa%20Annual%20Report%202013%20final%20website.pdf
📝 Original message:
Hi all,
A question that's been raised a few times in various places [0] is what
the impact of a fully armed and operational lightning network on miners
fees will be -- lightning depends on the security of the blockchain to
be functional, but the blockchain will eventually rely on transaction
fees to be secure, so lightning had better leave sufficient transactions
for the blockchain!
A trivial answer to this is "market forces will work it out" -- too many
lightning transactions reduces security, reduces lightning transactions,
so it will presumably stabilise at something sane, and everyone lives
happily every after.
But I think it's actually a tractable question, so we can probably
actually work out numbers!
Basic assumptions:
1. devs/miners limit the number of transactions per block
2. miners choose the transactions that pay the highest fees to fill
blocks
3. bitcoin watch what miners accept, and all settle on the smallest
per-transaction fee that will get them included in a block
4. some people would like to use bitcoin, but are priced out because
there are cheaper alternatives at the given per-transaction fee.
eg at 8c/tx, it might be cheaper to send 50c by paypal (at 5c+5%)
than the blockchain; whereas at 7c/tx bitcoin would be preferred.
If blocks were unlimited, miners would accept every transaction, no
matter how small the fee (2), which would set the per-tx fee to ~1
satoshi (3). Rational miners will thus limit the number of txs they
accept (1) to ensure fees don't go to zero.
Market assumptions:
5. the only thing preventing bitcoin from replacing credit card
transactions at point of sale is (a) adoption of bitcoin, and (b)
the transaction fees -- ie, if Visa/Mastercard is cheaper, people
will keep using it.
6. Visa does around $7e12 (7 trillion) in volume per year in the US;
and about 60e9 (60 billion) transactions [1]; on average that's 1900
tx/s, and about $117 per transaction.
7. The micropayments market is very small by comparison, with only
$1e10 (10 billion) in volume per year, counting anything under $12
as a "micropayment".
8. Imagine payments are distributed in a log-normal distribution,
then we can use the figures from (6) and (7) to get parameters
median=exp(mu)=77.669, sigma=0.9021.
9. Visa charges about 20c+2% per transaction
10. Lightning will charge 1% for a full transaction (eg, 8 hops,
0.125% per hop)
Basic conclusions:
A. First thing to note is that of the three alternatives, ie, Visa,
lightning and blockchain; that Visa and lightning get more expensive
as the transaction amount increases, but bitcoin doesn't.
Additionally, lightning is (by assumption) always chepaer than Visa.
B. Without lightning, then, the highest value N transactions will go
via the blockchain filling it up, at a fee equal to about 20c+2%
of the smallest transaction. (If the fee were any lower, smaller
transactions would be eligible for the blockchain, and higher value
transactions would bid higher fees to ensure they were included first)
So if the fee turned out to be 40c, transactions above $10 would be
in the blockchain, and smaller than that would be via Visa.
C. Without lightning, as bitcoin adoption increases, either fees rise,
or number of transactions per block increases proportionally. If
1% of people know about bitcoin, and use it whenever it's cheap;
then 2% of people knowing about bitcoin gives twice as many
transactions at any given price level. If blocks accepted 2000 txs,
and there were 1000 $20 tx/block and 1000 $10 tx/block, then
doubling adoption either means having 2000 $20 tx/block and a new
fee of about 60c (versus 40c), or doubling the block size and
keeping the fee.
D. Without lightning, fees increase rapidly with adoption: there are
1900 tx/s on Visa with an average value of $120, so there are probably
around 900 tx/s with a value greater than $100. With a 1MB block
allowing 2000 tx every 10 minutes, 0.4% adoption of bitcoin allows
everyone of those transactions to be worth over $100, which in turn
means the per transaction fee could be up to $2.20 (compared to
about 2c at present)
E. Without lightning, by this analysis, miners fees are mostly subject
to what the competition charges -- if Visa drops their rates from
20c+2% to 5c+1.5%, bitcoin transaction fees will drop
correspondingly.
F. With lightning, the only part of the above that changes is the
comparison to Visa -- instead of the only alternative to putting
your transaction in the blockchain being to pay 20c+2% to Visa; you
can pay 1% to lightning nodes to route your payment; so the outcome
to miners is exactly the same as if Visa dropped its rates to a
flat 1%. If the number of transactions per block stays constant,
the transactions actually selected will also be the same, but fees
paid to miners will reduce by about half (ie $2.20 to $1, 60c to 20c,
40c to 10c)
Numerical conclusions:
G. 60e9 transactions per year is 164M transactions per day or 1.13M
transactions every ten minutes. If each megabyte of block size allows
2000 transactions, then handling 1.13M transactions every 10 minutes
would require 565MB per block. However this would also drive fees down
to zero; so there is a smaller blocksize that induces optimal fees.
H. Given the log-normal distribution in (8), at 100% adoption and 100%
availability of lightning, this turns out to occur with a blocksize
of about 83MB, and a corresponding fee of about $2.02. This implies
a rate of 276 tx/second on the blockchain, and miner revenue of
about $335,000 in fees per block (compared to the inflation reward
of about $7500 per block, at 25 BTC and $300/BTC).
J. In such a scenario, lightning would be cheaper for any
transaction with a value under $202, by far the majority of
transactions. Lightning nodes would thus take the remaining 1624
tx/second, and earn what works out to be about $107M in fees per
day, or, for comparison purposes, about $750,000 in fees per block.
Collectively, lightning nodes would be handling 5.8 times as many
transactions for about 2.2 times as much in fees.
K. In the same scenario as above, but without lightning (and thus Visa
as the only alternative, pushing fees up), the optimal blocksize
works out to be 90MB, with a corresponding fee of about $4 per
transaction. That works out a rate of 300 tx/second, and miner
revenue of $720,000 in fees per block. Visa would handle the
remaining transactions, earning $232M per day, or for comparison
purposes about $1,615,000 per block.
L. If people adopt bitcoin and lightning independently of their
transaction amounts, and the log-normal model above is accurate,
those figures scale fairly simply: with lightning, $2.02 remains the
revenue-maximising per-transaction fee for miners; optimal blocksize
scales proportionally; ie with 10% adoption, an 16000 transactions per
block or about 8MB is optimal, and with 1% adoption, 1600 transactions
per block or about 800kB is optiomal.
M. Varying the fee lightning nodes charge in the scenario above has a
direct effect on the bitcoin fee, but does not change the optimal
block size for a given level of adoption. So halving the lightning
fee to 0.5% would result in the optimal fee also halving, with miners'
revenue halving to about $168,000 per block.
N. If lightning had fees at 0.22%, the optimal bitcoin fee would be
about 45c per transaction (with lightning still cheaper for
transactions below $200 in value); at 10% adoption, optimal blocksize
would be about 8MB or 16000 transactions per block, which would
result in about $7200 per block in fee to miners, which is about
24BTC per block given a price of $300/BTC. This might be a plausible
set of figures to target -- reasonable volume, reasonable profit,
still fairly cheap, and with wide but not completely crazy adoption?
Caveats:
Z. The log-normal distribution might not be reasonable. I've no idea of
anything better though. Also, the numbers from Visa might be
inaccurate or incomplete in the first place. They're also a couple
of years old, don't include Mastercard, Amex, etc.
Y. Visa, bitoin and lightning aren't exact subsititutes:
* Neither Visa nor Lightning can execute "smart contracts" like
bitcoin can; so the blockchain has additional demand on it beyond
Visa's current market.
* Visa is expensive or unsuitable for micropayments while lightning
is designed for them, so the potential demand may be larger than
estimated above (7).
* Unlike Visa, lightning and bitcoin do not naturally support
payments on credit or fraud protection for consumers, so some
proportion of Visa's market is probably not addressable by lightning
or bitcoin.
* Lightning payments are confirmed immediately, unlike bitcoin
transactions which take some time to be confirmed and can be
unconfirmed for a short period afterwards, and unlike Visa where
chargebacks are possible for month.
X. Increased adoption probably has some correlation to transaction
sizes rather than being completely independent; ie early adopters
probably have a different distribution of transaction amounts compared
to late adopters. No idea /how/ that's likely to differ though...
W. Current fees of up to ~2c/tx differs wildly from the above estimates
of $2 to $4 as the revenue maximising fees for miners above, given
alternative methods of payment take 1%-2% in fees. Maybe that just
means miners aren't maximising fee revenue at present (given low
adoption, and high inflation reward that's probably reasonable);
but maybe it means the distribution of payment sizes in bitcoin is
wildly different to the estimated distribution of Visa transactions
above (and skewed much lower). Alternatively, maybe it means that
miners aren't an effective cartel, and thus can't force fees to rise
to maximise revenue; that doesn't seem likely to me though...
Cheers,
aj
[0] https://www.reddit.com/r/Bitcoin/comments/3n89cu/lightning_network_onion_routing_proposal/cvlvskx
https://www.reddit.com/r/bitcoinxt/comments/3hf74y/lighting_network_ultimately_takes_fees_away_from/
http://lists.linuxfoundation.org/pipermail/bitcoin-dev/2015-October/011523.html
[1] http://investor.visa.com/files/doc_downloads/annual%20meeting/Visa%20Annual%20Report%202013%20final%20website.pdf