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From: Daniele Pinna <daniele.pinna@gmail.com>
Date: Sun, 30 Aug 2015 23:02:48 +0200
Message-ID: <CAEgR2PGu4XhAcxR=gmCxKMwJY_4ckNX=0mvbsxygWm83kTNNjA@mail.gmail.com>
To: Peter R <peter_r@gmx.com>
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Subject: Re: [bitcoin-dev] "A Transaction Fee Market Exists Without a Block
Size Limit"--new research paper suggests
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--089e01494220ca2dcd051e8da4da
Content-Type: text/plain; charset=UTF-8
"However, that is outside the scope of the result that an individual
miner's profit per block is always maximized at a finite block size Q* if
Shannon Entropy about each transaction is communicated during the block
solution announcement. This result is important because it explains how a
minimum fee density exists and it shows how miners cannot create enormous
spam blocks for "no cost," for example. "
Dear Peter,
This might very well not be the case. Since the expected revenue *<V>* in
our formulas is but a lower bound to the true expected revenue, and the fee
supply curve [image: M_s(Q)\propto 1/\langle V\rangle], if the true
expected revenue doesn't decay faster than the mempool's average
transaction fee (or, more simply, if it doesn't decay to zero) then the
maximum miner surplus will be unbounded and unhealthy fee markets will
emerge.
Best,
Daniele
Daniele Pinna, Ph.D
On Sun, Aug 30, 2015 at 10:08 PM, Peter R <peter_r@gmx.com> wrote:
> Hi Daniele,
>
> I don't think there is any contention over the idea that miners that
> control a larger percentage of the hash rate, *h */ *H*, have a
> profitability advantage if you hold all the other variables of the miner's
> profit equation constant. I think this is important: it is a centralizing
> factor similar to other economies of scale.
>
> However, that is outside the scope of the result that an individual
> miner's profit per block is always maximized at a finite block size Q* if
> Shannon Entropy about each transaction is communicated during the block
> solution announcement. This result is important because it explains how a
> minimum fee density exists and it shows how miners cannot create enormous
> spam blocks for "no cost," for example.
>
> Best regards,
> Peter
>
>
> 2) Whether it's truly possible for a miner's marginal profit per unit of
> hash to decrease with increasing hashrate in some parametric regime.This
> however directly contradicts the assumption that an optimal hashrate exists
> beyond which the revenue per unit of hash *v' < v *if *h' > h. *
> *Q.E.D *
>
> This theorem in turn implies the following corollary:
>
> *COROLLARY: **The marginal profit curve is a monotonically increasing of
> miner hashrate.*
>
> This simple theorem, suggested implicitly by Gmaxwell disproves any and
> all conclusions of my work. Most importantly, centralization pressures will
> always be present.
>
>
>
--089e01494220ca2dcd051e8da4da
Content-Type: text/html; charset=UTF-8
Content-Transfer-Encoding: quoted-printable
<div dir=3D"ltr">"<span style=3D"font-size:12.8000001907349px">However=
, that is outside the scope of the result that an individual miner's pr=
ofit per block is always maximized at a finite block size Q* if Shannon Ent=
ropy about each transaction is communicated during the block solution annou=
ncement.=C2=A0 This result is important because it explains how a minimum f=
ee density exists and it shows how miners cannot create enormous spam block=
s for "no cost," for example. "</span><div><span style=3D"fo=
nt-size:12.8000001907349px"><br></span></div><div><span style=3D"font-size:=
12.8000001907349px">Dear Peter,</span></div><div><span style=3D"font-size:1=
2.8000001907349px"><br></span></div><div><span style=3D"font-size:12.800000=
1907349px">This might very well not be the case. Since the expected revenue=
<i><b><V></b></i> in our formulas is but a lower bound to the true e=
xpected revenue, and the fee supply curve <img alt=3D"M_s(Q)\propto 1/\lang=
le V\rangle" title=3D"M_s(Q)\propto 1/\langle V\rangle" class=3D"va_li" src=
=3D"http://latex.codecogs.com/gif.latex?%5Cdpi%7B300%7D%5Cinline%09M%5Fs(Q)=
%5Cpropto%091/%5Clangle%09V%5Crangle" id=3D"l0.27594831259921193" style=3D"=
display: inline; vertical-align: -4.034px;" height=3D"16" width=3D"112">, i=
f the true expected revenue doesn't decay faster than the mempool's=
average transaction fee (or, more simply, if it doesn't decay to zero)=
then the maximum miner surplus will be unbounded and unhealthy fee markets=
will emerge.</span></div><div><span style=3D"font-size:12.8000001907349px"=
><br></span></div><div><span style=3D"font-size:12.8000001907349px">Best,</=
span></div><div><span style=3D"font-size:12.8000001907349px">Daniele</span>=
</div><div><span style=3D"font-size:12.8000001907349px"><br></span></div><d=
iv><span style=3D"font-size:12.8000001907349px"><br></span></div></div><div=
class=3D"gmail_extra"><br clear=3D"all"><div><div class=3D"gmail_signature=
"><div dir=3D"ltr"><div>Daniele Pinna, Ph.D</div></div></div></div>
<br><div class=3D"gmail_quote">On Sun, Aug 30, 2015 at 10:08 PM, Peter R <s=
pan dir=3D"ltr"><<a href=3D"mailto:peter_r@gmx.com" target=3D"_blank">pe=
ter_r@gmx.com</a>></span> wrote:<br><blockquote class=3D"gmail_quote" st=
yle=3D"margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div =
style=3D"word-wrap:break-word">Hi Daniele,<div><br></div><div>I don't t=
hink there is any contention over the idea that miners that control a large=
r percentage of the hash rate, <i>h </i>/ <i>H</i>, have a profitability ad=
vantage if you hold all the other variables of the miner's profit equat=
ion constant.=C2=A0 I think this is important: it is a centralizing factor =
similar to other economies of scale. =C2=A0</div><div><br></div><div>Howeve=
r, that is outside the scope of the result that an individual miner's p=
rofit per block is always maximized at a finite block size Q* if Shannon En=
tropy about each transaction is communicated during the block solution anno=
uncement.=C2=A0 This result is important because it explains how a minimum =
fee density exists and it shows how miners cannot create enormous spam bloc=
ks for "no cost," for example. =C2=A0</div><div><br></div><div>Be=
st regards,</div><div>Peter</div><div><br></div><div><br></div><div><div><b=
lockquote type=3D"cite"><div class=3D"gmail_extra" style=3D"font-family:Hel=
vetica;font-size:medium;font-style:normal;font-variant:normal;font-weight:n=
ormal;letter-spacing:normal;line-height:normal;text-align:-webkit-auto;text=
-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><span =
style=3D"font-size:13px">2) Whether it's truly possible for a miner'=
;s marginal profit per unit of hash to decrease with increasing hashrate in=
some parametric regime.</span>This however directly contradicts the assump=
tion that an optimal hashrate exists beyond which the revenue per unit of h=
ash=C2=A0<i style=3D"font-size:12.8000001907349px;font-weight:bold">v' =
< v<span>=C2=A0</span></i><span style=3D"font-size:12.8000001907349px">i=
f</span><i style=3D"font-size:12.8000001907349px;font-weight:bold">=C2=A0</=
i><span style=3D"font-size:12.8000001907349px">=C2=A0</span><i style=3D"fon=
t-size:12.8000001907349px"><b>h' > h.=C2=A0</b></i></div><div class=
=3D"gmail_extra" style=3D"font-family:Helvetica;font-size:medium;font-style=
:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-h=
eight:normal;text-align:-webkit-auto;text-indent:0px;text-transform:none;wh=
ite-space:normal;word-spacing:0px"><i style=3D"font-size:12.8000001907349px=
"><b>Q.E.D=C2=A0</b></i></div><div class=3D"gmail_extra" style=3D"font-fami=
ly:Helvetica;font-size:medium;font-style:normal;font-variant:normal;font-we=
ight:normal;letter-spacing:normal;line-height:normal;text-align:-webkit-aut=
o;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px">=
<i style=3D"font-size:12.8000001907349px"><b><br></b></i></div><div class=
=3D"gmail_extra" style=3D"font-family:Helvetica;font-size:medium;font-style=
:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-h=
eight:normal;text-align:-webkit-auto;text-indent:0px;text-transform:none;wh=
ite-space:normal;word-spacing:0px"><span style=3D"font-size:12.800000190734=
9px">This theorem in turn implies the following corollary:</span></div><div=
class=3D"gmail_extra" style=3D"font-family:Helvetica;font-size:medium;font=
-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;=
line-height:normal;text-align:-webkit-auto;text-indent:0px;text-transform:n=
one;white-space:normal;word-spacing:0px"><i style=3D"font-size:12.800000190=
7349px"><b><br></b></i></div><div class=3D"gmail_extra" style=3D"font-famil=
y:Helvetica;font-size:medium;font-style:normal;font-variant:normal;font-wei=
ght:normal;letter-spacing:normal;line-height:normal;text-align:-webkit-auto=
;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><=
span style=3D"font-size:12.8000001907349px"><b>COROLLARY:=C2=A0</b></span><=
span style=3D"font-size:12.8000001907349px"><b>The marginal profit curve is=
a monotonically increasing of miner hashrate.</b></span></div><div class=
=3D"gmail_extra" style=3D"font-family:Helvetica;font-size:medium;font-style=
:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-h=
eight:normal;text-align:-webkit-auto;text-indent:0px;text-transform:none;wh=
ite-space:normal;word-spacing:0px"><span style=3D"font-size:12.800000190734=
9px"><b><br></b></span></div><div class=3D"gmail_extra" style=3D"font-famil=
y:Helvetica;font-size:medium;font-style:normal;font-variant:normal;font-wei=
ght:normal;letter-spacing:normal;line-height:normal;text-align:-webkit-auto=
;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px"><=
span style=3D"font-size:12.8000001907349px">This simple theorem, suggested =
implicitly by Gmaxwell disproves any and all conclusions of my work. Most i=
mportantly, centralization pressures will always be present.=C2=A0</span></=
div></blockquote></div><br></div></div></blockquote></div><br></div>
--089e01494220ca2dcd051e8da4da--
|
