28
Yevhen Zolotavkin, Julian Garcia, Joseph Liu Time-dependent Decision-making and Decentralization in Proof-of- Work Cryptocurrencies CSF 2019
Yevh
en Z
olot
avkin
, Jul
ian
Gar
cia, J
osep
h Li
u
Tim
e-de
pend
ent D
ecis
ion-
mak
ing
and
Dece
ntra
lizat
ion
in P
roof
-of-
Wor
k Cr
ypto
curr
enci
es
CSF
2019
Mai
n po
ints
of t
he p
aper
1
With
out m
iners
PoW
cons
ensu
s is i
mpo
ssibl
e
Wha
t are
the
INCE
NTIV
ESan
d IM
PACT
of t
he m
iner
s?
COMPLICATION
affec
taff
ectIN
CENT
IVES
IMPA
CT
INCE
NTIV
E 1
IMPA
CT 1
Mine
r #1
decis
ion 1
Utilit
y
“Whe
re to
mine
?”
On d
istrib
ution
of p
ower
INCE
NTIV
E 2
IMPA
CT 2
Mine
r #2
decis
ion 2
INCE
NTIV
ES
IMPA
CT 1
Who
lesy
stem
IMPA
CT 2
IMPA
CT n
. . .
distri
butio
n
INCE
NTIV
ES
IMPA
CTS
Who
lesy
stem
distri
butio
n
… in
the
deta
ils
...
Ince
ntiv
es a
nd th
eir p
rope
rties
2
1. D
ecisi
on/a
ction
of a
mine
r at e
very
mom
ent c
an b
e ex
pres
sed
using
utili
ty
2. U
tility
of a
mine
r dep
ends
on
her
past
per
form
ance
and
fu
ture
p
erfo
rman
ce o
f the
poo
lW
hy?
Beca
use
pools
use
rewa
rdsy
stem
s tha
t enc
oura
ge lo
yal
and
stead
y mini
ng b
ehav
ior
Why
? Be
caus
e it i
s im
porta
nt to
know
how
(slow
/ fa
st) m
iners
will b
e re
ward
ed
3. F
utur
e is
unkn
own.
Mine
rsm
ust h
ave
belie
fs to
calcu
late
utilit
y and
mak
e de
cision
s.
4. P
robl
ems:
a) t
he sp
ace
ofbe
liefs
is un
know
n; b
) beli
efs
mus
t be
cons
isten
t
Alre
ady d
efine
d in
PROP
, PPL
NS, e
tc.
Need
s to
be e
xpre
ssed
info
rmal
way –
How
?
Utilit
y for
mini
ng in
a P
PLNS
poo
l à
time
disc
ount
ing
Futu
re c
ompe
nsat
ions
Wha
t is m
ore
valua
ble: 1
$ re
ceive
d to
day O
R 1$
rece
ived
tom
orro
w?
simila
rly, 1
$ inv
este
d to
mor
row…
howe
ver,
toda
y inv
estm
ent o
utpe
rform
s tom
orro
w inv
estm
ent…
ther
efor
e, to
day w
e sh
ould
disco
unt t
omor
row
rewa
rd…
and,
hen
ce, e
xpre
ss tim
e pr
efer
ence
in m
onet
ary t
erm
s.
1$ in
veste
d to
day g
ener
ates
pro
fit in
the
futu
re…
Is it
app
licab
le to
PoW
min
ing
mar
ket?
3
Inve
stm
ent o
ppor
tuni
ties
for c
rypt
ocur
renc
ies
Coin
lend
(http
s://w
ww.c
oinl
end.
org/
)Bl
ockF
i (ht
tps:
//blo
ckfi.
com
/cry
pto-
inte
rest
-acc
ount
/)
Fo
r exa
mpl
e, w
e ca
n us
eex
pone
ntia
l mod
elto
disc
ount
rewa
rd th
at is
defe
rred
n da
ys.
With
6.2
% o
f ann
ual y
ield
we c
alcu
late
par
amet
er
Furth
er: w
e de
mon
stra
te th
at in
tens
ity o
f tim
e di
scou
ntin
g pl
ays
impo
rtant
role
inde
cent
raliz
atio
n of
blo
ckch
ain.
4
The
syst
em c
onsis
ts o
f Se
tting
s an
d Li
mita
tions
Pool
#1
Pool
#1
Pool#2
and
Poo
l #2
Lim
itatio
ns:
SYST
EM
A. W
e co
nsid
er a
clo
sed
syst
em o
f 2 p
ools
B. W
e co
nsid
er P
ay P
er L
ast N
Sha
res
(PPL
NS) p
ools
only
PPLN
SPP
LNS
5
sam
e
C. P
aram
eter
N is
the
sam
e fo
r the
bot
h po
ols
Min
ers
may
mov
e be
twee
n th
e po
ols
base
d on
thei
r bes
t res
pons
e
Ince
ntiv
es a
nd D
ecis
ions
Pool
#1
Pool#2
SYST
EM
6
1. C
alcu
late
utili
ties
to ‘s
tay’
and
to ‘le
ave’
for e
ach
of th
e m
iner
s;
‘leav
e’
‘leav
e’
‘stay
’
‘stay
’
Proc
edur
e:
2. M
ake
decis
ion
for e
ach
min
er b
ased
on
which
utili
ty is
larg
er.
Past
Futu
re
Is th
ere
a st
ate
of s
tabi
lity?
Assu
mpt
ion
abou
t per
sona
l bel
iefs
allo
wed
us to
reas
on a
bout
utili
ties,
bes
t res
pons
es, a
nd to
dem
onst
rate
that
equ
ilibriu
m e
xists
.
Equi
libriu
m in
the
syst
em
Brie
f con
clus
ions
:
A. M
iner
s te
nd to
leav
e th
e sm
alle
r poo
l.
B. C
ompo
sitio
n of
the
smal
ler p
ool a
nd in
tens
ity o
f tim
e di
scou
ntin
g do
mat
ter.
7
Pool
#1Po
ol#2
noincen'
ve
noincen'
ve
SYST
EM
In o
rder
to u
nder
stan
d ef
fect
s of
pos
sible
mig
ratio
n be
twee
n th
e po
ols
we a
re g
oing
to d
iscu
ss:
The
rest
of t
he p
rese
ntat
ion
- PoW
min
ing
in th
e po
ols
- PPL
NS re
ward
sch
eme
- Utili
ty o
f the
min
ers
in P
PLNS
poo
ls
- Sim
plify
ing
assu
mpt
ions
abo
ut b
elie
fs
- Alg
orith
m to
find
equ
ilibriu
m
- Sim
ulat
ion
and
disc
ussio
n
8
Purp
ose
of P
oW m
inin
g: B
itCoi
n
Bitc
oin
com
mun
ity a
ward
s m
iner
s wi
th a
sta
ndar
d re
ward
(whi
ch is
bei
ng h
alve
d ev
ery
seve
ral y
ears
, now
it is
12.
5BT
C) p
lus
1.4
BTC
on a
vera
ge c
olle
cted
from
the
fees
of t
rans
actio
ns in
clude
d in
the
bloc
k.
imag
e so
urce
: www
.weu
seco
ins.
com
Min
ers
are
ince
ntivi
zed
by n
ew c
oins
but
they
hav
e to
follo
w th
e pr
oced
ure.
9
Sim
plifi
ed p
roce
dure
of b
lock
min
ing
imag
e so
urce
: www
.weu
seco
ins.
com
Solvi
ng p
uzzle
is th
e m
ost
com
puta
tiona
lly in
tens
e st
age
10
A ro
und
of p
uzzl
e so
lvin
g
Abilit
y to
org
anize
par
alle
l com
puta
tions
is th
eco
re re
ason
for p
opul
arity
of P
oW m
inin
g po
ols
Parti
al s
olut
ions
are
allo
wed
in th
e po
ols
and
are
calle
d “s
hare
s”.
Why
is th
at im
porta
nt fo
r the
min
ers?
11
Diffe
renc
es in
min
ing
pow
er
Min
ing
farm
“Poo
r man
’s” m
inin
g eq
uipm
ent
imag
e so
urce
: www
.weu
seco
ins.
com
imag
e so
urce
: www
.flick
r.com
Min
ing
diffic
ulty
is ri
sing
cons
tant
ly…No
t all m
iner
s ar
e eq
ual.
As a
resu
lt, s
mal
ler m
iner
s m
ay e
xper
ienc
e sig
nific
ant i
ncom
e va
rianc
e in
cas
e of
sol
o m
inin
g.
Pool
s at
tract
min
ers
as th
ey p
rovid
e st
eady
inco
me
(lowe
r var
ianc
e).
12
Cont
ribut
ion
of th
e po
ols
to P
oW m
inin
gNa
me
Rew
ard
Type
AntP
ool
PPLN
S &
PPS
BTC.
com
FPPS
BCMo
nster
.com
PPLN
S
Jonn
y Bra
vo's
Minin
g Emp
orium
PPLN
S
Bitco
inAffil
iateN
etwor
k ?
Slus
h's po
ol (m
ining
.bitco
in.cz
)Sc
ore
BitM
inter
PPLN
SG
BTCC
Poo
lPP
S
BTCD
igDG
M
btcmp
.com
PPS
BW M
ining
PPLN
S &
PPS
Eclip
se M
ining
Con
sortiu
mDG
M &
PPS
Eligi
usCP
PSRB
F2Po
olPP
S
GHas
h.IO
PPLN
S
Give
Me C
OINS
PPLN
S
Kano
Pool
PPLN
S
Merg
e Mini
ng P
ool
DGM
Multip
ool
Scor
e
P2Po
olPP
LNS
PolM
ineSM
PPS
Merg
eMini
ngPP
LNS
Pools
are e
xtrem
ely im
porta
nt for
BitC
oin ne
twor
k.
Many
of th
e rew
ard s
ystem
s calc
ulate
mine
rs’ pa
yoffs
base
d on t
he di
stribu
tion o
f their
shar
es in
time.
imag
e sou
rce: h
ttps:/
/bloc
kcha
in.inf
o
PPLN
S is
the
mos
t pop
ular
rew
ard
sche
me
in th
e po
ols
13
Rew
ard
prin
cipl
e of
PPL
NSM
iners
shar
e re
ward
from
the
full s
olutio
n in
prop
ortio
ns to
the
num
bers
of s
hare
s tha
t eac
h of
them
subm
itted
amon
g th
e m
ost r
ecen
t N sh
ares
.
For e
xam
ple,
on
this
sche
me
we ca
n se
e th
at th
e lat
est r
ewar
d is
ough
t to
be d
ivide
d am
ong
N=20
shar
es w
here
8 sh
ares
wer
e su
bmitte
d by
mine
r A a
nd 1
2 sh
ares
wer
e su
bmitte
d by
mine
r B. I
n “s
table
mini
ng”,
in ex
pecta
tion,
rewa
rd is
pro
porti
onal
to th
e in
dividu
al po
wer o
f a m
iner.
Howe
ver,
in or
der t
o un
ders
tand
ince
ntive
s to
migr
ate
we n
eed
to co
nside
r mar
ginal
utilit
y of a
mine
r fro
mm
ining
one
mor
e sh
are
in th
e po
ol. It
will
be d
emon
strat
ed th
at N
and
the
tota
l pow
er o
f the
poo
l play
impo
rtant
role.
14
Utili
ty o
f min
er A
– c
ontin
uous
mod
el (p
art 1
)
Min
er A
40%
of p
ower
Min
er B
60%
of p
ower
Prob
abili
ty to
rew
ard
Prob
abili
ty to
be
rew
arde
d
Anal
ogy
betw
een
disc
rete
and
con
tinuo
us m
odel
s fo
r min
ing
in P
PLNS
poo
l
AorB
AandB
disc
rete
cont
inuo
us
15
Utili
ty o
f min
er A
– c
ontin
uous
mod
el (p
art 2
)
Min
er A
40%
of p
ower
Min
er B
60%
of p
ower
Prob
abili
ty to
rew
ard
Prob
abili
ty to
be
rew
arde
d
disc
rete
cont
inuo
us
16
Utili
ty o
f min
er A
– c
ontin
uous
mod
el (p
art 3
)
Min
er A
40%
of p
ower
Min
er B
60%
of p
ower
Prob
abili
ty to
rew
ard
Prob
abili
ty to
be
rew
arde
d
Ther
efor
e, m
iner
A e
xpec
ts to
rewa
rddi
scre
te
cont
inuo
us
˅ ˄
˅ ˄
˅ ˄
17
Deci
sion
of a
min
er in
the
syst
em o
f tw
o po
ols
Ho
w to
exp
ress
migr
ation
bet
ween
2 p
ools?
wh
ere
are
the
fracti
ons o
f pas
t con
tribu
tions
in #
1 an
d #2
, res
p.an
d, a
re tim
e-di
scou
ntin
g co
effici
ents
in #1
and
#2,
resp
.
Tim
e-di
scou
ntin
g co
effic
ient
s ar
e af
fect
ed b
y th
e m
oves
of o
ther
min
ers
who
hav
e be
liefs
abo
ut th
e fu
ture
.
18
Assu
mpt
ions
, beli
efs a
nd th
eir ef
fect
s19
Syst
em o
f beli
efs:
1) E
very
min
er m
akes
at m
ost 1
mov
e;
2
) Lar
ger p
ool r
emai
ns a
lway
s la
rger
. Pr
oofs
CONS
ISTE
NT
simpl
ifies
reas
onin
g an
d co
mpu
tatio
ns
How
does
this
help
in fi
ndin
g eq
uilib
rium
?W
e stil
l nee
d to
analy
ze d
ecisi
ons o
f the
oth
er m
iner
s, bu
t…
Tim
e-di
scou
ntin
g co
effic
ient
s
With
out t
he lo
ss o
f gen
eral
ity, t
otal
min
ing
powe
r of 2
poo
ls is
1.
,;
,;
20
We
impr
ove
com
puta
tiona
l effic
ienc
y if
we ta
ke in
to a
ccou
nt th
e fo
llowi
ng p
rope
rties
(pro
ofs)
:
Prop
ertie
s of
the
mod
el 1)
Non
e of
the
min
ers
from
larg
er p
ool (
pool
#2)
has
an
ince
ntive
to jo
in s
mal
ler p
ool;
21
Algo
rithm
to fi
nd e
quili
briu
m
22
Expe
rimen
tal r
esul
tsDi
strib
utio
n of
min
ing
powe
r ins
ide
‘Kan
o’ po
ol
Is th
ere
a w
ay to
pro
tect
sm
alle
r poo
l?
23
Suffi
cien
t Ind
ivid
ual P
ower
(SIP
)
Exam
ple:
com
posin
g po
ol #
1 ou
t of m
iner
s wi
th in
divid
ual p
ower
gre
ater
than
3%
of t
otal
sys
tem
pow
er w
ould
be
suffic
ient
to p
rote
ct th
e po
ol in
a
quite
com
petit
ive in
vest
men
t env
ironm
ent.
Wha
t are
the
cons
eque
nces
for m
iner
s if
SIP
is n
ot a
chie
ved
?
24
Effe
cts
on c
umul
ativ
e ut
ilitie
s of
diff
eren
t min
ers
Obse
rvat
ion: e
ffects
on
cum
ulativ
e ut
ilities
diffe
r
signif
icant
ly fo
r diffe
rent
mine
rs!!
25
Conc
lusi
ons
2) W
e de
mon
stra
ted
that
tim
e-di
scou
ntin
g is
impo
rtant
for t
he d
ecisi
on (“
which
poo
l to
join
?”) t
hat m
iner
s m
ake;
3) W
e m
ade
reas
onab
le a
ssum
ptio
ns th
at lim
it th
e sp
ace
of m
iner
s’ be
liefs
abo
ut th
e fu
ture
;
1) A
clo
sed
syst
em o
f two
PPL
NS m
inin
g po
ols
(with
the
sam
e N)
is c
onsid
ered
;
7) W
e su
gges
t two
kin
ds o
f mitig
atio
n: a
) com
pose
poo
ls wi
th m
iner
s wh
o sa
tisfy
Suf
ficie
nt In
divid
ual P
ower
(SIP
) req
uire
men
t; b)
adj
ust p
aram
eter
N fo
r eac
h po
ol a
ccor
ding
ly.
26
Than
k yo
u fo
r you
r atte
ntio
n!
