Pl Plan fo for T Today Strategic behavior related to transaction - - PowerPoint PPT Presentation

SLIDE 1

Pl Plan fo for T Today

— Strategic behavior related to transaction fees in

Bitcoin

— Revisiting basics of equilibria — Best response dynamics and potential games — Online learning as a way to play games

SLIDE 2

Transaction fees in

Bitcoin

Q

what

will happen when block rewards

are

negligible

all reward

is transaction fees

Model

transactions

arrive

atonstrate

in

an

interval

g

t

units of the

total

ant

fees

in

is

C t

cel

blocks

are created

• utcast

rate

R

transaction

fees

available

miner

can put any fraction

into

block

miners

have enough space to

include everything

Strategic

decisions

which

block to extend

how

much of outstanding has aches to include

when

to publish found

blocks

Protocol

honest

miner

mine

an

longest

chain

tie breakingfor

what heardaboutfirst

Include

all

transachs youknow about

publish found

blocks

immediately

PeltyCompliant

strategy

43

EffEEainaw

most leftoverfees

SLIDE 3

Lazy

undermHg

suppose

a

b

J

10

Da

b

TDs

ss

a

Function

Fork

f

D

DIFF

Fios

Hx

Kx 0441

SLIDE 4

Selfish mining

goal to trick

• her miners

into

creating blocks

Naturel

be orphaned

creaky

private

chain

30

04

SLIDE 5

Equilibria

Cost minimization

games

K players

Ai

strategies ofplayer

Cics

I

tsysar.si

cFplayeri

s

c Hi

5

is

a

pure

NE

g

fi

f

sie Ai

Ci Csi Ei

3

c

si

Ei

15

17 ypk

• neprob

dishns

where pi

is

aprob dish

• ver

Ai

p

is

a mixed

ME

Y

Fi

Hsi

Ess

Cics siDsE np CICED

Pai

para

Ell

Pir

SLIDE 6

Any finitegame

has

a

mixed ME

Correlated

equilibrium

Dish

p

• n

A xAaX

xAk

• ver strategy profiles

is

a correlated

equilibrium

y

Fi

si

si

C Ai

Eep

Ci

Isi

sE pk

si

si

Traffic Light

us

ETTA

SLIDE 7

Dish p

• n

A xAgx

XAK

is

a

coarseconcledated

CCE

Y

f approx

fi

Hsi

F shops

a CED h Eznpf.ca sifsiD

tf

46

fi

1 6

46

ti

H

Best response dynamics

if this halts

pureME

not

guaranteed to reach

pune ME

even if one

exists

finite

EveypVdenhalgane

Potential games

has

a pure

NE

CI

TAI

IR

consider mind I

Eels

su

fi

si c Ai

cicsi.si

EsiEiEIT5D

f

SLIDE 8

Ne Network formation games

4

t

t

tGtGz

47 Pa

Pk

2

help

g

3

EAT

E

t

C5

help

g paths

trim edgee

Cy

• ils

5

i

I

ICs

cat Sgt Cy

C5

SLIDE 9

Online

learning

S

gane against adversary

A

setgpossible

achers

player

can take eachday

I Afn

for

f

l

gT

playerpicks

a c A

prob dish

• ver actions

pypa

pn

c

CIELOD

C

Cz

Ch

Fxp cost

dM y pic

investnutshaty

routes

t

t

Benchmark

Ex

2achs

T

every day

adv pious

E ma

Ma

f

ifeng.EE

Impossible

Export of any

alg

I

2

SLIDE 10

The regent of

an

aig

• n

a sequence of

cost

vectors

IEa

acetate

Ep'TalgEa

AEA

Goal

get

regret

Too play

ache

3

cost

I

ach3

O

• hms

algpap

T

F

aan

that has

cost

EIn

his

gains

i

Any alg

hasexposttz

EE.ie tiII3

E

ft

SLIDE 11

For each

actor

maintain

weight

wt fwf.us WI initialize

wya

l

Fa

for

f

I

fo

T

choose

at

with prob proportonel to wt

pta

wTaT

gwen

C

Tachn

a

wth

a

w4a

l E

ELITISTSbeset

Thm

This algfq

Yf

Ai

si

cf

Ei

Let

31,83

It

No regret

let

p

be

theuniform dish

dynamics

• n

E

in

IT

p

is

approx

CCE

testifygsni

FCE.ae

sng EIicsisEtiI