hello everyone welcome to the
presentation so today I will talk about
Searcher competition in Block building
so this is the paper title and it was
coauthored with kristofh Schlegel and
Dani from flash pods and Ben sudakov
from
eth and I'm a researcher at of chain
labs
so motivation was me and we we know that
there are many forms of me extraction
and I'm listing only the most popular
ones here so there is this sexex
Arbitrage background sandwiches and
liquidation and in each form there are
also many different spe specializations
that you can take as a Searcher and here
the main point is that there are many
different types so Searchers are
different in their
specializations so it create some kind
of heterogeneity among Searchers so we
tried to model this uh with the tools of
Game Theory and for that we need to
identify who are the players and the
main player is validator or a proposer
that proposes the next blog and then
there are these specialized arbitragers
that in the ethereum setting are called
Searchers and in current market there
are also builders that aggregate
Searchers and also men
public manol transactions but we are
ignoring um it for this uh simplified
game because for us the fundamental
players are Searchers and the proposer
here we denote the set of Searchers by S
that we can identify by their addresses
then Searchers submit their bundles of
transactions to include uh in the block
and typically now they send it to um
block Builder but in principle they
could have sent it to a proposer then
from these bundles there are some uh in
these bundles there are some conflicts
so you cannot build the block that is
the union of all
bundles so you can build many different
blocks for a build block Searcher
generates some value and validator or
the proposer also generates a value so
these are the uh smallest building
blocks of our game so we are abstracting
away from all part particular mechanisms
how they interact and that includes
Builders and we only try to understand
who will get how much among these
players depending on their
bundles so for this we are using uh
tools from Cooperative Game Theory and
for that we need to define a value of a
coalition and value of a coalition is
the best block that the Searchers in
this
Coalition uh
build okay if uh there is no uh proposer
in the Coalition then the value is zero
so proposer or validator can uh block
any or veto any block so you need to
agree uh with a proposer the The
Searchers and this already gives a
coalitional transferable utility game
and in these games the most natural
solution we think is the
core and uh let me Define what is core
it's very simple and intuitive uh the
core solution gives uh payoffs to all
players so that no uh Coalition of
players prefer to deviate from the
allocation and create their own block
together because if if they can they
will and so we need to specify the
payments to all Searchers and the
validator of the global
game so there are nice properties that
core has first of all it's uh always non
empty you always have one solution in
particular you can give all the value to
the
validator but of course there are this
would be very unfair to Searchers and
there are other core Solutions too often
but not always so for example there are
cores such that Searchers capture all
the
value and if we have uh additive value
over the bundles then we actually have
uh nice characterization of the
core so to make it more interesting we
look at the St stochastic setting where
we have a number of opportunities
denoted by m and number of searches
denoted by n and each Searcher generates
some value for each opportunity so we
have this Matrix and by P we know the
probability that each Searcher finds
each opportunity okay then we have very
nice
um simple result that as soon as uh
probability slightly high so it's larger
than this to log n divided by n and
there there are not too many
opportunities so m is less than and then
with high probability the validator
captures everything and this can be in
particular uh empirically checked in in
the data so thank you for your attention
happy to answer your
questions yeah uh thank you very much so
um I posted one question u i wonder I
wonder if you know how many search
providers are currently in ethereum
ecosystem So currently today I don't
know but uh it's in the order of
hundreds hundreds yes okay and uh we
have one more question how do you know
that the core is non empty and this is
usually requires strong
assumptions so we know because if you
give all the value to validator it
satisfies all these inequalities that
core
requires it's very easy to check and
strong assumption is that what you may
refer as strong assumption is that
validator validator can block any or
veto any
Coalition so that that has a veto power
and that's what that's why core is
nonempty and in particular we give exact
uh example of a
core uh okay uh thank you very much
please give a round of applause to our
speaker thank
so