foreign
[Music]
you know I probably don't need to talk
about what Mev is as much uh given that
there were if I remember right 17 or 18
talks about Mev um but you know I think
in the spirit of trying to understand
the incentives uh hidden in a lot of
these these systems one question you
might ask is does there exist sort of
some type of formal theory for Mev does
there exist some type of mathematical
structure to this thing that seems to be
you know Captivate people's imaginations
yet no one can describe it and so I'm
going to talk a little bit about
different ways of addressing this
problem including some work we've done
and um I I like to call any analysis of
Mev sort of measuring the cost of
feudalism so that's that's sort of where
the title comes from let's start with
the operative definition of Mev you know
when you see it like the of course the
famous Supreme Court ruling on porn uh
and uh you know Mev comes in many shapes
and sizes uh you know of course we have
everything from Sandwich attacks
liquidations Arbitrage nft front running
and cross chain
um and as you can see there's it's sort
of quite a variable form of revenue for
for validators and Searchers uh and
somehow we because we know there are
many examples and we feel like we can't
enumerate all of them it might feel like
the space of all mevs super big so how
do you analyze it you know I know there
were two talks yesterday about what is
and isn't uh Mev but I think we're going
to focus on uh kind of an operative
definition that can be used and
uh we could we could sort of say Mev is
any excess value that can be captured by
validators
by reordering transactions strategically
adding or removing transactions the idea
is most of this is currently managed via
off-chain auction so people bid on
transaction priority atomicity you know
and within bundles uh and you know if we
take a step back and look at the history
of ethereum of as to why we got to the
auction world
um part of the reason is the blockchain
was just getting spammed by people doing
liquidations and back running oracles
and instead of normal users being able
to get their transactions in you'd have
the you know entire blocks filled with
people's you know spam background
transactions on the other hand of course
as the previous talk was focused on uh
there's a lot of centralization risk
with off-chain auction so let's you know
try to maybe schematically look at you
know what how Mev works we have users
who submit transactions which are the
Deltas we have a mempool uh the Searcher
has sort of their own view of the
mempool and maybe they have some
transactions that are directly given to
them which you know people would call
Private order flow and then the Searcher
sends their bundle which uh they're
willing to pay for to the validator and
the validator added to the block the
philosophical question here though is
how do we know value captured by Mev is
excessive or in a notion of excess you
know in this sort of first definition I
said any excess value well how excessive
is excess describing value Flows In Mev
is actually quite difficult so in in
algorithmic Game Theory you usually have
two main ways of thinking about the
world one is optimizing social welfare
social welfare means if everyone has
some notion of utility some notion of
how happy they are with the world you
want to maximize the sum of everyone's
utilities on the other hand revenue is
you know the the the person selling the
good
uh you know maximizing how much they
earn and and then in cryptocurrency it's
actually interesting that you have to
optimize both jointly so obviously user
welfare is important for the success of
any network
I don't need to really convince anyone
of that but validator Revenue being
optimized is actually important for
Economic Security if validators are not
making sufficient income from it then
they're unable to to Really secure the
network and in decentralized networks
versus centralized networks these are
two competing goals and I think the one
reason there's a broad view of how
Theory you know algorithmic Game Theory
it's different for crypto is that you
have to sort of balance these two goals
instead of trying to optimize one of
them
so what pieces are sort of missing so
how would we kind of describe welfare as
how would we describe Revenue
um you know one thing is understanding
the user's utilities what is the user
getting out what is their notion
individual notion of value and that can
vary over the entire network the other
thing is some notion of transaction fees
and payments that you know the
distribution of payment sizes that users
are willing to handle and the last thing
is an understanding of how an Auctioneer
so in flashbots or you know in PBS how
they allocate block space is to users
and that that last part is actually
quite complicated and these three things
are quite entangled when you want to try
to write a mathematical theory for me
being and these sort of things actually
depend a lot on the application right
the user's utility for minting in nft is
extremely different for a user's utility
for borrowing uh against some collateral
uh and inevitably that means that the
allocation mechanism should somehow be
tied to that okay so let's let's try to
do kind of like the eli5 simple version
of those
which is uh you know we have a notion of
block space which is sort of a notion of
Max number of transactions or slots or
size or gas you can choose a unit but
for Simplicity just assume they're sort
of fixed number of units there's sort of
a notion of a binary allocation to a
user of whether a particular user gets a
particular slot the users have the
utility functions I'm unspecifying the
domain and range because of course it's
actually quite complicated in a world of
cross-chain bridging
and we see here that social welfare is
defined as sort of the expected total
utility of all the users given an
allocation so these X variables are
effectively whether that slot is given
to a certain person then this is sort of
measuring their sort of net happiness
let's say
uh Revenue however is just the expected
value of the payments and notice these
are quite different
um in in particular the social welfare
includes the utility of the auctioneer
which means that all of the payments
that the the users send are subtracted
or sorry our negative terms for the
bidders and it's a positive term for the
auctioneer so the payments cancel out in
social welfare so you have no dependence
on payments explicitly whereas in
revenue of course you you depend on
payments so you know if we wanted to try
to formulate what is an economic
equilibria for the system you might say
okay well let's try to find joint up you
know Maxima of the social welfare and
revenue functions
however
given an allocation that optimizes
social welfare it implies a set of
payments and it can be true that the
payments that you get from optimal
social welfare are very far from the
payments that you you get from optimal
Revenue right that there's some
intuition to that right like if if
flashbots just basically gave every
bundle for free obviously the there's a
lot of user gains but like you know the
auctioneer is pretty pissed aka the
validator slash minors
and this happens all the time in mud the
the idea that the optimal revenue
equilibria and the optimal social
welfare equilibria are sort of disjoint
so you know the the name cost of fee or
cost of feudalism is really a pun on the
concept of the price of Anarchy which is
sort of a common Concept in algorithmic
gain Theory roughly speaking you can
think of the price of Anarchy as
if I take if I have a set of many
equilibria I want to look at the ratio
of the worst case behavior of an
equilibria to the best case Behavior
it's an approximation ratio
and so what this for instance this
formula says is what's the worst case
that the equilibria the payments earned
by the validator deviate from the
payments earned at optimal welfare and
what's the best case and what's the
ratio of those
and you could basically think of this as
if this is really large or depends on
the number of transactions or users
that's really bad and so you know uh
tongue-in-cheek uh you know of course
nothing in real life is asymptotic but
you know I I Feel Like These are good
heuristics which is constant price of
Anarchy is really good it means that
even if you get to a shitty equilibria
uh it's not that much worse it's not
that much uh worse than the best
equilibria if the price of Anarchy is is
weekly growing uh so little o of n so
like maybe it's logarithmic in the
number of users or slots maybe it's
square root of the number of user slots
that's okay it's you can deal with that
um and if the price of Anarchy is linear
in the number of users that's horrible
that that basically means that the more
users join the system the worse the
equilibria is for everyone which is like
the opposite of a network effect it's
like the anti-network effect right
no one wants that um and the interesting
thing is that this quantity if you try
to write it out depends a lot on your
choice of how you what applications
you're modeling because to compute the
prices you need to sort of know these
utilities of the user and that of course
depends not to keep belaboring that
point but I think the the one of the
reasons Mev has this you know both meme
ability and inability for anyone to
write down equations for it is because
it's so dependent on the application
which is something I think you know the
early designers of cryptocurrency
networks did not
you know Divine at that time so let's go
through an example a stylized example of
kind of what this looks like how would
you analyze this for amms
um there's a very famous Paradox in
algorithmic Game Theory called braces
Paradox and braces Paradox is really
about how traffic flows on a network so
we have this network on the left and we
have a source City s we have a
destination city d
and imagine that there's a bunch of
traffic that needs to go from source to
destination each Edge that it takes is a
latency and so when you see a latency of
one that's sort of like a a link that
can take arbitrary capacity it takes the
same amount of time for everyone to to
cross that link when you see a link of X
it's dependent on the amount of flow in
that Network so you could basically
imagine that say we have 100 cars
um if 100 cars all go down the route X
then it's proportional to the number of
cars that are going
on there and so what you can do is you
can say Hey what if everyone is selfish
or greedy they're not cooperating they
don't have Google Maps so Google Maps
effectively gets around this because it
it sort of implicitly coordinates people
whether you you know you're thinking
about it or not
uh but assume everyone's selfish and
they they know this map how would they
how would they choose which path to take
and the the thing you can show is
basically it they would split themselves
up 50 50. the traffic would go half on
the upper path half on the lower path
and so the the time it would take is
three half you know we choose some units
uh such that X's from zero to one on the
other hand
you might think that adding more roads
always you know decreases traffic and
this is not true so there's this
interesting thing of if everyone's
selfishly optimizing if you add a link
between the two middle cities
that lets you teleport
um then everyone just takes the X middle
link X path
and the total congestion that everyone
realizes goes up and so the the this
sort of you know paradoxical Behavior Uh
I think philosophers would not call this
a paradox but but uh economists call the
Paradox uh is that you know even though
you added a road you've actually
worsened congestion because people
aren't routing themselves across the
network well because they're not
coordinating
so you might say okay great what does
traffic have to do with crypto well you
know first
before we even get to that you may think
Med is always bad you know there's
always these articles that people are
writing that are like
front running is theft it's bribery it's
you know whatever you will pick your
favorite negatively connotated weasel
weasel word
and you might just say okay like yeah it
we we need to get rid of it at all costs
with that instead of thinking hey maybe
maybe it's just endemic to such systems
we we saw abrasive Paradox and what
we're going to see is we're going to see
that for some examples of applications
in crypto you can get around braces
Paradox by having nav which sort of says
Mev has some positive externality in
some situations which is you know the
opposite of front running is theft as a
service or whatever
um and again not all applications are
the same so that that's where the the
conundrum in defining your sort of
optimization problem shows up
um another thing that's actually really
important to pay attention to is if we
classify users into two types of users
strategic users who are Mev Searchers or
people who are trying to optimize routes
on chain and non-strategic user like the
person who pays 80 bips for a metamask
swap if we kind of look at you know
those two two sides routing is actually
one of the hardest problems for
non-strategic users so non-strategic
users actually in fact Outsource that to
third parties right now right so if I
want to trade token a for token B but
there's no pool directly from A to B or
there's not enough liquidity you know I
go to one inch matcha gem I'm including
gem from the you know you could argue
nfts have the same properties
um and you know routing is actually
quite complicated so you know
algorithmic game theory is studied
routing in fact braces Paradox is a
great example of of how how to study
routing
uh and one question you might ask is hey
does this apply to amms does this apply
to one inch to supply the mantra
and the interesting thing that you'll
see is now imagine in this prior example
instead of teleporting in the middle
link we actually add a small amount of
congestion Epsilon times the traffic now
you can show that equilibria basically
approaches something uh as Epsilon gets
really large you go back to the
condition where everyone routes
themselves across the two paths and when
Epsilon is really small you get back to
the the purely selfish thing and the
idea is the Mev Searchers are actually
adding this extra Epsilon so that people
route themselves across the graph more
efficiently and that's something that's
a weird positive externality that if you
write out the math you know I I try to
not add a lot of the equations to this
talk but if you write out the math it's
actually quite compelling that the
social welfare somehow has improved by
Mev in some scenarios right that's not
the narrative you hear right the
narrative you hear is like oh I'm just
grannies are getting robbed in metamask
and that's just not true always so I uh
like I said I'm not gonna go through how
you show such a thing but I'll at least
give you an idea of like what such the
theorem statement looks like for such
thing
and the idea is is we we showed that
even when they're sandwichers the price
of Anarchy is constant remember price of
Anarchy constant that's good that's very
surprising you would think that hey as
more users come to network sandwich
attackers make more of a profit they
cause more of a loss but in some
liquidity conditions they do not and
this this sort of bottom chart shows you
the expected profit on the y-axis and it
shows you sort of the amount of slippage
in your by the the user and you'll see
that it has a Maxima it's not like it
keeps growing and that that's the thing
that's actually quite interesting and
nice about this example
so you've listened to me try to convince
you that mev's not bad it can have these
positive externalities maybe there's
something really interesting uh about it
and maybe you can direct it into uh
being used for some particular
applications that uh are just net net
beneficial to your network so one
question is what do you do to to harness
it for good
so one thing I think that's interesting
and and this goes a little bit to Alex's
talk before
is
suppose you did have a mechanism where
it was just extremely expensive for
people to bribe a validator off chain
and in fact people were willing to
basically
uh share their Mev Revenue imagine like
a mining pool for Mev Revenue now the
reason that that's very hard to design
is it's very hard to make it collusion
proof where people pay one minor ahead
of time who in the pool and they don't
share Revenue with everyone but suppose
you have a way of doing that and there's
a lot of people working on really really
interesting stuff both on the
cryptography side as well as on the sort
of distributed system side for for
trying to to to do such a thing but
suppose you have such a mechanism then
you can redistribute Mev
to all the validators in the system and
one very interesting thing is you can
show in some some sort of different
types of for different types of Mev you
actually can lower the overall inflation
rate of the network if the Mev subsidy
is large enough so the x-axis on this
plot is the percentage of Mev Revenue
shared and the y-axis sort of is a
measure of how much people are adjusting
their stake so let's say there's sort of
opportunities outside of uh staking that
people can earn yield on their assets
with uh one question you might ask is
like what what are the incentives that
keep people staking and the interesting
thing is that Mev actually adds this
feedback loop such that you can lower
your inflation but also ensure that
people stay staked and so you know the
y-axis is sort of a notion of percentage
of how much is of the network is staked
and you can see that at around 25 to 50
in this stylus model
of Revenue sharing you actually get
people to continue staking which is just
you know it's just kind of surprising
right like everyone's always like oh
we've always needed kind of
hyperinflationary economics and there's
lots of reasons for that but but but Mev
distribution also allows you to avoid
having to do that so that's sort of like
a kind of amazing blessing in disguise
and there's a lot more research that can
be done in this space that I think we we
mainly looked at how liquidations impact
uh Staker incentives uh another
interesting thing and I think this is
the type of thing that we're seeing in
multiple ecosystems whether it's
ethereum especially with roll-up
auctions whether it's in Cosmos
um but everyone sort of is starting to
realize the Mev auction of having a
single Mev auction for everyone to kind
of compete in may not be the best form
of an auction you may want to have an
auction per roll up you may want to have
an auction per application and so that
you can tune the aux you can tune the
social welfare versus Revenue trade-off
right now if you think about it everyone
who's making a flashbulance bundle for
an nft mint is competing with everyone
who's sandwiching for the same sort of
block space but they may actually if you
segment to the block space and say only
this amount goes for sandwiching in this
amount goes for nfts you might have a
very different equilibria uh and I think
you know a lot of the roll-up developers
are are basically kind of talking with
us but an interesting thing is and some
some current work is you can actually
show that disaggregating uh a single
auction into many auctions can actually
have better social welfare for the end
user and that's sort of like an
interesting kind of trade-off uh that I
think as things like PBS get developed
you have to sort of analyze these types
of incentives
um so you know I uh I think I want to
just at least impress upon people that
theoretical foundations for Mev are
really important and I think we've sort
of started with this thing as this like
emergent unstudied phenomena we sort of
backed our way into some mechanisms for
like you know doing an auction coming up
with sort of rough reputation scores
which you know it's not totally clear
exactly how that whole system can be
analyzed
uh to a point where we actually are
really able to start thinking about okay
how do we optimize
for things like redistribution how do we
optimize for social welfare how do we
optimize for validator Revenue in a sort
of joint manner
and formalism
uh I think it provides us this way of
finding these truths about Mev where
which show that hey it's not always
robbing grannies in metamask and the
interesting thing is I think people you
know this is sort of the beginning of
this kind of new branch in my mind of
algorithmic Game Theory where you're
really focused on the joint optimization
of social welfare and revenue because
both of them are extremely important to
network survival in cryptocurrencies
and so I I want to leave you with some
open problems in case anyone kind of is
is interested in this type of stuff
uh the first thing is what's a notion of
optimality for an auction right right
now if you look at flashbots
it's sort of a first price auction with
some filtering because they use a
scoring function that removes some
public mempool transactions is that
optimal does that work when you have
multiple chains or multiple this sort of
hierarchical system
um also does it does it sort of uh deal
with uh some of the problems of hey how
do I trust the auctioneer right now we
have a system where everyone basically
trusts the auctioneer and
you know economists have copied
cryptocurrency enthusiasts and made some
trilemmas recently on proving things
about when auctions uh when you when you
when and when you can't trust an
Auctioneer and a lot of that work
you know I think if the right people
were focused on it could really
determine how PBS functions as an
auction and what sort of like the
expected properties of it are on the
other hand there's sort of some notion
of lower bounds like in an open
permissionless system with a some notion
of value there sort of has to be some
lower bound to the amount that's
extracted because within without any
extraction it's very hard to imagine
validators being able to to continue to
sustain the network and so one question
is how do you construct those lower
bounds you know in information Theory
and in theoretical computer science the
lower bounds are extremely hard upper
bounds are always easy lower bounds are
are really sort of some of the hardest
kind of things to show and I think the
Mev space of lower balances is still
quite open I think you know
in in spite of kind of there being some
a camp of some people who believe with
sort of fair ordering that there exists
no such lower bound I I would I would
argue I would argue just proving that
the lower bound's not zero is already a
quite difficult problem that would you
know
be worth solving
and the last thing that's a very big uh
open problem research-wise in Mev is
this concept of aggregation versus
disaggregation effects and so I think a
lot of people in
in the Mev parlance we'll focus on
talking about things like private order
flow order flow aggregation like what
happens when a builder has all of a
certain type of order flow there are
ways to to talk about what the
equilibria of the system are what's the
distribution of Revenue to different
participants uh based on these kind of
aggregation versus disaggregation
effects but if I were to kind of give
you the stylized version of what this
question is asking and saying what is
the coast theorem for Mev so cos theorem
for for for those who don't know is sort
of a a very famous thing that I think
basically says imagine you have a
company
now suppose the company had everyone at
the company as an individual contractor
why is it more inefficient why is it
more efficient to actually organize as a
group versus individual contractors who
are giving payments to each other and
the coast theorem sort of says there's
some equilibrium the Middle where
there's aggregation effects where it's
cheaper for people to work together and
share common infrastructure up to some
point and then after that point the
overhead of managing that many people
starts causing you to to lower your
welfare
and this notion of aggregation versus
disaggregation and Mev is is completely
unsolved yet people are always talking
about it it's it's kind of implied in
people's language yet yet not formalized
cool and so that with that I'll leave
you for questions and also yeah thank
you uh do you have any questions for
tarun if so please raise your hand we'll
get you a mic we got one question on
this side we'll get to you in a second
got another question at the back hi uh
so my question is you gave an example of
uh you gave first theoretical example of
how uh removing an edge from a network
can make traffic more efficient and then
you give an analogy for how this can
also happen with amms and you gave a
practical example of how it could happen
with amms but I I did not understand how
this practical example works so could
could you explain more like how could
Mev improve the efficiency of trading on
this scenario with three two pairs
yeah so so think of it this way I
imagine that there's uh people who want
to trade from token a token B and
there's an order flow of n orders from A
to B
uh
if I look at how to optimally route the
orders from A to B
um if everyone gets routed on the same
route the price that everyone pays on
average could be a lot higher right if
everyone gets routed on different routes
throughout the network you could have
sort of your your load balancing what
the price impact is and the point is
that the med Searchers are sort of
acting in some weird capacity is almost
like air traffic controllers when
there's a bunch of traffic going on the
same route it increases the Mev profit
but as the Mev profit goes up then
people start routing away from that and
you could effectively think of it as a
way of sort of having a decentralized
coordinator where where it comes from
the fact that the more traffic going on
one route the more the sandwich profit
but then once people start realizing the
sandwich profit they route elsewhere and
so this routing problem is actually you
know the quintessential example of uh
these cases where
congestion sort of
you can you can add in some sort of like
incentives to avoid congestion and and
you know a lot of internet routing
traffic routing on the internet a lot of
that kind of work is like where this
initially started and this is sort of
making an analog about here but the key
is that someone is getting the worst
price by being sandwiched there's no
doubt
but everyone going across the graph is
getting a better price on average and
that that's the social welfare versus
Revenue trade-off if that makes sense
awesome we have another question at the
back
hello uh good afternoon I love the
presentation as usual my question is
have you made any studies around uh
Central Bank digital currencies or even
Fiat currencies using the same Theory
yeah I mean I think the hard part with
any of these sort of like pseudo
centralized Federated type of things is
well I I mean the validator should can
just always do the Mev themselves right
like the limit of of the centralized
thing is like well what does Facebook
what are Facebooking Google doing
they're just doing Mev on their own
auctions right they're constructing the
bidding strategies for you they're like
we're using the highest machine learning
to give you optimal like targeting it's
like it actually means actually we're
just going to front run you in our
auction but it's too complicated to
explain how
so in the centralized World these types
of things are not that interesting to
analyze from that perspective in the
sense that the centralized coordinator
will just like choose the most expensive
route for you all the time right but in
the decentralized world is actually
quite interesting because the user has
to choose their own way uh through the
network
um so yeah that that sort of you great
well one last question on that side and
we'll move on to the next talk so please
go ahead cool yeah hi I'm following up
on the first question in the brass
example the conditions under which the
routing would actually or in which Mev
would be beneficial is and if you can
teleport right these conditions are
usually not met what are the you said
under certain conditions this applies
for MMS what are those conditions does
it mean if I can trade you know if I can
print free money or trade it unlimited
or zero exchange rate or what are the
conditions in which no yeah actually
that's a good point so so the the zero
uh is in the traffic example in the amm
example you can never have zero
effectively in that Edge there's always
some amount of liquidity uh price impact
unless it's like you know a linear amm I
I think the main thing we showed is that
the liquidity difference on certain
edges on that graph relative to the
center edge has to be large so it's not
necessarily that it's saying that hey
you're teleporting or it's like you're
you're you have some sort of like
non-balanced budget Condition it's
actually just that the liquidity
relative liquidity differences on
different edges has to be high and that
those are the conditions and
you know I'd say our proof is pretty
pessimistic in our conditions and there
definitely were ways of like getting
much better bounds on it um yeah awesome
thank you so much please give a big
round of applause for tarun
[Applause]