Akaki Mamageishvili - Shared Sequencing and Latency Competition as a Noisy Contest

Transcript

thank you thank you for the introduction welcome everyone and thank you for joining this presentation so I will talk about shared sequencing economics and uh we will look at this from the latency competition perspective which we model as a noisy contest this is a joint paper together with kristofh Schlegel who is researcher at flash pods but first let me give you some motivation we all know that ethereum is very good with the calization and security but it has problems with the scaling and uh ethereum decided to go with the pass of uh rollups that it created this rollup

Centric road map and this resulted into at the moment at least 50 functioning rollups and maybe more than hundreds of announcements of rollups that are under development so far so good we can assume that if eum is really scaling at least let's say 50 times if we assume that all rollups have the same parameters as ethereum chain does and most of them do because they are implementing EVMS ethereum virtual machines and even trying to optimize for example arbitrum that is the rollup that was developed by my company of chain Labs but it comes at

a cost and the cost is this fragmented liquidity so instead of all liquidity being on one chain and move on that chain freely now you need to move them from one rollup to another rollup and there are of course no direct uh channels to move money probably first you need to withdraw from a rollup to ethereum and then move to another rollup okay so this creates this fragmented liquidity and you can also see it on the for example def Lama you can see that um it's still the case that ethereum has most of the liquidity but already some rollups have some significant amount of

liquidity at least few of them but we have arbitragers that are trying to like adjust the prices of different Assets in the exchanges decentralized exchanges and they are helping the market to be efficient so to have equal prices on different different rollups and different domains but of course it comes at a cost to arbitragers also as I said coordinating this Arbitrage activities are quite difficult you cannot withdraw money from one roll up and move it to another rollup through ethereum because that's too slow someone

else maybe already has funds on another roll up and that Arbitrage will be faster so to solve this problem at least partially sheared sequencing solution was proposed and there are at least several projects that I'm aware that are Solly focused on Shear sequencing these are espresso and Austria and I would say that even um swab which is a chain or uh solution that is proposed by flash BS can also facilitate some shared sequencing so I will talk about what are the shared sequencers so let's the Simplicity for this presentation to at look at two domains for example two rollups this is

the simplest case but it can be also one rollup and ethereum main chain and actually all the shared sequencing solutions that I have seen so far they are offering the same transaction ordering policy namely creating blocks from the main pool of transactions that is already live on ethereum so they don't go with first come first serve Solutions so far but uh there is there are some promises given in that direction as well okay so now we are assuming that shared sequencer can sequence transactions on both domains both chains okay that makes life of

arbitrager simpler because now it can submit one bundle of transactions and hope that they will be executed automically on both chains actually those solutions that uh offer shared sequencing they also make promise that they can execute automically so both of transactions will be executed condition that other transaction on another chain will be executed in the order that is defined by the transaction sender but for the sake of this paper we look only at the sequencing so transaction is sequenced and the guarantee that it will be executed but she sequencer may not be able to give this guarantee okay then we

are analyzing what does it mean for cross domain Arbitrage trading okay so we look at the Arbitrage trading as a contest where if the transaction ordering is designed by shared sequencing for example if it's first come first serve on both chains or one chain then competition is who is fastest so competition is about the latency but if we have ethereum style priority gas auctions then Traders are incentivized or they are competing on higher bids so whoever has higher bid is included

fastest and we only look at this kind of competition so you cannot so we are not looking into cases where you are sandwich attacking some attack some transaction but we only look at let's say back running competition where you just want to be fastest once price changes either outside Market or inside the chain exchange you want to be fastest to take this advantage and yeah backround the previous transactions and this way we can see shared sequencer as a tool to reduce noise so noise is just Randomness because if you try to be fastest on Two Chains chances that you will fail on one of them is higher than

if you fail on one of them okay only on one of them okay then we are interested what happens with the investment how they how it changes the strategies of arbitragers and we develop a very simple model that captures shared sequencing versus separate sequences okay so we should be able to compare these two solution Concepts at least along some dimensions and we managed to do it at least for two Dimensions so one is quite trivial as I said if you're competing on Two Chains separately the chances are that both players or all players lose because

you win some and other players win some others so it can be that all the players are failing so nobody wins all the comp competitions all the contests all the races but in case of sh sequencer it is guaranteed that someone wins okay so at least user experience in this uh regard is better with sheared sequencing but now we are also interested in the revenue that the chains extract because chains need to join this shared sequencer they need to allow shared sequencer to run a sequencing rule on on them and therefore they need to get some revenue from that

okay so we have very simple model where we have again two players two domains and they are trying to be fastest on both domains both chains and in case of winning they are getting let's say the same value of course this is not always true but for the sake of this presentation and this paper this is the simplest model and it already shows some difference between shared sequencing and separate sequencing so I think this is fair enough and again they need to win both competitions okay so what do arbitragers do they invest some amount to create their signal and Signal will be defined in some different context and of course if

you want your signal to be better for example if you want to be faster you need to invest more so we have some cost function that is increasing differentiable that we need for deriving analytic results and conx this is yeah quite intuitive condition to assume but there is also random noise so for example in case of pure time competition when you send your transaction to a sequencer you are not sure how fast it reaches and there are some random factors that may delay a bit okay so the the arbitrager I wins the race against arbitrager J if the signal plus this noise term is larger than signal plus noise term for

the other player okay and if we have a distribution on the difference of this um noises then um we can calculate the probability that one arbitrager wins the race so this just probability is given we assume that uh there is this distribution then we assume it's normal again we we want to have analytic Solutions but we can have arbitrary distribution and give results for that arbitrary distribution as well okay so now some examples first is first come first serve where your signal is how fast you are and more you invest

faster you are so that defines basically your time stamp but there is also of course noise parameter as I said that you are never sure that you will be reaching the sequencer in exactly the time you have calculated okay so another example is time boost which is a recent proposal by including myself and kristofh and co-authors uh from of chain labs and Cornell University at Felton and mahimna kelar so we any user and in our case arbitrager invests so bits to buy a Time boost which will be subtracted it from the

time stamp and time stamp is a yeah some random noise let's say in case of ethereum type block building you can imagine that s is a how much you users invest in searching and Epsilon so the noise parameter is some random factors in the market for example if they manage to reach the Builder Etc but uh I want to make a disclaimer we are not really analyzing this last part very carefully in our model okay so now what is the difference with shared sequencer there is just one sequencer so

you aim this sequencer you have one noise term and you have one signal that you need to generate for example you want to relocate close to this sequencer and Trace where the sequencer is located at different times with separate sequencers you need to to Target both sequencer be closer to both sequencers and there are two noise terms of course okay but of course in the equilibrium and that's what we are looking into you may invest slightly less when you have two different separate sequencers we assume that noises are independently distributed so sequencers for example are not sitting together and they so separate sequencers they move

around independently from each other also not always correct but this allows us that instead of distribution function f we can just take F square and that simplifies the analysis considerably okay so we have unique symmetric equilibrium of the game and equilibrium in the equilibrium we can find signal so this S Prime with a very simple equation so it's basically first order condition for both separate sequencing sequencers and shared sequencers so one sequencer so a simple as that we can just solve what is the equilibrium

signal okay so now the question is what does it mean does shared sequencer bring more Revenue because that's the first intuition of everyone that now okay arbitragers really love just one sequencer so they will invest more to win because at least one of them is winning so don't don't forget that and we show that this not always true and it really depends on the shape of this cost function and what is the variance of the noise so how different the noise can be so we look at constant elasticity cost functions so cost is just x to the power

beta and we see that if the value from the winning Arbitrage opportunity is large enough we have this number to be the investment with one sequencer so shared sequencer and this number so I will not read what are these values but what we obtain is that if beta is larger than one and for convexity we need beta to be larger the investment with in case of one is always higher than investment with two and now if you go back and consider that this is just latency competition it

means that players will waste more because that's a waste it just goes to Outsiders not to chain so waste is more with share sequencer okay so in case of latency competition this is a bad news Okay in case of time boost I don't want to I don't have time to go very slowly here but so you are generating some signal which is you are paying for time Advantage so more you pay more time Advantage you get and that time Advantage is subtracted from your time stamp so your adjusted time stamp will be your real time step minus some uh

signal s and you can get at most G Advantage so we we are thinking to get for example at most half second advantage and this is the cost function and we obtain a proposition that Revenue that is obtained through this time boost mechanism is higher for separate sequencers as long as this condition holds so we can look so do some comparative stat on these parameters so you know what is V is value Sigma is a variance basically G is the maximum Advantage you can buy C

is how much it costs to buy so this is this parameter and this constant is something related with two so two is number of rollups or number of domains and square root of 2 pi this comes from normal distribution so this not just some random constant here it has some meaning so we can go through what does it mean so if for example valuation is large enough for the Arbitrage it's actually better to have two separate sequencers you don't need to have shared sequencer because separate sequencers will obtain higher Revenue so also quite unintuitive result and also then it depends if uh Sigma is

small so there is small noise in some cases you can assume that noise is small so you know how fast you reach the sequencer and and there is no random much Randomness there then you again have that two separate sequencers is actually better and that makes sense because if there was no noise there would not be need of shared sequencer in the first place let say okay so that's all from my side thank you if you have questions please ask me now I think there's sometime or I'll be around here thank you we still have a couple of minutes

you can ask uh one or two questions actually if you have any hi just wanted to know um do you see also or do you have a feeling or an intuition on how the results generalize to even more rollups like three or four um oh that's a good question so if you assume Independence again so that you can still solve the equilibrium

condition so it will be F cubed instead of squared in case of three rollups so one thing about more rollups is uh I don't believe it will be often the case that you trade on three different rollups at the same time because if you adjust the price between two rollups or centralized exchange and rollup or layer one exchange and some rollups there is no need to do this cyclic um adjustment but it can happen that sometimes arbitrages are careless and leave some opportunity behind uh I think all the insights will carry

over so it can still be that shared sequencer for very large Valu valuation Arbitrage still collects less so we didn't do this for many rollups in the paper we did it for for many players and there it really generalized easily and I believe for rollups will be the case too so more rollups thank you very good presentation akaki I have a question if

there are other applications of a shared sequencer than cross rollup Arbitrage and my second question is I mean will the cross rollup Arbitrage be used more often than the Arbitrage between rollups and the ethereum main net yeah so about second question I believe most of the arbitrages between centralized exchange and rollup except for some weird tokens that are only sold on rollups or the uh L layer one but there is let's say some 20% or 15% of the Arbitrage which is also sign significant number about other uses of

shared sequencing I'm pretty sure there are other uses as well but main demand comes from arbitragers and these me Searchers but I can imagine other uses actually that's a good question we should ask those companies that create uh such services but I can imagine like regular retail users also using sometimes this option that's a good question