Atomic Execution is Not Enough for Arbitrage Profit Extraction in Shared Sequencers - Maria Silva

Transcript

[Music] okay um hello everyone so today I'm going to talk about um an analysis about Arbitrage profits under share sequencing um but before um we start I want to build a common understanding of share sequencing um and what it means and so in the context of this talk uh share sequencing uh will be when an entity or a protocol is taking the responsibility of selecting and ordering transactions for other rollups so this usually takes the form or of this single

entity or protocol combining all the transactions from multiple rollups and uh uh sequencing them all together as one um there's uh a few advantages that the components of share sequencing uh claim that these setup Rings um two of them are uh first they say that the share sequencing brings a better ux for end users because now they can interact uh with different rollups in a unified system and secondly uh share sequencing can also increase revenue for rollups due to increased or better me extraction and uh um in the uh in in our

case so in this talk we're going to focus on the second claim so we're going to investigate how me extraction in rollups is impacted uh under share sequency and uh to to to talk about this first I need to give also a brief introduction on M on rollups um there were great talks yesterday so this will be a bit repeated if you if you watch them but I'll do it anyway so we are all on the same context and um today uh me on rollups is mostly dominated by Arbitrage and uh this happens because most uh rollups don't have uh public men

pool and so this is uh one of the most common um strategies and Arbitrage here involves essentially exploiting price mismatches between two exchanges um and usually exchanges that are of course trading the same tokens um and these exchanges can be uh dexes across different chains uh but they can also be a DEX and a centralized exchange such as binance um and so here we have an example where we have two uh exchanges with price mismatch on the eth usdc token pair and arbiture can exploit this

uh price mismatch by submitting two uh independent swaps so first uh we are uh buying or the arure is buying e and um paying usdc on the second swap uh the arbitrageur uh is doing the opposite trade so he paying eth and getting usdc back and here the amount of eth is the same and so uh at the end uh you have a little bit more usdc because the prices the price on Exchange B was cheaper than on Exchange a and I must note that while on ethereum usually this is done atomically so you

have a single bundle where these swaps are executed and depend upon each other and so they are essentially using the same tokens in the up upward and downwards uh swap usually on rollups this doesn't happen so arbitrageur need to either hold liquidity on both sides of the swaps or they need to use Bridge okay but for the most part they usually maintain liquidity on both sides of the trade um and uh and so this is just to say as I was uh saying before that at the end the Arbitrage is extract in a little bit of

profit um in this case it will it's denominated in usdc and this profit is simply the difference in liquidity across the two sides of the trade um and because of the price mismatch he gets a little bit of usdc back okay so uh now uh going back to the share sequencing and uh how then does this uh new uh setup of of sequencing impact these Arbitrage uh type traits um and here I'm I'm going to focus on two properties and within share sequencing there's tons of different ways of naming

these things and different ways of splitting it so I will just focus on these two properties and give you a brief uh overview of of what I mean by this okay and so the first property uh is atomic execution and by this I just mean the property where you can ensure that two transactions across different rollups execute together or not at all okay so if one happens to fail you can guarantee that the other will revert as well okay so this is what I'm meaning by atomic execution the other property which is atomic bridging is going a little bit further and now is

allowing Atomic Bridge operations so there's uh uh no need to wait multiple blocks uh you essentially can in the same bundle um use uh tokens from one chain and Bridge them to the other okay and this has a huge uh benefit in Arbitrage because it means that now you don't need to hold liquidity on both sides of the swaps uh you can just uh even take a flash loan do the first swap Bridge do the second Swap and then repay back The Flash LA and as you can imagine this Atomic bridging is a stronger property right

and has the potential for more benefit for arbitrageurs however this is also more challenging to implement okay and so for the for this uh work we decided to actually focus on just Atomic execution and understanding the value of this first simpler level of share sequencing let's say and I would say Atomic bridging is also another interesting thing that we should look at but I leave it for further work okay so um going back to uh the example we had before um so here um we are we have the

same um Arbitrage uh so we have two exchanges but here I'm assuming that we have we are arbitraging ing um the same e usdc pool on Unis swap uh but now across two different rollups so we are focusing on cross-chain Arbitrage okay so we are uh we are doing an Arbitrage on arbitrum and op or optimism in this case okay and uh if the arbiture wants to exploit this price mismatch they will submit two independent transactions so we are assuming that they hold liquidity on these two sites um and they will submit two uh independent uh swaps um

and they will look the same as we saw before so on Exchange B exchange B we are swapping usdc with eth and uh on a is usdc okay so in this example if we assume we don't have Atomic execution the Arbitrage is submitting these two swaps and one of them can fail and if one of them fails the other can go through there's like no guarantee of uh both failing at the same time while on Atomic so under the atomic regime if the first swap fails the other

will fail as well so they are failing together and in our analysis and the results I'm going to show uh at the end we will be focusing on the difference in profit of these two regimes okay so the uh nonatomic regime and the atomic regime okay so we have always these these these two regimes and we are Computing the difference okay um and so the we we we did the model and uh we used some assumptions um so it was easy to uh reason about these things um and uh in this uh in this model we are

um assuming that an arbitrager is submitting a single um Arbitrage um trade so he's doing two swaps um they are doing the same of um arbitraging two different rollups um with uh the same token pair pool okay this pool has the same trading fee okay another assumption is that we are completely ignoring transaction fees and in reality we know that transaction fees will likely have an impact on the final results um but at the moment rollups have really low transaction fees um and also this

assumption allows us to have a simpler formula that we can reason with um and this helps as a first step um we are also as I was saying we are also assuming that the arbiture is holding liquidity on both uh chains and uh he is valuing that liquidity at its own price which we call P external and the rational for this price you can think of it as is the price that the arure either paid for the liquidity is holding now or some price that he expects to pay in the future when he settles the liquidi like it's only evaluation of how these tokens are

worth and once again the metric we are interested in in this case is the difference in expected profit of the two regimes so the atomic regime minus the non-atomic regime so when this metric is positive there's a benefit in atomicity so um now looking at the very scenarios so we have four possible scenarios in terms of failure probabilities or failure cases let's say so in the first one both swaps are failing okay and in this case the difference so our our metric of interest

is zero because there's no difference both fails at the same time so there's no difference between atomicity and non atomicity on the second one we have the swap on be failing sorry the swap on B executing and the swap on a failing okay and in this case uh the atomic regime the profit is zero because both swaps are being reverted so the change in liquidity is zero there's no profit okay either positive or negative but now in the regime where there's no atomicity we have swap B executing and so there's a change in liquidity on that side of the

of the trade and that uh Chang in liquidity uh is uh simply the the the difference in the eth tokens purchased minus the usdc tokens that the arbitr got back okay the third case is also simple we just have both swaps executing and the difference in profit is again zero the same as the first case and the fourth case is similar to the second but it's the other way around now you have uh the atomic regime the profit is zero but on the non-atomic regime uh there's swap a that executes and so you have to see the difference in liquidity there and I

should note that uh because we need to compare apples with apples uh when we are Computing these uh differences in liquidity we always need to convert one of the tokens uh to the other so in this case we have to convert the value of the eth tokens into usdc and so we are using here that uh price of the Arbitrage or the P external okay to do that conversion so that we can otherwise we'll be calculating e tokens and adding them to usdc tokens it wouldn't make sense so far so good okay so if we now uh take these four scenarios we can compute the expected

difference in profits uh using the failure probabilities and after some derivation we get this nice uh formula um I won't go over the derivation if you want you can check the paper and we have all the details there um but the interesting thing here is that uh this final difference in profit essentially depends on three things so first we have the trade sites um the trade size doesn't change whether the difference is positive or negative so it's not uh it doesn't tell you in if these um uh if atomicity is beneficial

or not but it changes how much or the dimension of the profit difference and usually the trade size depends on the setup of the pools at the moment so the liquidity in the pools and also the price differences and these control these straight sides the uh second one is the failure probabilities so here we have for each rollup uh we have a probability of of failure and we are representing it here with this small F fa for roll up a and FB for roll up B and then finally we have these differences between three prices so the

first one is the arbitral price so P external and uh the other twos are the prices that the Arbitrage or executed on when they were doing the swap okay it's not the price before the swap or after the swap it's like the actual price that the arbitrager experienc in their trade okay and so to reason a little bit about this formula we did some simulations in Python so essentially here we have uh three matrices and they correspond to three different cases of where these Arbitrage or Price lies in relation to the other two Pool

prices and then for each of these three scenarios we have the metric so the difference in the two regimes um for different failure probabilities okay so we have the failure probabilities for B on uh on the on the X axis and for a on the Y AIS um and so if we now focus on the first one okay so this is the case where the P external is larger than the pull prices um in this scenario when the the the matric is red it means that the matric is negative and when it's green

is positive so in this uh uh red uh um area of the Matrix um here we are uh in the situation where roll up a is failing more often on average than roller P okay and so this means in in consequence that swap B is executing more often on average and we can think about what is happening here so on Swap B the arbitrageur is buying e but the price is getting in SW p is actually a better price than its own uh internal price okay and so this means

that when swap a is failing it's better for him to have swap B executing than failing okay so on average he actually gets a positive profit by having just that leg of the uh swap executing and that's why we get uh the red on the other hand on uh the this lower part it's the opposite so we have roll AP pay is failing less often and so the swap B is executing more um sorry swap a is executing more um and in this case uh the arbitrageur is selling e okay because it's in the other side of the

trade but now we selling e at the worst price than the internal price right um and so here it generates a profit when if swap B fails actually failing swap a is also more profitable because otherwise you'll get a worse price okay and if you look now I think this the the other scenario where the price is uh lower than the two prices is fairly similar just sort of inverted the relationships I think the other interesting Cas is is middle price where it seems like it's always nonbeneficial to have a the atomic regime and here the

rationale is very similar as well so what is happening here now is on this upper part the logic exactly the same as the previous scenario okay so we sorry we have swap B executing more often and in that case the arbitrager is buying e and the price is better okay um but on the lower part now the difference is that we are still executing a more often but selling e is not happening at the worst price okay because the the PX is lower than um than pa okay so again we get the net uh

loss and so the key takeaway of this analysis is that it is not always profitable for an arbitror to be in an atomic execution regime um and so this property alone might not be enough to convince um rollups to change um and this can be seen in a simple to token swap okay in addition uh the in this simple case the profitability of the atomic regime uh depends on just two parameters so the first one is the failure probabilities on each rollup and the second is the price of the

arbitrageur in relation to the price of the pools that he's executing on um so this was a first step into investigating these uh question and so there's tons of future work that we could do um the first one would be to consider transaction fees in the model and seeing how that uh changes the the the final results um our model is also assuming that um the um the liquidity that the arbitrager is holding is in the native tokens is uh arbitraging but we know in reality this doesn't happen so in reality arbitr will hold their

liquidity in some stable token and then converted back and forth and so another exential could be to have that additional conversion and consider that as well well um I think it's also very important to study a bit more deeply um how prevalent these cases where atomicity is beneficial versus it's not are empirically okay so this means calculating or um looking into the failure probabilities of uh uh different rollups and seeing like where they lie on that Matrix that I will show you that I showed you before um and also um comparing pull prices uh in different

rollups and seeing how they Fair against the generalized index um and finally there's the atomic bridging part which we didn't look into and I think it's uh fairly important to also do a similar analysis but now looking into Atomic bridging and trying to understand the actual profit that could be uh generated there um if you found found this uh interesting uh you can connect with me on LinkedIn or telegram you can also check the the paper um on archive and um I'm happy to take questions I don't know if we still have time um absolutely we have time okay and you have a bit more time because of the bit Rocky beginning

but um first of all a round of applause it was really interesting thank you very much and now I'm hoping for some great questions thank you do you know how often it's the case that we are in this intermediate regime where the the prices the external price is in between so we that's a good question I I we haven't looked into it um but I think it's one of those things we should look together with the failure uh probabilities to actually see but I think the the the the hard part there is that you can look into uh the pull prices and a generalized index and and compare it but in the end that might not

be the price that the Arbitrage would benefit from so it's it's a bit I think this uh mid this uh price external is a bit a theoretical concept and it's hard to really really measure it uh empirically but yes I using a generalized index we could try to have a sense of it um is it really possible like to have Atomic cross chain swaps like what do you mean do you mean just Atomic execution in in Cross chain like how can you guarantee like like on ethereum like you have the a bundle where you bundle the transactions like

how is it possible to do this on rollups so I if we are thinking just on Atomic execution so I'm not uh considering uh bridging okay just Atomic execution uh the idea is that the share sequencer will have this responsibility of uh um running so selecting the transactions first and then uh running the full notes of All rollups to verify that these transactions are valid and so but right now it's not possible right I mean you you you could do this you have some um vendors that are already doing this so you have espresso systems asria so they and there's a I think asria I'm not sure if it's still

in testet but if two of them are in test net and one of them I think it was Austria was already in production nice thank you well thank you very much again [Music]