Who Should Benefit When Transactions Are Ordered? Fair MEV Redistribution

Transcript

[music] [music] >> Thank you for the introduction. And thank you, dear Con community, for giving us opportunity to present our work here. So, today I'm going to talk about MEV and how we redistribute it. So, already I've been introduced, so I won't introduce myself again. So, this is joint work with Yash and Rashid and Parth. Uh so, Rashid and Yash are already in the audience. Parth could not make it.

I am at Machine Learning Lab, so I also work on AI, but today I will be talking more about game theoretic aspects in blockchains, especially MEV world. So, most of these numbers, I don't think this audience need introduction like digital assets are moving on chain, like crypto assets are more than 3 billion, NFTs were 25 billion. In all these things, what is important? Every trade which happening on chain waits in a public queue. All the transactions which are broadcasted goes to queue and then some proposer or builder puts it in a block and then your transaction is complete.

So, whoever ordered this queue will control the value. That's the important thing. And this is even from uh especially what happened in 2022, Ethereum moved from proof of work to proof of stake. So, every time slot we know who will be the next proposer. So, you can bid to the proposer, okay, you write my block. Rather than you constructing block, I will do that work. You write my block and I will pay you. And proposer is happy because you don't have to do the work, but what is my advantage? Why I do that work?

Any guesses? What profits? >> [snorts] >> The difference between my block of work and the bid. >> Exactly. So, typically when I write a block, what is expected that I collect transaction fees, I get the block reward. But, the way I order the transactions can earn me more profits. Suppose there is a one transaction where you are purchasing some 1 million securities of some particular company. When I see that you're doing it on DeFi, I can buy a front. I know that no price is going to be up. So, that is called front-running.

So, I can benefit, or sometimes I can back-run. Or sometimes I can switch your transaction between two of my transactions. This is called sandwiching. This can earn me more profits. Arbitrage, many times within DeFi, there are some network latencies which I might be able to exploit that something is trading at lower value in one exchange and higher value in another exchange. I can exploit that. Or even liquidation, there are many places where if I'm controlling the way transactions are ordered, I can make more money.

And I can ask a proposal to do this. So, proposals in the Ethereum, they have not invested into uh uh uh finding out what is best ordering. So, rather than they investing, they are relying on these builders. They are called builders. And from 2022, uh more than 1 billion dollars have been extracted as a maximal extractable value, which is called MEV. And out of this, 80% is coming via private order flow.

That is from wallet uh to these builder transactions are builders are purchasing these transactions from wallet service providers. So, let's a little bit recap on how block is getting built today. Users or traders, they announce their transactions. It is called private flow, they go to wallet service providers. They're searchers. They're small entities. Which actually purchase these transactions from order flow providers. And they create smaller bundles and they sell it to builders.

Builders collect these bundles from different searchers and construct a block. And sell this block actually purchase the block space rather than sell this block they purchase a block space from proposers which is called block auction. So there are two auctions happening here. One is order flow auction. Between order flow and searchers. And another auction is between builders and proposer. It is called block auction. Now what is happening?

Builders are making money but where is that money going? They have to pay to the proposers. And searchers pay some part to order providers. But how that money which is generated is distributed to users or how that extra money which has been generated should be distributed among all these entities fairly. That's the topic of today's talk. Now I'm not going to talk about there are again debates whether MEV should be there or no. When we write papers some people object that MEV should be removed.

It's unfair. Yes especially sandwich attacks are a bit unfair to users. And arbitrage actually uh existence of arbitrage actually improves the market efficiency and these delays are getting settled very quickly. So arbitrage and back running are not actually negative. Yes front running and sandwiching are negative effects but I'm not going to talk about how to remove it but what are the extra money generated how to fairly distribute among these all the entities which are part of this ecosystem.

So just users, order flow providers, searchers, builders, and proposers. So first we'll talk about how what are order flow providers are making money by selling transaction searches should be distributed to users. So, right now is arbitrarily, we are saying that could be more scientific and game theoretically backed ways. And the second part of the talk, I will talk about how the money which builders are making from writing these bundles and selling their block to proposers, how they should be distributed between these four entities.

So, currently users are split ad hoc or might be wallet providers don't pay them. What has happened in recent times is 85% of the blocks are built by just four builders. So, is it not in the spirit of blockchain which we talk about decentralization? Very decentralized. Only four builders are controlling this ecosystem. But at the same time, the proposers' margins are much higher than builders. And even sometimes builders are making losses in that competitive environment.

And even searchers have to give away 90% of their MEV to the order flow providers. So, this is what is happening today. So, our approach is split the value which you are generating not by where you are there in the system because order flow providers are the first one to listen to the transactions. Proposers are the one close to the slot. They will finally be writing block. So, these are the closer to the end-to-end. So, they are making more money, but the builders, searchers, and users, they are not making money. So, our approach is the value should be split according to the way you contribute.

You what is your worth in this ecosystem based on that. It should be fair. And in game theory, there is exactly one rule that will do it. So, it's called Shapley value. Shapley is a Nobel laureate. He proposed Shapley value in when multiple players are interacting with each other. How the net worth generated by these agents or players should be distributed among these agents? So, idea is very simple. Suppose I order these agents randomly. 1 2 3 4 5.

And the sixth agent or sixth player is added to the system. How much value he or she adds to the system? That is its marginal contribution to the system. So, we should pay the agents their marginal contribution. But many times the order in which you are put, your marginal contribution will change. If already MEV has been extracted and I got added, I could not add much value to what you are doing. But if I was the first person to extract MEV of this transaction, I will add more value.

So, this random ordering matters. So, what Shapley proposed, consider all possible random orderings. And in each random ordering, what is your contribution? Take average over it. And that is your Shapley value. And it satisfies multiple fairness for example, all which is generated should be paid out. If two agents always contribute equally, they should get equal Shapley value. If you don't add anything, you should not get anything.

And finally, sum of all Shapley value should be sum up to the net value. And it has interesting problem It has been found very useful in economics and many places and also in machine learning. People are using nowadays SHAP for explainable AI. They find out importance of each feature using Shapley value. So, this is the same Shapley value we are going to talk about. So, let's start with how user should get paid. So, there are four transactions. Transaction 1 2 3 4.

The searcher one bids 10 for transaction one and two. Searcher two bids nine for transaction three plus four bundle. Whereas searcher three is bidding eight for any one of TX2 or TX4 or if you get both, you will pay 16. And the auction mechanism, I will not get into details of how auction and the second price rule. So, what will happen is out of this auction, searcher one will get bundle TX1 TX2, searcher two will get bundle TX3 TX4, and each one of them will end up in paying eight. So, these transactions have generated more value of 16 rupees, say.

So, one way is you distribute them equally, 25 percentage. But, that's not what we say is believe uh fair. Because transaction two and four, if you look at them, it has more demand. So, if had not been transaction two in the system, searcher one wouldn't have bidded for transaction one. Or TX4, in absence of TX4, searcher two would not have bid for TX3. Then, only searcher three would have been there. So, two and four, they are more important transactions. So, Shapley value will capture exactly this. And if you compute Shapley value in this context, this should be distributed according to uh this decision. Uh 25 is like uh equal

distribution where 15.4 is Shapley value distribution. And TX2 and TX4, they should get more than double of TX1 and TX two uh TX3 because they are adding more value to the system. So now a Shapley value says you compute all possible orderings. There are n transactions, there will be n factorial uh orderings. N factorial grows very fast. And if there are many transactions, so really you may not be able to compute Shapley value quickly. And we know that we need how to write block in 12 seconds.

So, all these computations should be in milliseconds. So, if searchers values are per transaction, the bid is per transaction, which is typically not the case, then we can model it as a simple game. And we have a closed-form solution, and we show that this can be computed very quickly in fraction of millisecond, not even millisecond. But, if searchers are bidding for bundles on only single bundle, not even multiple bundle, that is much more complex. We showed that the number of different combinations we have to average out will be at least two power root n, which is exponentially increasing in n.

So, we cannot compute in polynomial time or quickly. So, if n is large, it will take it may take even days, and we have to be in 12 seconds. So, we proposed a simple algorithm. Instead of being exactly, do it approximately. Randomly select n squared samples of different orderings, and take marginal average over only these n squared combinations orderings. And we observe that on smaller instances, if we do this our simulation based our our algorithm and exact computation, they are almost closely matching. So, n squared is a typically quite good orderings possible, which captures most

of gist of your contribution to the system. And this kind of Monte Carlo simulations are already used in chap libraries. So, this is not a new thing, but what we proved is we proved theoretical guarantees how good you will be on shapley value. That's what we proved in this paper. This paper was presented at AAMAS 2025. So, this takes care of whatever OFP's order flow providers are making, how that should be distributed to these users. This is also called matchmaking. So, next 10 minutes I will talk about how this MEV should be distributed among all these four entities.

Take a simple setup. There's a proposer who itself can have looking at transaction field that he can generate arbitrage of 0.75. And builders believe that they can have arbitrage of 1.25 and 1 respectively, two builders. That two searchers. Searcher one at order flow one, provider whatever the transaction it has, it believe that he can generate value of two. And order at order flow of service provider two, he can generate value of three. Whereas searcher two believe it's three and two.

So, order service providers for auction, so searcher one will win at order two and searcher two will win at order provider one by paying two each. And then S1 sends the bundle to say B2 and S2 sends to both the builders. So, B1 will bid end up in bidding 1.25, B2 will end up in bidding 1.4, and B1 will win the block. So, S1 who would have generated more value that never ends up in the block. I mean, that value is not realized.

So, whatever transactions that O2 would have generated extra value, that is not realized. That is wasted. And what will happen is um So, total 4.25 net worth will be generated. Whereas they would have done optimally if they would have cooperated with each other, they could have generated total by doing optimal ordering by cooperating between S1, S2, B1, B2, they could have generated 7.25. So, we need to define a game. So, in cooperative game theory or whatever Shapley value, we have to find out worth of each coalition.

In um you users' case is not much easier if we because it's a bid that searchers are bidding for the transaction, you can just order transaction different way then you could define worth. Here we have to come up with proper definition. So, what the way we defined, one is if proposal is not cooperating with you, is not willing to write the block which you are proposing, then you cannot generate any MEV. So, proposal must be there. Any coalition, if proposal is not there, whatever order they join the coalition, is not going to generate any value.

So, proposal must be there. And some wipers should be there. And if there are multiple searchers, multiple builders, so we can actually because they are cooperating, we can generate best value out of them. So, no proposal, no blocks, so no value. And we try to generate best from all the who have gathered together. And then uh what we showed this game though Shapley value computation is n factorial orderings we have to look at we could reduce this game that we can construct this into smaller games and we

can add up the values. That's what we proved. We theoretically we proved. So, we can add a Shapley value across all these games for each agent. And for each game the value we could get a closed form solution directly. That your value in this game, Shapley value is this. So, now we don't have to do n factorial combinations. So in the same example proposer would have made 1.4 builder one would have made only 0.15 builder two loses on not making anything

seller one searcher one does not make anything uh gray one seller other one existing system searcher two has one so he makes some one rupee order of provider one makes 1.8 order service provider two doesn't make anything. But now if we deploy Shapley value based solution so we'll be generating 7.25 instead of 4.25 and the net worth for each player the proposer's also increases from 1.4 to 3.38 builder one increases to 0.17 builder two in the existing system will not make anything if he loses the auction.

He will also get some value. Searcher one increases, searcher two little bit dropped. He was getting advantage of because he was sending up to both these builders. So, that advantage and now because of cooperation a little bit dropped. Order service providers were making more money. They are also dropped. But, we believe this is fair distribution. And then we also did simulation based analysis. Yeah, so before talking about the analysis um These are the computational results.

Those who are into more technical side. They're all one just sorted their bids and then once you are done sorting valuations They're all linear in terms of the number of agents and number of searchers and number of transactions. All these computations are very linear. So, you just structure a millisecond is sufficient to compute. So, we don't have to worry about that oh Shapley value is computationally heavy. That argument is no more valid in this setting. And code is also very simple like the code is available publicly and then it's a few lines of Python code.

So, now we tested on some data available on Ethereum minute. So, this data we took from Dune Analytics. So, they have published all the MEV relay boost data of 1.2 million block over 238 days consecutive days. So, from that we try to fit distributions like technically we try to fit chi square test and all those things and we observed that log normal distribution fits the best here. So, we generated the the bids according to this distribution for 10 million blocks.

So, from the data searchers keep about 15% of the MEV they find and keep rest of the to the order flow like searchers also have to make money. They give some back to OFP, in existing system. So, So, typically they keep 15% and the rest is flowing to OFP and builders. So, we also run assuming that they will be keeping 10% and 20% both, the results are similar. So, our results say that on simulated data from which data is generated using distribution which is fit for the existing 2022 data.

MEV increase by the MEV extraction increase by 37% because system efficiency increased. Proposer in the Shapley value best per block will get 0.262 ETH whereas it was receiving 0.229 in existing system. Builders will see huge improvement. They were making 6% of the total MEV actually. They are the one Searchers and builders are the one who are trying to help in uh extracting MEV, but they are making less money. So, builders were making 0.026 ETH whereas Shapley value best, they will make 0.19 which is 18% of total MEV extracted.

Searchers on average don't change anything. So their fraction of MEV drops, but their net ETH per block doesn't drop. And all the pro proposers, we observe that if you go with Shapley value, we'll improve their profits. But um uh one question could be why searchers will join. The searchers right now it's either their bundle it's picked up by the builder, then they get paid, otherwise no nothing.

Whereas in Shapley value, they will get every block something. So, just expected reward is not the what we should look at. So, what what economics uh major your risk adjusted thing as Sharpe ratio, from that we define risk adjusted return where the Sharpe ratio with zero benchmark because it compares with benchmark. So, there is no benchmark, so we consider it with zero benchmark. Basically, it's a ratio of mean divided by standard deviation. And uh this RAR, risk-adjusted returns, every party increases. Proposal increases from 42.2 to 53.8.

Builders also improve. And actually, searchers' net gains are not there, but there is a lot of variation per block in existing system, whereas they will see a lot more improvement in uh their RAR. Same with order flow provider, and you want whole system also sees a better RAR. The variation drops. And we also did because the data is a bit older, so what if data Because we have to We have observed in recent times is builders are becoming very competitive, and that's why many builders are dropping out.

So, builders I'm not claiming that this will solve centralization problem, but this could be one of the way it will help in solving centralization problem because builders are making less money in existing system, so new builders are not joining. They don't want to invest additionally because thin margins. So, only the one which have more money, they are sustaining. But if you do fair distribution, then again uh more builders may join. So, right now in competitive environment, if we do simulations, uh we observe that Oh sorry. Uh almost builders will make a 0.69 to 0.7 ETH per block, which is like 20 26 times what they're making right now.

So, if you go with Shapley value-based approach, they will make more money. Obviously, uh proposers' profits might drop if we have more competition Proposers' profit is not dropping. Shapley value, their profits will not increase much. It will go back to builders more. Right now, uh proposers are making more money because of too much competition. So, this is all our in research. So, the second part is under review and not yet published, but if you want to take it forward, we all thought about it. We are not practitioner, but just some questions might arise, what if in this cooperative value, uh the searchers or builders start lying how much MEV

they are able to extract? So, we have bounds on that. We also proved that they will not be able to bound lie too much about how much they will be able to extract to get more Shapley value. And maybe if you put it in some trusted uh executive environment to teach, maybe when you will not be able to know others' bids, and um you'll be able to achieve much better truthfulness. So, builder net is currently doing some sort of uh uh rebate to the builders, and that is not exactly Shapley value. They just consider one particular ordering, that and if you would have arrived last in that ordering, how much value you would have generated.

So, but that's not the According to game theory, that's not the fair or precise way. We believe Shapley value is scientific and precise, and can be done in polynomial time. So, from here, there are many interesting open questions for you in academia. Do we model one slot behavior? But if some builder is not able to write in this block, maybe some of the bundles are still valid MEV for the next block.

That is lagging in this. Our data simulation data is a bit older. We don't have uh data for recent blocks bit data. Then, it's not a coalition proof. So, the existing system, what we propose, maybe some subset of builders, they are more powerful, and they come together, and they decide we will not uh accept this completely Shapley value best. We'll do our own uh coalition. Yes, Shapley value is not coalition proof. So, can we look for other concepts from game theory to ensure coalition proofness?

The uh builders may builders or searchers may lie about how much MEV they are extracting though we have bounds, but still can we prevent such manipulations? Uh so, there are many interesting open questions. So, in summary, what we have seen is like in MEV, if you want to do fair distribution, you should get paid what you have added to the system. And for that, Shapley value is a very natural way and too slow is no more excuse. And with Shapley value, we can get a fair split, which will increase even efficiency in the MEV extraction, which will Our simulation said that it can increase up to 37% uh more MEV extraction.

And builders also share will increase from 6% to 18%. And for searchers are everywhere. For all the entities, it will be much steady returns than varying returns, so risk has also reduced for all the entities. So, that's all I wanted to talk about. If you are having any data or interested for taking this forward or you are a developer of the stack, we will will be happy to hear from you or talk offline. So, I talked about these two papers in this work. There are many other around this topic. We have other papers. If you're interested, you can look at my This is my webpage. This is my LinkedIn and this is my group's webpage. So, you can

connect with me. Okay, thank you. >> Wonderful. Thank you. So, first of all, big round of applause for Dr. Gujar. >> [applause] >> Thank you for introducing us to a new way or option that we could have for MEV and uh also talking us through the whole um game theory behind it. Now, as I said before, for Q&A, we have this little microphone box here. So, whoever wants to ask a question Yes, wonderful. So, catch it. And yes, like this.

>> Uh thank you for the talk. I have two questions. >> Yes. >> Uh personally, I have a problem with the shapely way of thinking. Because transaction fee mechanism design the whole whole literature which goes to uh creating uh uh transaction fee mechanism how to divide uh uh money amongst all the proposals and builders was for incentive compatibility, right? And so, you're representing fairness from a macroeconomic point of view. But, uh when you say something when you say something is fair, uh it might not be equal to which you which I like which at the end I think you mentioned.

>> Yeah, it's not incentive compatible. >> Exactly. Exactly. So, do you have any ideas there? That's my first question. And my second question is uh you remember that I I remember there was a slide where you were talking about how it's linear. >> Yeah. >> Uh I feel like it can go to n squared a lot easier than it looks linear, right? It was n plus m k as I feel it. K uh So, m you have m plus one games, right? Amongst n sub agents. Uh sorry, n plus sorry, m plus one sub games amongst n n agents. That might be very way closer to n that you might think it is than you might think it is. So, that becomes uh n into n into n plus n kind of a thing. No?

So, I would just like these two questions answered. >> Yeah, so incentive compatible is a big concern right now. That's what we say that it's open problem. So, we have bounds like suppose how much I can lie? Because if I lie too much, maybe I will be losing and my bundle will not be put into the actual the we'll be ordering in a way where which will generate maximum MEV. So, if I start lying, I it might not go into the system. So, there are some bounds by which I can lie. So, those bounds we have proved and in competitive world that bound might not be too too much flexibility I will have, but yes, there is. So, we don't have any idea about because in general shapely value is prone to manipulation. If we get into

coalition then it becomes a lot easier than manipulation becomes harder. So, there are other solution concepts, but then they are not fair in terms of like what Shapley value offers. So, someone has to look into the trade-off between these two. And the values are linear because this M plus one games, but in the end we have finally closed-form solution. From these M plus one games, we have generated closed-form solution. So, what we assumed it you already sorted. The sorting competition is like some log terms will be there, but they apart from that, it will be sort of linear in terms of number of players, but yes, if M and K become of the order N, then it will become order N squared but N is number of builders, and right now

there are hardly 37 builders, I believe, which could in between, right? There are many valid builders available, but I don't think they are anymore writing the blocks, and most of the blocks are written by four. So, even if it becomes order N squared, and there are say 100 builders in the system, or even with computing power order N squared is also not a big thing. >> It's a scaling problem. >> Yeah, but I don't think scaling is that big here. >> Not yet. >> What? >> Not yet, right? >> Yeah, so unless you have millions of builders available in the system.

>> Yeah, makes sense. >> Yeah. >> But for the first one, didn't you say truthfulness was an assumption? >> Yeah, we assumed it. So, our system can be manipulated, but we have bounds how much each builder or searcher can manipulate in, and those are very competitive bounds. So, if the bids are very competitive, how much I can manipulate is very small marginal gains I can gain. Yeah okay welcome. >> Thank you so much for this talk, and also this these questions and answers. It seems like there's more interest, so please, if you want to discuss more, take it outside, or just ambush Dr.

Gujar anywhere out there. >> [music]