By Ben Marsh, Sei Labs Research for Sei Research Initiative

Introduction

We previously went over the potential issues of public DA [Mar25] in Autobahn which touched on several MEV cases but that work failed to outline the full MEV landscape. Here we will introduce, informally, the MEV landscape in a Giga style MCP context. This work will also describe several potential mitigations. A full formal model is under active research. In order to fully understand the discussion we will first define a generalized architecture for Giga [MA25] with some assumptions which simplify the models. 

The work should be viewed as a skeleton outline of MEV in this context. Assumptions such as the distribution of fees and a fixed tx block size have been made for simplicity to make this work more digestible. Several ideas in this work such as PBS and inclusion lists are included due to their interest as opposed to necessity.

Architecture

Sei Giga uses Autobahn [Gir+24] as the base consensus protocol where \(n\) block producers, or proposers, create blocks concurrently as opposed to sequentially. In a traditional blockchain, say Ethereum, each block is built sequentially. This means that each tick of the protocol may produce more than one block, each proposer can propose as many blocks as they desire, though they have an incentive to propose just one, unless bound by gas, in an attempt to maximize their revenue and create their block based on others when possible. 

The transactions are ordered within a block by the proposer and the blocks are then ordered at the point of a tip cut and the ordering of the set of blocks within a tip cut is agreed on through the consensus vote. In Giga there is not a global mempool and proposers receive transactions from RPC nodes, where the transactions are randomly allocated. A proposer may run a local mempool. Tip cuts happen multiple times a second at a rate in the order of hundreds of milliseconds.

MEV

In this work we refer to standard definitions of maximal extractable value, where a proposer attempts to extract more revenue from a block than they would by just directly including the transactions they have access to.

Censorship

In a traditional sequential blockchain censorship [FPR23] in a given slot is trivial since the producer has no competition and the tx issuing agent cannot bypass that producer. The only thing they can do is wait, which is sufficient for a patient user but yields a utility of 0 for an impatient user who needs to be included in that block. In a MCP blockchain the tx issuing agent has the ability to send the transaction to multiple producers increasing the probability of inclusion in a given slot at the cost of issuing extra transactions.

Basic censorship resistance

Assume a fixed set of \(n\) validators labeled \(1, \dots, n\). We assume all nodes may censor a transaction if it yields a greater utility than not doing so. Let a tx issuing agent submit a single transaction \(T\) to the blockchain with a valuation \(V>0\). The agent may choose to submit the tx to a subset \(S \subseteq \{1, \dots, n\}\) of size \(|S| = k\). Each tx has a fixed cost \(c>0\) to submit where the cost of submitting \(k\) txs is \(k \cdot c\). \(T\) is included on chain if one validator in \(S\) includes it. Assuming all validators independently censor the probability of inclusion is therefore

\[P_{\mathrm{inc}}(S) = 1 - \prod_{i \in S}p_i\]

where \(p_i\) is the probability of censorship from \(i\) not known to the tx issuing agent ex-ante.

Suppose a common prior for each \(p_i\), for simplicity we assume they’re i.i.d. draws for some distribution with a mean \(\mu = \mathbb{E}[p_i]\). In equilibrium the agent chooses to fan out \(k\) transactions to \(k\) distinct validators to maximize the utility in expectation

\[U(k) = V[1-\mathbb{E}[\prod^{k}_{i=1}p_i]] - k\cdot c = V[1 - \mu^k] - k \cdot c\] 

The gain of increasing from \(k-1\) to \(k\) transactions is therefore \(V \mu^{k^*}(1-\mu)-c\). At equilibrium the agent picks the largest \(k^*\) such\(V \mu^{k^*-1}(1-\mu) \geq c\) and \(V\mu^{k^*}(1-\mu) < c\) giving

\[k^* = \lfloor1 + \frac{ln(\frac{c}{[V(1-\mu)]})}{ln \mu}\rfloor\] 

clamped to \([0,n]\).

For example let’s assume a scenario with \(V = 10, c = 1, \mu = 0.8, k \in \{0, 1, \dots, 6 \}\). Computing the marginal gains \(\forall k \in \{0, 1, \dots, 6 \}\) gives a peak utility at \(k = 4\) therefore the tx issuing agent should send their tx to 4 validators to increase their censorship resistance taking into account their valuation.

Inclusion lists

Inclusion lists have been proposed elsewhere before and here we abuse the notion of an inclusion list. In this context we assume each RPC node which receives transactions no longer randomly allocates each transaction to a proposer but bundles b transactions together and forwards them to a proposer along with a signed certificate. When the proposer proposes a block to the network the block is only valid if all included transactions are accompanied by a signed certificate from an RPC node and that each transaction noted on a certificate must be present.

Let \(b\) be the bundle size where the bundle is made up of transactions \(\{T_1, \dots, T_b\}\) with a total revenue for the bundle of \(R = \sum_{i = 1}^{b} r_i\) for a revenue per tx of \(r_i\). We then have three situations.

Proposer tx inclusion

The proposer can no longer include their own tx directly for any purpose, honest or malicious. Assume the proposer could previous insert a malicious tx directly for \(r\) in revenue. The miner now has two choices sending the transaction to RPC nodes for inclusion or by paying an RPC node, such as through a revenue split, for a valid certificate. If the tx is sent to honest RPC nodes for inclusion for a cost \(c\) the revenue is now \(r' = r - c < r\) making the attack trivially less profitable. If a profit share approach is used to ensure a valid certificate then \(r' = (1 - \alpha) r < r\) for some split \(\alpha > 0\). Though the attack may be profitable in some circumstances it is less profitable then without the inclusion lists.

Small censorship revenue

Assume an unordered bundle where censoring \(T_1\) will provide an \(\epsilon\) utility to the proposer. Without inclusion lists the proposer may opt to censor that transaction for the revenue. When \(\sum_{i = 2}^{b}r_i > \epsilon\) the proposer no longer has an incentive to censor \(T_1\).

\[\pi_{\mathrm{inc}} = \sum_{i=1}^{b}r_i\]

\[\pi_{\mathrm{cen}} = 0 + \epsilon\]

Thus when \(R > \epsilon\) including the bundle strictly dominates any censorship the unique NE is to include the entire bundle. This offers more resistance than the non-inclusion list approach where the decision is

\[\sum_{i = 2}^{b} r_i + \epsilon > \sum_{i = 1}^{b} r_i\]

not

\[0 + \epsilon > \sum_{i = 1}^{b} r_i\]

Large censorship revenue

Suppose censoring \(T_1\) yields standalone revenue \(r'_1\). With inclusion lists, omitting \(T_1\) invalidates the entire bundle, so

\[ \pi_{\rm inc} = R = \sum_{i=1}^b r_i, \quad \pi_{\rm cen} = r'_1. \]

If

\[ r'_1 > R, \]

then censoring strictly dominates inclusion and the proposer will now censor the entire bundle. In this regime, inclusion lists provide no additional resistance the tx issuer must fall back on multi‐proposer submission to ensure censorship resistant inclusion.

Tx auctions

As noted in the public DA work one issue in MCP is the creation of a side auction where proposers are able to sell transactions to another proposer if they expect to extract more revenue from doing so.
Let the revenue from some tx \(T\) be \(\epsilon\) from both tips and MEV to a given proposer. The proposer has 3 strategies with that tx. To include that tx immediately. To offer the tx in a snap time-bound auction and otherwise include. Or to censor the tx and offer in a longer auction.

Include immediately

If the proposer chooses to include immediately then the utility is trivially given by

\[U_{\mathrm{norm}} = \epsilon\]

Quick auction

The proposer can create a time-bound side auction knowing that they will include the tx in their own block if nobody else values the tx more than them. The proposer sets a reserve price \(\epsilon' > \epsilon\) and a time limit on the auction such that they can include \(T_1\) in their own block to ensure \(\lfloor U \rfloor = \epsilon\). The expected utility in this case is

\[U_{\mathrm{quick}} = p \cdot \epsilon' + (1-p) \cdot \epsilon = \epsilon + p (\epsilon' - \epsilon)\]

for some probability of the auction succeeding \(p\) where \(p\) is likely to be very small given the millisecond scale of the auction so \(U_{\mathrm{quick}} \approx U_{\mathrm{norm}} = \epsilon\) limiting the scope of the strategy to occasions where \(\epsilon' >> \epsilon\) or \(p\) is non-negligible.

Censor and auction

Given the millisecond requirement of the quick auction a proposer could opt to censor the transaction entirely to run a slower auction with the hope of increasing \(p' > p\) and/or \(\epsilon'\). Notably however the proposer does not know if the tx will be included by another proposer in the round where they chose to censor, if it is then then \(\epsilon' = 0\).

\[U_{\mathrm{slow}} = (1-q) \cdot (p') \cdot \epsilon'\]

Where \(q\) is the probability that another validator included the transaction that is the probability of uniqueness in the round. This means the utility is zero unless nobody else included it and someone bids on the tx. Given the tx issuing agent is likely to have sent their tx to multiple proposers assuming they have a non-negligible valuation, as seen before, \(1-q\) is likely to be small in the real world meaning the expected utility would be lower for the censor and auction approach.

\[U_{\mathrm{slow}} \approx 0 < U_{\mathrm{quick}} \approx U_{\mathrm{norm}}\]

Spam

Some blockchains have faced spam attacks in an attempt to extract MEV revenue, the chains typically facing such attacks tend to be sequential single leader protocols. In our MCP model such an attack is obviously more costly given the random proposer assignment meaning the targeting of a given proposer, and the second round of ordering that takes place at consensus where transactions are ordered by priority fee, well considering dependencies, meaning the benefit of being first in a given proposers block without paying with a non-trivial priority fee will be negated at execution.

Let a searcher \(s\) attempt a spam based MEV attack where it attempts to place a tx \(T'\) early in a block. Let the validators \(i = 1, \dots, n\) be randomly allocated incoming transactions. We assume any tx is randomly allocated to a validator with a probability \(\frac{1}{n}\). We assume each block holds up to \(B > 1\) transactions and the first \(B\) transactions in the validators queue will be included. The cost of submitting any tx is \(c > 0\) and each tx has a priority fee \(z \geq 0\). The searcher sends \(m \geq 0\) total transactions. The probability of the tx ending up at a given proposer is

\[P(m) = 1 - (1 - \frac{1}{n})^m\]

If the reward for success is a fixed \(R>0\) then

\[U(m) = R\cdot [1 - (1 - \frac{1}{n})^m] - m\cdot c\]

By simple manipulation we derive a condition where \(\Delta U(m^*) \geq 0\) and \(\Delta U(m^* + 1) \leq 0\) at

 \[(1- \frac{1}{n})^{m^*} \geq \frac{c \cdot n}{R}\]

hence

\[m^* \leq \frac{ln(\frac{c\cdot n}{R})}{ln(1 - \frac{1}{n})}\]

This means a no spam one shot equilibrium occurs, even without the second round of ordering if

\[\Delta U(0) = \frac{R}{n} - c \leq 0\]

After consensus the blocks in the tip cut are executed with a reordering on the priority fee. Assuming honest fees are i.i.d. with a CDF \(F(z)\) and the spammer wants their tx to be first in the execution order

\[P_{\mathrm{success}}(z) = \mathrm{Pr}(z > \max_{1\leq i \leq nB}z_i) = F(z)^{nB}\]

giving an expected utility of

\[U(z) = R F (z)^{nB} - (c + z)\]

The optimal fee \(z^* > 0\) solves the first-order condition

\[\frac{dU}{dz} = R(nB)F(z)^{nB-1}f(z)-1=0\]

To use this in an example where we assume honest bids i.i.d. uniform on \([0, 1]\) so \(F(z) = z, f(z) = 1\). We let \(n = 50, B = 200, R = 2, c = 0.02\).
The first order condition is now \(0.948\) meaning you would bid approximately \(0.95\) for \(P(z^*) = (0.948)^{10000} = 0.004\) giving \(2 \cdot 0.004 - (0.02 + 0.948) = - 0.96\) in expectation.

PBS

Some chains decouple block building from proposing via PBS. While MCP doesn’t require PBS, its MEV implications are interesting.

Assume \(P\) proposers and \(B\) builders. Each builder \(j\) can extract MEV \(V_j\sim F\), i.i.d. draws from CDF \(F\) with density \(f\). Each proposer runs an independent auction among these \(B\) builders.

First-Price Auction

Builders bid \(b_j\le V_j\). The highest bid wins and pays \(b_j\). In the unique symmetric equilibrium

\[ b(v) = v \;-\;\int_{0}^{v} \frac{F(x)^{\,B-1}}{F(v)^{\,B-1}} \,dx. \]

Let \(V_{(B)}\) be the maximum of the \(V_j\). The proposer’s expected revenue is

\[ \mathbb{E}[b(V_{(B)})]  = \int b(v)\,dF_{(B)}(v). \]

Second-Price Auction

Builders bid truthfully (\(b_j=V_j\)). The highest bidder wins and pays \(V_{(B-1)}\). Hence

\[ \mathbb{E}[\text{Revenue}] = \mathbb{E}[V_{(B-1)}]. \]

Revenue Equivalence & Large-B Limit

By revenue equivalence,

\[ \mathbb{E}[b(V_{(B)})] = \mathbb{E}[V_{(B-1)}]. \]

As \(B\to\infty\), \(V_{(B-1)}\to V_{(B)}\), so proposers capture almost the full MEV.

Many-to-many Matching

With \(P\) proposers and \(B\) builders, let \(v_{ij}\) be proposer \(i\)’s value for builder \(j\). Solve

\[ M^* = \arg\max_{\text{matching }M} \sum_{(i,j)\in M}v_{ij}. \]

Define total welfare \(W=\sum_{(i,j)\in M^*}v_{ij}\), and \(W_{-i}\) the welfare without proposer \(i\). If \(i\) is matched to \(j\),

\[ p_i = W_{-i} - (W - v_{ij}), \]

a VCG price that yields welfare‐maximal, incentive‐compatible outcomes. If \(P\gg B\), builders extract nearly all surplus; if \(B\gg P\), proposers do. As \(P,B\to\infty\), matching payments converge to the competitive equilibrium prices.

Inter-block MEV

Inter-block MEV has been discussed before but has primarily focused on the sequential block model where MEV is over sequential blocks. The public DA layer in Autobahn along with the concurrent block production introduces the opportunity for games to exist between blocks in the same round. The obvious case here, given the assumption of a second round of ordering at execution, is that a tx in a later block in the same round could allow an existing tx to be beaten given its public tip. Assume a tx \(T_\alpha\), with a tip \(t_\alpha\) and a bid \(b_\alpha\), exists in block \(\alpha\) which is attempting to buy an asset \(A\). Block \(\alpha\) is published to the DA layer. In a subsequent block \(\beta\) a new tx is submitted attempting to buy  \(A\) where the bid\(b_\beta < b_\alpha\) but \(t_\beta > t_\alpha\). The greater tip allows \(T_\beta\) to be executed first given its priority despite the lower bid. Such an example can be trivially extended to other MEV contexts.

The problem is not necessary so straightforward however since \(\alpha\) has an incentive not to publish immediately to prevent such attacks and to attempt to maximize the revenue of the block through better MEV searching which is monotonically with time [Bur24] or more transactions arriving, and \(\beta\) has an incentive to ensure the block is published early enough to ensure \(f+1\) votes on the DA layer to ensure a PoA for consensus.

Assume both \(\alpha \text{ and } \beta\) are candidate blocks in the chain. Each agent can choose when to release the block to the DA layer waiting for some time \(d_i \in [0, T]\). If \(d_i > T\) they miss the consensus round and their myopic utility is 0. \(M(d)\) is a strictly monotonic MEV revenue gained from a longer search time and extra transactions received before the block is published. \(L > 0\) is the extra revenue received by the agent if the other block is published first.

\[ U_i(d_i, d_j) = \begin{cases} 0, & \text{if } d_i > T,\\[6pt] M(d_i) - L, & \text{if } 0 \le d_i < d_j,\\[6pt] M(d_i) + L, & \text{if } 0 \le d_j < d_i,\\[6pt] M(d_i), & \text{if } d_i = d_j \le T. \end{cases} \]

This represents a pure timing game over \([0, T]\) with the pure strategy NE at \(d_i = d_j = T\) implying proposers release their block at the last possible moment to ensure the votes meaning the risk of public DA is minimized unless the proposer can ensure some \(T' > T\) such as having \(f-1\) Byzantine nodes willing to coordinate a vote and only needing \(2\) real votes. An encrypted DA layer would allow the effective \(T\) timing game to be avoided entirely though it is likely limited in scope in a real network.

Join the Sei Research Initiative

We’re actively working on a formalization of MEV in this context. We invite developers, researchers, and community members to join us in this mission. This is an open invitation for open source collaboration to build a more scalable blockchain infrastructure. Check out Sei Protocol’s documentation, and explore Sei Foundation grant opportunities (Sei Creator Fund, Japan Ecosystem Fund). Get in touch - collaborate[at]seiresearch[dot]io

References

[FPR23] Elijah Fox, Mallesh Pai, and Max Resnick. “Censorship resistance in on-chain auctions”. In: arXiv preprint arXiv:2301.13321 (2023).

[Bur24] Jonah Burian. “The Future of MEV”. In: arXiv preprint arXiv:2404.04262 (2024).

[Gir+24] Neil Giridharan et al. “Autobahn: Seamless high speed BFT”. In: Proceedings of the ACM SIGOPS 30th Symposium on Operating Systems Principles. 2024, pp. 1–23.

[Mar25] Ben Marsh. Blockchain Bandits: How Public DA Creates New MEV Attack Vectors. 2025. Url: https://seiresearch.io/articles/blockchain-bandits-how-public-da-creates-new-mev-attack-vectors.

[MA25] Ben Marsh and Vangelis Andrikopoulos. Autobahn: Sei Giga’s Multi-Proposer Approach to Blockchain Consensus. 2025. url: https://seiresearch.io/articles/autobahn-sei-giga-s-multi-proposer-approach-to-blockchain-consensus.