How to Serve Your Sandwich? MEV Attacks in Private L2 Mempools

We study the feasibility, profitability, and prevalence of sandwich attacks on Ethereum rollups with private mempools. First, we extend a formal model of optimal front- and back-run sizing, relating attack profitability to victim trade volume, liquidity depth, and slippage bounds. We complement it with an execution-feasibility model that quantifies co-inclusion constraints under private mempools. Second, we examine execution constraints in the absence of builder markets: without guaranteed atomic inclusion, attackers must rely on sequencer ordering, redundant submissions, and priority fee placement, which renders sandwiching probabilistic rather than deterministic. Third, using transaction-level data from major rollups, we show that naive heuristics overstate sandwich activity. We find that the majority of flagged patterns are false positives and that the median net return for these attacks is negative. Our results suggest that sandwiching, while endemic and profitable on Ethereum L1, is rare, unprofitable, and largely absent in rollups with private mempools. These findings challenge prevailing assumptions, refine measurement of MEV in L2s, and inform the design of sequencing policies.

💡 Research Summary

The paper “How to Serve Your Sandwich? MEV Attacks in Private L2 Mempools” investigates whether sandwich attacks—one of the most notorious forms of Maximal Extractable Value (MEV)—are feasible, profitable, and prevalent on Ethereum roll‑ups that use private transaction pools managed by centralized sequencers. The authors make three major contributions: (i) a rigorous theoretical model of optimal front‑run and back‑run sizing for both constant‑product AMMs (CPMMs) and concentrated‑liquidity AMMs (CLMMs), (ii) an execution‑feasibility model that captures the probabilistic nature of co‑inclusion under private mempools, and (iii) an empirical measurement study on major roll‑ups (Arbitrum, Optimism, zkSync, StarkNet, etc.) using a swap‑event‑based heuristic rather than the traditional address‑matching approach.

Theoretical Model.
Starting from the small‑trade regime (normalized inputs α_f, α_v ≪ 1), the authors expand the AMM swap function to second order. For CPMMs the attacker’s incremental profit is ΔΠ ≈ (1‑ϕ)² L (V_f V_v − V_f²) − 2ϕ V_f, yielding a unique interior optimum V_f* = V_v/2, the classic “half‑the‑victim” rule. For CLMMs the price impact is piecewise quadratic because liquidity is constant only within a tick. If the combined front‑run and victim trade stays inside a tick, the same CPMM solution applies. If the joint flow crosses a tick boundary into a region of lower liquidity, the attacker can gain an extra “boundary‑jump” profit, and the optimal front‑run size becomes the minimal V_gap_f needed to push the flow across the boundary. This analysis predicts two distinct empirical signatures: (a) in‑tick attacks with V_f ≈ V_v/2, and (b) boundary‑crossing attacks clustering around V_gap_f.

Execution‑Feasibility Model.
In private‑mempool roll‑ups there is no builder market guaranteeing atomic inclusion of the three transactions (front‑run f, victim v, back‑run b). The authors model two common sequencer ordering policies: (1) First‑Come‑First‑Serve (FCFS), where arrival time dominates ordering, and (2) Priority Gas Execution (PGA), where descending tip values determine order within a batch. They derive a joint inclusion probability

p(co‑inc) ≈ max(0, 1 − Δ/T_s) · p_policy · exp(−Δ²/(2σ²))

where Δ is the attacker‑chosen time gap between f and b (FCFS) or effectively zero (PGA), T_s is the sequencing window, σ captures network latency variance, and p_policy encodes the probability that the tip ordering (or arrival ordering) respects f ≺ v ≺ b. Using realistic roll‑up parameters (block time 200‑500 ms, window 300‑800 ms, σ≈50 ms) they obtain p(co‑inc) between 5 % and 20 %, far below the near‑certain inclusion achieved on L1 via bundle markets.

Expected Value and Minimum Victim Size.
Combining the economic profit with the inclusion probability, the expected profit is

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