Short Paper: Atomic Execution is Not Enough for Arbitrage Profit Extraction in Shared Sequencers

TL;DR

The paper addresses whether atomic execution in shared sequencers increases cross-rollup arbitrage profits by modeling a two-pool cross-rollup arbitrage with an external price $P_{ext}$ and failure indicators $F_{S_A}, F_{S_B}$. It derives optimal trade sizes under constant-product pool dynamics with fee $f$ and provides a closed-form expression for the expected profit difference $E[Profit_{diff}]$ between atomic and non-atomic regimes, showing that profits depend on failure probabilities and the relative positioning of $P_{ext}$ and the effective pool prices $P^*_A$ and $P^*_B$. The analysis identifies regimes where atomic execution yields positive, zero, or negative expected gains, and highlights that atomicity alone is not a sufficient condition to boost arbitrage revenue for sequencers or arbitrageurs. The work suggests future extensions—such as allowing liquidity in a stable asset, incorporating transaction costs, and empirical evaluations—to better assess adoption incentives for shared sequencing.

Abstract

There has been a growing interest in shared sequencing solutions, in which transactions for multiple rollups are processed together. Their proponents argue that these solutions allow for better composability and can potentially increase sequencer revenue by enhancing MEV extraction. However, little research has been done on these claims, raising the question of understanding the actual impact of shared sequencing on arbitrage profits, the most common MEV strategy in rollups. To address this, we develop a model to assess arbitrage profits under atomic execution across two Constant Product Market Marker liquidity pools and demonstrate that switching to atomic execution does not always improve profits. We also discuss some scenarios where atomicity may lead to losses, offering insights into why atomic execution may not be enough to convince arbitrageurs and rollups to adopt shared sequencing.

Figures (1)

• Figure 1: Expected value of the difference in arbitrage profits between the atomic and non-atomic regimes for varying failure probabilities and relative external prices. Pool states are kept unchanged: $f=0.05\%$, $P_A=1.01$, $P_B=1$, and $y_A=y_B=100,000$