Quantifying risk in cross-rollup arbitrage without shared sequencing

Determine a quantitative model for the risk faced by cross-rollup arbitrageurs who submit the two legs of an arbitrage to independent rollups’ mempools, by characterizing the probability and expected magnitude of failure or loss due to price drift before sequencing on one or both rollups. Specify assumptions on sequencing order, block production times, and finality, and derive metrics or estimators that capture this risk under the current non-shared sequencer landscape.

Background

The paper analyzes non-atomic arbitrage across L2 rollups and between rollups and CEXs, highlighting that transactions on different rollups are currently sequenced independently and at high frequency. Without a shared sequencer, cross-rollup arbitrageurs face state (price) drift between submission and sequencing, which can cause one leg of the arbitrage to fail and lead to losses.

While the authors discuss how a shared sequencer could mitigate this risk by ordering transactions across rollups, they explicitly leave the task of formally quantifying the risk in the current, non-shared setting as an open problem. This quantification would need to account for mempool submission, sequencing delays, block times, and finality nuances on the involved rollups.