Cryptocurrency trading is one of the biggest use cases of blockchains that support smart contracts. Decentralized exchanges (DEXes) that run on different chains handle daily exchange volumes of billions of dollars equivalent. A lot of (potential) trading volume in DEXes is generated through arbitrage trading between different exchanges on the same chain, as well as between exchanges on
different chains or between DEXes and centralized exchanges. While arbitrage opportunities on the same chain can be exploited through the atomic execution of bundles of transactions, cross-domain arbitrage is generally riskier (harder) to capture. We propose a game theoretic model that captures the different nature of same-domain versus cross-domain arbitrage on blockchains. One of our main motivation for the model is recent proposals around shared sequencing for rollups. Rollup chains are layer-two chains built on top of Ethereum for the purpose of scaling the Ethereum main chain. They are offering lower fees and faster execution of transactions. Because of these properties, DEXes built on them already attract significant trading volume. Rollups have a designated operator, called a sequencer, which receives transactions from users and schedules these transactions for execution. Shared sequencing schemes propose to jointly process transactions for several rollups, with the ultimate aim of improving user experience. For example, with a shared sequencer the users will be able to schedule their transaction bundles atomically even if they include transactions on different rollup chains: either all transactions will be scheduled and executed or none. A secondary aim of shared sequencing is improved economics through lower operating and maintenance costs and through collecting more of the increased arbitrage value captured by traders. More specifically, users send bundles of transactions to the shared sequencer. The sequencer distributes them to corresponding chains for execution. This gives flexibility to cross-domain arbitrageurs to get their transactions scheduled on different chains simultaneously. A proposed platform for shared sequencing is for example Espresso Systems. One fundamental economic question that we address in this paper is whether shared-sequencing services really lead to improved value capture as advertised by their proponents. As, in any trading activity, it is important how sequencers order transactions. Similarly to traditional finance exchanges, rollup sequencers usually use a first come first serve (FCFS) policy. This often generates latency competition, where parties invest into latency reduction to be competitive in arbitrage trading. FCFS competition may even affect the sequencer’s operation. For example, Arbitrum’s sequencer distributes its feed to other nodes in a fair (random) order, that is exploited by parties creating many nodes. Recently, there have been proposals to extract some fraction of MEV for rollups. In this approach, transaction senders bid per resource unit (in the case of chains using Ethereum’s EVM, per-gas) that the transaction consumes. Our game-theoretic model allows us to study FCFS-based transaction ordering, as well as bidding-based ordering. We are interested, in particular, in the latency investment resp. bidding expenditure by traders in the shared sequencers versus the multiple sequencer case and derive these quantities in equilibrium. We consider two versions of our model: the baseline version assumes that traders’ expenditure on executing a transaction is irreversible and independent of whether they succeed in capturing the arbitrage. This is for example the case if traders compete in latency investment with an FCFS policy. In other cases, it might be reasonable to assume instead that traders can partially recoup their cost if their arbitrage trade fails. More precisely, if bidding for inclusion is done per resource unit of the chain (per gas), the user may save a significant fraction of their cost by adding conditional statements to the transaction that check whether the price moved away from the target and not executing the transaction if it does. This approach may save a significant portion of gas usage in case of losing the race. However, it does (slightly) increase the overall cost by adding one conditional statement, which is added independently of the outcome. If the race is lost sufficiently often, which is the case in our model with few symmetric players, such a strategy is dominant and will be applied. Therefore, we also consider a version of our model where the loser of the race for the arbitrage trade only pays a fraction of the bid.