Unity is Strength: A Formalization of Cross-Domain Maximal Extractable Value (2112.01472v2)

Abstract: The multi-chain future is upon us. Modular architectures are coming to maturity across the ecosystem to scale bandwidth and throughput of cryptocurrency. One example of such is the Ethereum modular architecture, with its beacon chain, its execution chain, its Layer 2s, and soon its shards. These can all be thought as separate blockchains, heavily inter-connected with one another, and together forming an ecosystem. In this work, we call each of these interconnected blockchains "domains", and study the manifestation of Maximal Extractable Value (MEV, a generalization of "Miner Extractable Value") across them. In other words, we investigate whether there exists extractable value that depends on the ordering of transactions in two or more domains jointly. We first recall the definitions of Extractable and Maximal Extractable Value, before introducing a definition of Cross-Domain Maximal Extractable Value. We find that Cross-Domain MEV can be used to measure the incentive for transaction sequencers in different domains to collude with one another, and study the scenarios in which there exists such an incentive. We end the work with a list of negative externalities that might arise from cross-domain MEV extraction and lay out several open questions. We note that the formalism in this work is a work in progress, and we hope that it can serve as the basis for formal analysis tools in the style of those presented in Clockwork Finance, as well as for discussion on how to mitigate the upcoming negative externalities of substantial cross-domain MEV.

• The paper introduces the formalization of Cross-Domain Maximal Extractable Value (MEV), extending the concept to multi-chain blockchain architectures.
• A detailed formalism quantifies MEV across multiple domains, incorporating pricing functions and generalizing from two to n domains.
• The research explores implications like sequencer collusion dynamics, new negative externalities, and open questions regarding cross-chain MEV extraction.

Analysis of Cross-Domain Maximal Extractable Value

The paper "Unity is Strength: A Formalization of Cross-Domain Maximal Extractable Value" by Obadia et al. discusses an intricate aspect of cryptocurrency ecosystems, particularly focusing on the concept of Maximal Extractable Value (MEV) across interconnected blockchains or ‘domains’. This research is crucial as it navigates the complexities inherent in a future characterized by multi-chain blockchain architectures, and introduces a formalization of a potentially emergent phenomenon within these systems: Cross-Domain MEV.

The foundational premise of the paper is that the interconnected nature of modern blockchain ecosystems — manifested through Layer 1s, Layer 2s, and additional side-chains — necessitates a comprehensive understanding of MEV not as a single-domain concept but as a cross-domain construct. MEV, initially defined for understanding incentives at a micro-level, requires reconceptualization to accommodate this growing inter-chain interaction.

Definitions and Motivation

The authors establish several foundational definitions, starting with that of a ‘domain’ as an interconnected blockchain entity with a shared global state manipulated by transactions, and a ‘sequencer’ as the actor responsible for ordering these actions. Central to this work is the expansion of MEV from its traditional confines within a singular domain to ‘Cross-Domain MEV’, encapsulating the value implication of transactions ordered across multiple domains.

To motivate this concept, the paper provides examples of arbitrage that take place across different blockchain domains. Notably, it highlights the opportunities arising when liquidity pools of the same asset, but across distinct domains, become imbalanced. Such scenarios where simultaneous cross-domain transactions can generate significant financial returns exemplify the practical relevance of the research.

Formalization of Cross-Domain MEV

An elaborate formalism is established to quantify MEV across multiple domains. Building upon single-domain reachable states and extractable value, the authors extend these notions to accommodate cross-domain dynamics. Through a detailed formal definition, the paper articulates how a single entity can extract maximal value by manipulating the interplay of two or more domains’ transactions jointly. This formalization notably incorporates a pricing function to translate cross-domain balance changes into a common valuation metric, acknowledging the necessity for a standard measure when spanning multiple blockchain assets or states. The work then progresses from a two-domain scenario to an n-domain generalization, providing a robust framework for analyzing these opportunities as multi-chain interactions burgeon.

Sequencer Collusion and Economic Dynamics

The exploration into cross-domain MEV naturally leads to the topic of sequencer collusion. With the distinct possibility of entities controlling transaction sequencing across multiple blockchains, the paper evaluates economic incentives for sequencers to collaborate. By comparing potential rewards from coordinated cross-domain transaction ordering against independent operations, the work identifies conditions under which collusion becomes economically advantageous. Consequently, this introduces challenges for protocol design, particularly underlining the need for mechanisms to address potential centralization risks and collusion-induced inefficiencies.

Negative Externalities and Future Outlook

Unlike single-domain MEV, cross-domain MEV is posited to introduce new externalities. The paper hints at possible trends such as sequencer centralization and time-bandit attacks exacerbated by cross-chain dynamics. These implications pose new risks to the blockchain's economic and security models, necessitating vigilant monitoring and proactive research to mitigate undesirable outcomes.

The authors also list several open research questions that present fertile ground for future inquiry. These include refining the actionable space for MEV extraction, understanding non-arbitrage cross-domain MEV scenarios, and devising protocols that could facilitate cross-chain MEV extraction in a manner congruent with network health and fairness.

Conclusion

In summary, the paper offers a comprehensive exploration of cross-domain MEV, articulating a rigorous foundational framework for understanding and analyzing these dynamics as multi-chain interactions become more prevalent. Though the formalism and insights presented are under active development, they constitute an invaluable step towards anticipating and managing the complexities of a future defined by blockchain interconnectivity. As the field evolves, these insights will likely prompt significant discourse and innovation around economic design, security, and fairness in distributed ledger technologies.