Recently, interoperability between Layer 2 networks (L2s) has become one of the key objectives of the Ethereum roadmap [10]. However, the UX of cross-chain activities, including cross-chain swaps, is still far from optimal. Moreover, due to its high capital requirements, there are fewer than five entities that can handle large (1M+) cross-chain swap orders [11], which creates centralization risks and suboptimal quotes. Even worse, unlike atomic arbitrages, most of the MEV and revenue generated from such activities are not shared with L2s; the share of revenue from such activities for L2s is comparable to that of CEX-DEX arbitrages [12, 13]. We believe the main cause of such revenue leakage is due to the risk of partial execution of two trades (buying on one venue, and selling on the other), and enabling atomic execution of transaction bundles that cross many chains can (at least partially) address these problems. In this article, we introduce a new combinatorial auction mechanism for shared sequencing, which enables such bundling of transactions. Our mechanism requires only minimal adjustments to the execution environment, and off-chain logic handles distributing the revenue generated from cross-chain bundles.
Before introducing our work, we review previous works that have attempted to solve similar or related problems.
In [1], the Espresso team proposed a market (Espresso Market; EM) for shared sequencing. Their mechanism is a combinatorial extension of the PBS auction, with additional tweaks to prevent the market from becoming a monopoly or oligopoly. Especially, their unique design of (practically) enabling L2s to set the reserve price while determining the winner by lottery should be noted. The lottery part is similar to the execution ticket mechanism proposed in [8] as well.
Proposed in [2], Resonance is a market mechanism for a network such that each node has different resources and capacities. While it is not designed for shared sequencing exclusively, there are many points that resemble our setting; it shares many structures and core design problems. Resonance is used by Ritual, and for more reader-friendly expository articles, refer to [3] and [4]. In Resonance, the WDP is completely outsourced to external entities known as brokers, and the mechanism focuses solely on computing payments. The most important merit of Resonance is that it does not require any prior assumptions about the valuations of players, such as single-mindedness or submodularity.
In [5], the sketch of the mechanism named state lock auction (SLA) is described. SLA is designed to enable a collaborative block building, especially by decomposing the auction into two parts, that is, one for transactions that compete on the right to touch (read and write) the storage slot that contains MEV opportunities, and the other for ordinary transactions. To the author's knowledge, the idea of setting slot-by-slot reserve prices is introduced in the article for the first time.
Other than those mentioned above, combinatorial auctions and double auctions are already widely used in many industries, such as cloud computing markets and energy markets. In this section, we mention a few of the important works for interested readers.
Cloud Computing
The market for pricing the resource for cloud computing resembles that of a block auction, and there are already many studies focusing on its market mechanism. In [9], the two mechanisms named CA-LP and CA-GREEDY are introduced. CA stands for combinatorial auction, and LP (linear programming) and GREEDY (greedy method) stand for the methods used to determine the allocation. Including this study, most of the literature focuses on mechanisms that prove strategy-proofness while maintaining a moderate level of computational complexity and loss compared to the optimal solution. As a result, most of the mechanisms are in large identical groups; they somehow score the bids and asks, sort them in descending (ascending) orders, and run the greedy algorithm to allocate the goods. To find a better solution, some mechanisms might leverage heuristics and meta-heuristics such as hill-climb method, ant colony optimization, and others, but the core mechanism remains the same.
Energy Markets
Combinatorial and double‐auction designs are now integral to many electricity-sector platforms. At the wholesale level, European day-ahead and intraday exchanges already let generators and large consumers submit package (XOR) bids so they can express inter-temporal constraints such as start-up lags or storage charge/discharge cycles. These combinatorial bids are cleared by the EUPHEMIA market-coupling algorithm. In [7], the mechanism is studied focusing on its efficiency and welfare loss.
As we have seen above, there are already numerous works addressing the same or similar problems. However, none of the works considered how to distribute the revenue from cross-chain bundles between the L2s on a transaction-by-transaction basis. For instance, EM divides the revenue from a bundle of blocks by the reserve price per block. That is, if Base sets the reserve price at 1 ETH and Optimism sets the reserve price at 0.5 ETH, and the accepted bundle pays 3 ETH, Base receives 2 ETH, and Optimism gets 1 ETH.
However, in some cases, this may result in an unfair distribution of revenue. Consider a “popular” chain A and an “unpopular” chain B. Then, for most of the time, the reserve price for chain A would be higher than that of chain B. Now, assume some builder C submits a bundle of blocks for A and B, and that bundle contains some ad-hoc or long-tail MEV, for instance, cross-chain arbitrage between A and B. In that case, although A and B's contribution to that opportunity may differ from popularity of each chain (e.g., if price at pool in A is similar to that of CEX and other chains while price at pool in B differs a lot, it is fair to give B more share), the profit is distributed according to the popularity. In short, the mechanism will favor the “popular” chain much more, hindering the participation of smaller and newer L2s. To resolve this problem, it is vital to distribute the revenue on a transaction-by-transaction basis, effectively decoupling the value distribution from the popularity of each chain.