<aside> 🤖 TL;DR: I propose a simple model of competition for earlier transaction execution to make sense of several aspects of transaction ordering policies:

Can we avoid latency competition by using bidding to determine the ordering and inclusion of transactions? (not really)

How does latency competition look like in a batch auction world? (we have zero average profit for bidders in equilibrium when accounting for the cost of latency investment)

What are the performance differences between batch auctions and hybrid formats such as the time boost proposal for Arbitrum? (depends on the parameterization, but in general they look very similar)

The results are particularly relevant for roll-up sequencing but should also inform the broader transaction ordering discourse for L1s or off-chain aggregators.

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Many thanks to Quintus, Akaki, Sergio and Alejo for discussions and feedback on earlier versions. Forum for discussion and comments.

Suppose you want to choose a transaction ordering policy for your new roll-up sequencer, L1 blockchain, DEX aggregator, or new financial exchange. The following categories seem to cover your available options pretty well:

  1. First Come First Serve orders transactions by time stamp of arrival at whatever server orders the transactions. Questions of decentralized implementation aside, this policy seems appealing and intuitive to many. It is the go-to policy in traditional finance and hence users are used to interacting with it. FCFS appeals to basic intuitions about fairness. But there is also an efficiency argument to be made: FCFS provides an incentive to incorporate new external information quickly into the state of the system.
  2. Bidding Based Ordering: Orders are processed in batches or blocks. Transactions ****within a batch interval are ordered according to a function of the attached bids. The function can (hypothetically) be arbitrarily complex: we could order transactions by bid, we could auction individual slots in the batch, or even allow combinatorial bidding where users express preferences over the entire content of the block. Also the “bid” can sometimes be interpreted broadly, for example in Ethereum block building, the bid could contain the amount of MEV the user allows the block builder to extract from him.
  3. Random ordering or other non-conventional policies: Questions of implementation aside, randomness is a means to achieve ex-ante fairness when ranking transactions. In a different direction, verifiable sequencing rules are designed to make it detectable if a sequencer deviates from the rule. But, so far, they only have been designed to order AMM transactions for a single trading pair.
  4. Hybrid policies: The above policies can be mixed and matched. For example, FCFS can be implemented with discrete buckets where orders within a bucket are ordered randomly. A recent proposal by Offchain Labs, orders transactions by a scoring rule called “time boost” that scores transactions by a combination of time stamps and bids.

While these policies look very different from each other, a substantial aspect of all of them is that they organize a contest for earlier transaction execution among those users that care about it (arb traders, liquidators, etc.). ****The term contest here has the usual meaning from economics: users exert effort (investing in latency, spending money on bidding, spamming your server with transactions) to produce a signal (a timestamp, a bid, a set of transactions IDs) and based on these signals, we decide which transactions to include and in which order (and therefore decide who wins the different contests).

The framing as a contest is helpful, in so far as it gives us an indication of what it means to choose a transaction ordering policy: we organize a contest among users and users maximize whatever signal maximizes their chances of winning the contest. Thus, we need to decide on what dimension we want them to compete: latency investment, expenditure on bidding, the number of transaction requests you receive, increasing entropy, a mixture of all of them, etc?

In the following, I want to focus on the first two categories of transaction ordering policies, time stamp and bidding based policies, and hybrid policies mixing between the first two categories. This is because these policies have an implicit or explicit focus on efficiency (broadly understood) which is desirable.

To motivate the following discussion I would like to start with three somehow obvious observations:

  1. A pure bidding mechanism is impossible: This simply follows from the fact that the bidding phase of an auction cannot run forever. Thus, necessarily some bids end in different batches than others, and time plays a role.

  2. Latency competition necessarily happens, even in a pure batch auction: This is a corollary of the first point. In a batch auction, there still is an advantage for low latency bidders when approaching the end of the batch. This has for example been well-documented in Ethereum block building, where searchers specialized in CEX-DEX arbitrage need low latency to be competitive in “top of block” MEV.

    Illustration of the latency game at the end of a batch auction, source: 0xpandebug on Arbitrum Research

    Illustration of the latency game at the end of a batch auction, source: 0xpandebug on Arbitrum Research

  3. Bids are more informative signals of users’ preferences than time stamps: If time stamps are used to order transactions, then users are incentivized to create early time stamps. This can lead to investment into colocation and latency reduction. While the negative effects of excessive latency competition has been recognized, investment in latency is not wasteful per se. It incentivizes quick information incorporation in the state. Moreover, it allows users to express their value for transaction inclusion; users who can generate more value from fast inclusion will invest more in latency reduction. However, everything else being equal, this signal is necessarily less information than a bid because in contrast to bidding, it happens ex-ante before the precise value for transaction inclusion is known to users.

If we agree with the three statements, it seems necessary to focus on hybrid policies that take both bidding and time into consideration: batch auctions and other bidding based procedures are in reality a particular instances of hybrid policies and FCFS is, in most cases, not appealing. But how should we choose, on economic grounds, among different policies that use combinations of time stamps and bids to order transactions?

A first step is to analyze the equilibrium bidding and equilibrium latency investment of users interacting with the policy and to derive the equilibrium welfare and revenue achieved in different designs.

Some disclaimers: The following analysis is purely economic. I abstract away from questions of consensus and implementation and assume that the policies considered can be implemented, because they are run by a trusted centralized sequencer or because we know how to decentralize these policies in a satisfying way. I abstract away from incentive compatibility problems (MEV extraction, censoring etc.) on the side of the party that implements the transaction ordering policy and assume that the policies are implemented as stated.

Equilibrium Analysis of Bidding and Latency Investment

The starting point of my analysis is a bidding and/or latency race between two bidders, who each want their transaction to be executed before the other bidder’s transaction (I would expect similar results to hold for more than two bidders). A typical situation that triggers such race could, for example, be an arbitrage opportunity arising through a price discrepancy between an off-chain CEX and an on-chain DEX. Another typical example would be a competition for executing a liquidation. While there are other MEV games played in reality, where bidders have more complicated preferences over transactions orderings than just about how two transactions are ordered relative to each other, these atomic contest for earlier inclusion constitute a large fraction of trading activity on most platforms. Moreover, many other strategies contain an element of it, as it might be a necessary part of the execution of a more complicated trade.