Exclusive Order Flows (EOFs)

• Exclusive Order Flows (EOFs) are order flows routed exclusively to selected builders, altering execution incentives and reinforcing market concentration in systems like Ethereum PBS.
• An information-theoretic metric using KL divergence weighted by revenue is employed to distinguish EOFs from regular flows based on routing deviations from market share.
• In auction settings, EOFs function as exclusive execution options where higher upfront fee components improve execution probability and revenue while reducing effective spreads.

Searching arXiv for papers on Exclusive Order Flows and EOF auctions. arxiv_search(query="Exclusive Order Flows Ethereum builder centralization order flow auctions contingent fees", max_results=10, sort_by="relevance") Reviewing the most relevant arXiv results. Exclusive Order Flows (EOFs) are order flows whose execution rights or routing are restricted to a particular intermediary, builder, or small subset of counterparties, rather than being exposed to open competition. In Ethereum Proposer–Builder Separation (PBS), EOFs are defined behaviorally as flows whose routing preference across builders deviates persistently and substantially from the baseline market share distribution (Zhang et al., 6 May 2026). In auction design for exclusive execution rights, EOFs can also be modeled as exclusive options over execution, where the winner of an auction observes new information and then decides whether to execute the order (Resnick, 2023). Across these settings, exclusivity is economically important because it changes both execution incentives and market structure: it can create option-like distortions at the micro level and reinforce concentration and network effects at the market level.

1. Concept and scope

EOFs are conceptualized along a behavioral dimension of exclusivity and, in the Ethereum PBS setting, analyzed jointly with an economic dimension of value extraction purpose (Zhang et al., 6 May 2026). Under this definition, an EOF is not simply a high-revenue flow. Rather, it is an order flow whose routing is disproportionately concentrated to specific builders beyond what those builders’ general market shares would predict. This distinguishes EOFs from “influential” flows, which prior work defined by their revenue contribution to leading builders. The behavioral definition is intended to avoid conflating dominance with exclusivity and to capture smaller but strategically important flows that may not rank highly by absolute revenue (Zhang et al., 6 May 2026).

The unit of analysis for order flow in the PBS study is the destination contract, or “entry-point” contract: an order flow is all transactions that invoke the same destination contract (Zhang et al., 6 May 2026). This contract-level definition is used because it provides coverage across swaps while avoiding address-level fragmentation associated with searchers rotating externally owned accounts. In this framework, EOFs embody private access and routing arrangements, including wallet or exchange integrations and searcher–builder private channels that persistently favor one or a few builders (Zhang et al., 6 May 2026).

A different but complementary formalization appears in the study of contingent fees in order flow auctions. There, the platform auctions the exclusive right to execute a particular order or order bundle, and exclusivity means that no one else can execute that flow in that round once the winner has obtained the right (Resnick, 2023). If the winner declines execution, the order does not execute, or executes only through an exogenous automatic mechanism. This exclusive routing right is modeled explicitly as an option over execution states, making EOFs a setting in which incentive design and exclusivity are tightly linked (Resnick, 2023).

2. Formal definitions and measurement

In the PBS analysis, exclusivity is measured through an information-theoretic score based on the divergence between a flow’s routing distribution and the contemporaneous builder market-share distribution (Zhang et al., 6 May 2026). Time is partitioned into epochs $t \in \mathcal{T}$, weekly in the study. For each epoch, the builder market share distribution is $S_t = \{s_{t,i}\}$ with $s_{t,i} = Q_{t,i}/Q_t$, where $Q_{t,i}$ is the number of blocks built by builder $i$ and $Q_t = \sum_i Q_{t,i}$. For flow $j$, the routing distribution is $P_{t,j} = \{p_{t,j \rightarrow i}\}$ with $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$, where $R_{t,j \rightarrow i}$ is the revenue that builder $S_t = \{s_{t,i}\}$0 receives from flow $S_t = \{s_{t,i}\}$1 in epoch $S_t = \{s_{t,i}\}$2 and $S_t = \{s_{t,i}\}$3 (Zhang et al., 6 May 2026).

The epoch-level deviation is measured by KL divergence:

$S_t = \{s_{t,i}\}$4

To mitigate stochastic noise for small flows without allowing large flows to dominate mechanically, each epoch’s divergence is weighted by $S_t = \{s_{t,i}\}$5. The exclusivity score is then

$S_t = \{s_{t,i}\}$6

Higher $S_t = \{s_{t,i}\}$7 indicates that the flow persistently routes to a subset of builders more than market shares alone would predict, with greater weight on epochs in which the flow has meaningful volume (Zhang et al., 6 May 2026).

Using a 175-contract ground-truth set, the PBS study selects a binary threshold $S_t = \{s_{t,i}\}$8 by F1 maximization. The optimal threshold is $S_t = \{s_{t,i}\}$9, achieving $s_{t,i} = Q_{t,i}/Q_t$0 (Zhang et al., 6 May 2026). One false positive, Uniswap Router, was removed after manual review because it was a public protocol with massive volume, reported as 11,810.02 ETH bribe, that barely exceeded the threshold (Zhang et al., 6 May 2026). The paper states that it does not add explicit entropy normalization, min–max scaling, or Gini for exclusivity measurement, and that HHI is reserved for market concentration rather than exclusivity (Zhang et al., 6 May 2026).

In the auction-theoretic setting, exclusivity is not measured statistically but embedded directly in the timing and payoff structure. A single limit-sell order with strike $s_{t,i} = Q_{t,i}/Q_t$1 is auctioned; after the auction, ex-post information $s_{t,i} = Q_{t,i}/Q_t$2 is realized, and the winner then decides whether to execute (Resnick, 2023). Under a mixed contract, a bid $s_{t,i} = Q_{t,i}/Q_t$3 is split into an upfront component $s_{t,i} = Q_{t,i}/Q_t$4 and a contingent component $s_{t,i} = Q_{t,i}/Q_t$5, with $s_{t,i} = Q_{t,i}/Q_t$6. The winner executes if and only if

$s_{t,i} = Q_{t,i}/Q_t$7

This threshold formulation makes the contingent part of the payment behave like an added strike, and thus ties the economics of EOFs directly to option exercise incentives (Resnick, 2023).

3. EOFs in exclusive execution auctions

The contingent-fee model treats the sale of exclusive execution rights as the sale of an option whose exercise decision occurs after the winner observes new information (Resnick, 2023). If fees are contingent on execution, the winner receives what the paper terms a “free option”: the right to execute only in favorable states and decline otherwise. In this environment, bids under contingent contracts do not function like option premia; they set the strike price of the option. This changes equilibrium incentives because larger contingent components make execution less attractive ex post (Resnick, 2023).

The baseline primitives are a limit-sell order with strike $s_{t,i} = Q_{t,i}/Q_t$8, an ex-post value upon execution of $s_{t,i} = Q_{t,i}/Q_t$9, and a continuous distribution $Q_{t,i}$0 for $Q_{t,i}$1 with connected compact support. In the mixed-fee contract, the winner’s payoff is $Q_{t,i}$2 if execution occurs and $Q_{t,i}$3 if it does not. The endogenous exercise threshold is therefore

$Q_{t,i}$4

The winner’s expected payoff is

$Q_{t,i}$5

and competitive equilibrium is defined by the zero-profit condition $Q_{t,i}$6 (Resnick, 2023).

Auctioneer revenue and execution probability are correspondingly

$Q_{t,i}$7

and

$Q_{t,i}$8

The paper also provides a notation mapping often used in EOF contexts: $Q_{t,i}$9, $i$0, and $i$1, with baseline execution cost set to zero (Resnick, 2023).

The model’s corner cases are central to the interpretation of EOF auctions. Under pure upfront payment, $i$2, the competitive-equilibrium bid is $i$3, execution probability is $i$4, and revenue is $i$5 (Resnick, 2023). Because the payment is sunk at the decision stage, execution incentives are undistorted. Under pure contingent payment, $i$6, the bid rises to $i$7, but execution probability and revenue both collapse to zero in competitive equilibrium (Resnick, 2023). The paper’s interpretation is that competition drives the contingent bid up to the maximal ex-post value, so the threshold exceeds the support almost surely and no execution occurs. In the paper’s terms, the free option annihilates both execution and revenue (Resnick, 2023).

For mixed contracts, the key comparative statics are monotone in the upfront share. Execution probability is increasing in $i$8, auction revenue is increasing in $i$9, and effective spread is decreasing in $Q_t = \sum_i Q_{t,i}$0 (Resnick, 2023). Equivalently, increasing the contingent share reduces execution and revenue while worsening execution quality. This suggests that, in exclusive execution auctions, the structure of payment timing is not a secondary implementation detail but a determinant of equilibrium outcomes.

4. Execution quality, contingent fees, and reputation penalties

The execution-quality metric in the auction model is the effective spread, defined as the expected gap between the execution price and the order’s limit conditional on execution:

$Q_t = \sum_i Q_{t,i}$1

For a general distribution, this is

$Q_t = \sum_i Q_{t,i}$2

with $Q_t = \sum_i Q_{t,i}$3 (Resnick, 2023). The mechanism is straightforward: when the contingent component rises, the threshold $Q_t = \sum_i Q_{t,i}$4 rises, eliminating executions near the money. Only larger in-the-money states remain, which increases the conditional execution-price gap and therefore worsens execution quality for the order originator (Resnick, 2023).

A benchmark closed form is provided for $Q_t = \sum_i Q_{t,i}$5 and $Q_t = \sum_i Q_{t,i}$6. In that setting,

$Q_t = \sum_i Q_{t,i}$7

and

$Q_t = \sum_i Q_{t,i}$8

As $Q_t = \sum_i Q_{t,i}$9, the model gives $j$0, $j$1, and $j$2; as $j$3, it gives $j$4, $j$5, and $j$6 (Resnick, 2023). The paper reports a numerical example at $j$7 with no reputation penalty: $j$8, $j$9, $P_{t,j} = \{p_{t,j \rightarrow i}\}$0, and $P_{t,j} = \{p_{t,j \rightarrow i}\}$1 (Resnick, 2023).

The same paper studies a “reputation penalty” as a negative contingent fee. Let $P_{t,j} = \{p_{t,j \rightarrow i}\}$2 be a penalty imposed if the winner does not execute. Then the payoffs become $P_{t,j} = \{p_{t,j \rightarrow i}\}$3 if execution occurs and $P_{t,j} = \{p_{t,j \rightarrow i}\}$4 otherwise, giving the execution rule

$P_{t,j} = \{p_{t,j \rightarrow i}\}$5

The penalty lowers the effective strike and raises execution probability to

$P_{t,j} = \{p_{t,j \rightarrow i}\}$6

If the penalty is proportional to the promised contingent payment, $P_{t,j} = \{p_{t,j \rightarrow i}\}$7, then the threshold becomes $P_{t,j} = \{p_{t,j \rightarrow i}\}$8 (Resnick, 2023).

The paper identifies a “perfect” calibration at $P_{t,j} = \{p_{t,j \rightarrow i}\}$9. In that case the threshold is exactly $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$0, so the contingent-fee distortion is fully removed; execution probability is restored to $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$1 and revenue is restored to $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$2, independently of $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$3 (Resnick, 2023). If $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$4, some distortion remains; if $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$5, the threshold falls below $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$6, implying inefficient execution in states that are insufficiently in the money (Resnick, 2023). The paper also notes practical caveats: reputation must be enforceable and identity-sticky, and penalties must be measurable and tamper-resistant (Resnick, 2023). This suggests that reputation systems can mitigate, but do not automatically solve, the option problem created by exclusivity and contingent fees.

5. Empirical characterization in Ethereum PBS

The PBS study develops an end-to-end empirical framework for defining, measuring, and attributing EOFs and related value extraction mechanisms in Ethereum (Zhang et al., 6 May 2026). The dataset covers September 1, 2023 to August 31, 2025 and includes 5,226,578 blocks, spanning heights 18,037,988 to 23,264,565, and 889,227,817 transactions (Zhang et al., 6 May 2026). Total bribe revenue, defined as priority tips plus direct transfers, is reported as 503,853.69 ETH. Within this universe, 152,466,013 swap transactions, or 17.15% of transactions, generate 397,903.86 ETH, or 78.97% of revenue (Zhang et al., 6 May 2026).

The study identifies 59 builders and 102 receiving addresses, with builders categorized by peak weekly share into dominant, influential, and niche groups (Zhang et al., 6 May 2026). Dominant builders are Titan and Beaverbuild, defined as exceeding 50% peak weekly share; influential builders are those above 10% and up to 50%; all others are classified as niche (Zhang et al., 6 May 2026). Public versus private flows are inferred through mempool presence checked against Mempool Guru, with transactions absent from the mempool but present on-chain classified as private (Zhang et al., 6 May 2026).

For value-extraction taxonomy, the study manually labels the top 210 contracts by bribe, representing approximately 95% of revenue, using Etherscan labels and deployer linkage, ZeroMEV labels for atomic MEV, forensic sampling, and a criterion for non-atomic MEV based on consistent unidirectional swaps without an on-chain reverse leg in the same block (Zhang et al., 6 May 2026). This yields 113 atomic MEV contracts, 64 non-atomic MEV contracts, 30 protocol contracts, and 3 others (Zhang et al., 6 May 2026). A Random Forest classifier trained on these labels, using nine continuous features and seven-fold cross-validation, achieves average single-tree accuracy of 91.61% with standard deviation 0.0250 and ensemble accuracy of 92.06% on held-out test (Zhang et al., 6 May 2026). The most predictive feature is the average number of swap events, with non-atomic flows described as approximately single-swap per transaction (Zhang et al., 6 May 2026).

Applying the exclusivity pipeline and the non-atomic classifier produces the paper’s main empirical counts. It identifies 75 EOFs, of which 68 are previously unreported, contributing 280,554.89 ETH, or 70.53% of trading-related builder revenue (Zhang et al., 6 May 2026). It also identifies 322 non-atomic MEV flows, 316 of them new, contributing 91,483.07 ETH, or 22.99% of trading-related builder revenue (Zhang et al., 6 May 2026). Within the non-atomic segment, the top two flows account for 56% of non-atomic bribes, the top ten account for 77%, and the distribution exhibits a power-law tail with $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$7 and Kolmogorov–Smirnov statistic $$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$8 (Zhang et al., 6 May 2026). Nine non-atomic flows are exclusive to top builders and contribute 64,986.14 ETH, or 70.96% of non-atomic bribes (Zhang et al., 6 May 2026).

6. Centralization, network effects, and market structure

The PBS study argues that EOFs are a major mechanism of builder centralization and that their effects interact with non-atomic MEV and network effects to produce oligopolistic market structure (Zhang et al., 6 May 2026). Weekly concentration is measured by the Herfindahl–Hirschman Index,

$$p_{t,j \rightarrow i} = R_{t,j \rightarrow i}/R_{t,j}$$9

and the paper reports a time series with four eras: Genesis, Algorithm Wars, EOF Moats, and Oligopoly (Zhang et al., 6 May 2026).

In the paper’s chronology, the Genesis era runs from September 2022 to January 2023 and is associated with early PBS and MEV-Boost, proposer-linked advantage, and infrastructural latency races. Algorithm Wars, from January to October 2023, is the period of lowest concentration and a shift toward algorithmic efficiency, with builder0x69 peaking and Titan and rsync-builder emerging. EOF Moats, from October 2023 to October 2024, is characterized by a sharp rise in HHI and by Beaverbuild’s ascent, with EOF access becoming the primary determinant of bids and wins. Oligopoly, from October 2024 to August 2025, is the period in which Beaverbuild, Titan, and rsync-builder account for approximately 90% of blocks, while BuilderNet cannibalizes incumbent share without deconcentrating the market (Zhang et al., 6 May 2026).

The study reports that by September 2024 Titan and Beaverbuild together account for approximately 87.7% of the market (Zhang et al., 6 May 2026). It also states that, by January 2026, BuilderNet produces 25.5% of blocks, but that its TEE requirements raise entry barriers and its cooperative design removes within-cohort competition, enabling rent maximization without internal bidding pressure (Zhang et al., 6 May 2026). The reported policy conclusion is that measures which do not alter ordinal bidding, information asymmetry, or the need for private and non-atomic capital tend to mitigate symptoms rather than remove EOF-driven centralization pressures (Zhang et al., 6 May 2026).

The EOF–market share relationship changes over time. Pearson correlations between builder market share and EOF bribe share are strong for leaders during the EOF Moats era but decouple in Oligopoly (Zhang et al., 6 May 2026). The paper interprets this as evidence that EOFs were instrumental in establishing early dominance, whereas incumbents later sustain market share through entrenched network effects. Those effects include searchers clustering around builders with consistent inclusion, favorable fee splits, and dedicated APIs, as well as incumbents subsidizing searchers through negative-EDR blocks to preserve throughput (Zhang et al., 6 May 2026). A plausible implication is that EOFs function not only as a direct source of revenue but also as a bootstrap mechanism for later self-reinforcing concentration.

The paper’s architectural argument is that builder centralization is an emergent property of PBS because the framework violates three prerequisites of a competitive market: diminishing returns to scale, information symmetry, and low entry barriers (Zhang et al., 6 May 2026). Scale in compute, mempool vantage, and integration breadth benefits incumbents; deep searcher integrations and off-chain data produce persistent information asymmetry; and the need for access to exclusive flows and capital-intensive non-atomic MEV creates cold-start barriers (Zhang et al., 6 May 2026). The winner-take-all nature of ordinal bidding is presented as an additional accelerant because losing by 0.001 ETH yields zero (Zhang et al., 6 May 2026).

7. Case studies, limitations, and design implications

The PBS study provides representative case studies that illustrate the range of EOF manifestations (Zhang et al., 6 May 2026). A non-atomic flow routed to Beaverbuild, contract 0xa69b…e78c, has exclusivity score $R_{t,j \rightarrow i}$0, bribe 27,161.48 ETH, activity over 105 weeks, and average KL of 0.86; it is identified as routing exclusively to Beaverbuild and exemplifies top single-swap behavior and heavy private usage (Zhang et al., 6 May 2026). Another non-atomic flow, contract 0x51c7…2a7f, has exclusivity score $R_{t,j \rightarrow i}$1, bribe 24,543.74 ETH, activity over 105 weeks, and average KL of 1.58; it is attributed to rsync-builder exclusivity and described as one of the top two non-atomic flows (Zhang et al., 6 May 2026). The paper also cites niche-builder atomic EOFs: contract 0x6980…bdd0, an atomic arbitrage flow with bribe 5,715.40 ETH, routes 97.4% to “I can haz block?” and has $R_{t,j \rightarrow i}$2; contract 0x6454…4bfa, also atomic arbitrage, has bribe 4,361.08 ETH, routes 94.7% to a single builder address, and has exclusivity score approximately 2,697.17 (Zhang et al., 6 May 2026).

The auction-design paper yields a set of direct design implications for EOF auctions. It states that pure contingent fees yield zero execution and zero revenue in competitive equilibrium, that any increase in the contingent share worsens execution probability and elevates effective spreads, and that higher upfront share $R_{t,j \rightarrow i}$3 raises execution and revenue while lowering effective spreads (Resnick, 2023). If contingent fees cannot be avoided, the paper recommends a calibrated negative contingent penalty, specifically $R_{t,j \rightarrow i}$4 when feasible, which restores the threshold to $R_{t,j \rightarrow i}$5, restores revenue to $R_{t,j \rightarrow i}$6, and restores execution to $R_{t,j \rightarrow i}$7 (Resnick, 2023). The paper emphasizes that exclusivity heightens the stakes because, when the winner alone controls execution, threshold distortions translate directly into non-executions and worse user outcomes (Resnick, 2023).

Both papers note important limitations. The PBS study highlights labeling uncertainty, temporary ZeroMEV gaps on March 15–16, 2024, possible undercounting in private-flow identification due to reliance on Mempool Guru, the absence of explicit smoothing documentation for edge cases in the divergence metric, and limited long-tail coverage because the supervised model targets the top 1,000 flows, representing approximately 98.63% of trading-related revenue (Zhang et al., 6 May 2026). It also states that causal inference is limited to correlations and timing analyses, as builders may adapt via subsidies, routing agreements, or cross-domain strategies (Zhang et al., 6 May 2026). The auction paper assumes risk-neutral bidders, competitive zero-profit equilibrium, a single-unit order, and immediate exclusivity, while noting that multi-unit flow, dynamic games, and endogenous order arrival would change the algebra without necessarily changing the core option logic (Resnick, 2023).

Taken together, these results support a two-level understanding of EOFs. At the microeconomic level, exclusivity coupled with contingent execution rights creates an option problem that can depress execution, revenue, and execution quality unless fee design is carefully structured (Resnick, 2023). At the market-structure level, persistent exclusive routing is measurable as a deviation from baseline shares, accounts for a large share of builder revenue, and is associated with centralization dynamics that become self-reinforcing under PBS (Zhang et al., 6 May 2026). This suggests that EOFs are best understood not as a single mechanism but as a family of exclusive-access arrangements whose significance depends simultaneously on incentive design, routing behavior, and the surrounding market architecture.