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RANDAO Manipulation in the Presence of MEV

Kaya Alpturer, Nicholas Hope, S. Matthew Weinberg

arXiv:2610.02143v1cs.GT

TL;DR

RANDAO manipulation has been studied mainly through proposed-block share, although Ethereum rewards increasingly include variable execution-layer rewards. The paper develops an ε-optimal strategy methodology for general reward models and finds that rollover and multi-block MEV amplify manipulation incentives, while tail slashing can restore honest behavior under appropriate conditions.

  • Problem

    Prior analyses focus on proposed-block share, leaving how variable execution rewards affect RANDAO manipulation incentives unresolved.

    Source: §1 · p. 1

  • Method

    The authors model rewards through functions of non-tail proposals and tail actions, then use a sampling-based methodology to compute ε-optimal manipulation strategies.

    Source: §1 · p. 2, §1.1 · p. 3

  • Results

    Partial reward rollover and multi-block MEV amplify manipulation incentives in the modeled regimes, while appropriate tail slashing can make honest behavior ε-optimal.

    Source: §1.1 · p. 4

  • Takeaways & Limitations

    Manipulation incentives depend on the reward model, and the framework can analyze RANDAO incentives across a variety of settings.

    Source: §7 · p. 17

    The framework assumes epoch-level commitment, although online adaptation may improve the adversary’s strategy; reported analyses focus on α≤0.35 because bounds degrade above that range.

    Source: §4 · p. 11, §7 · p. 17

Abstract

from arXiv · show

Ethereum's randomness beacon (RANDAO) is well-known to be manipulable, and prior work [AW24] computes the precise fraction of blocks a strategic proposer can propose. The fraction of blocks proposed, however, is only a proxy for participants' rewards. We propose a generalized reward model capturing many canonical forms of rewards: consensus reward rollover, multi-block MEV, CEX-DEX arbitrage, oracle manipulation, and others. We provide a methodology that computes an {\epsilon}-optimal strategy for any reward scheme in our model (and in particular, any combination of the above rewards). Finally, we apply our methodology to several canonical examples, and establish the sensitivity of RANDAO manipulation to the underlying rewards. We find that if rewards partially roll over, or scale super-linearly with consecutive blocks, the incentive to manipulate RANDAO is amplified. Lastly, we investigate tail-slot slashing, which can be modeled as a reward function, and show that honest equilibria can be recovered.

1 Introduction

RANDAO manipulation research has largely measured proposed-block share, while Ethereum’s increasingly variable execution rewards make that an incomplete view of participants’ incentives. The paper develops a general reward-modeling and optimization approach, then applies it to reward models and mitigation strategies.

1 Introduction

  • Prior RANDAO analyses measured proposed-block share, while the open question is how MEV and other variable rewards affect manipulation incentives.Execution-layer rewards have increasingly been dominated by DeFi activity rather than constant rewards per proposed block.Source: §1 · pp. 1–2

1.1 Overview of Methodology

  • The methodology represents reward schemes with f for non-tail proposals and g for a specified Tail sequence, and computes an ε-optimal strategy for models expressible by those functions.Tail denotes the largest final run of epoch slots controlled by the adversary.Source: §1.1 · pp. 2–3
  • Partial reward rollover and multi-block MEV amplify manipulation incentives in the modeled regimes; MEV rollover evidence is scarce, and smooth and threshold models are stylized.The authors note that systematic multi-block MEV is weak in current Ethereum, while modeled regimes may matter under future block-building redesigns.Source: §1.1 · p. 4

1.3 Main Contributions

  • Increasing epoch length decreases manipulation gains across the considered reward models, while appropriate tail-slashing magnitudes can make honest behavior ε-optimal.The authors compute minimal slashing curves for each MEV reward model to recover honest behavior at equilibrium.Source: §1.1 · p. 4, §1.2 · p. 4, §1.3 · p. 5

1.2 Related Work

  • The framework is the first to find optimal strategies for execution rewards beyond uniform block rewards, but unlike [6] it does not adapt to realized transaction-fee draws.Earlier RANDAO work focused on the fraction of proposed slots rather than variable execution rewards.Source: §1.2 · p. 4

1.3 Main Contributions

  • A novel truncation provides provable upper and lower bounds, making complex reward instances tractable; the methodology also has robustness guarantees and a replication codebase.The methodology targets varying reward models and supports quick exploratory runs at coarse ε.Source: §1.3 · p. 5

1.4 Roadmap

  • The paper proceeds from a general reward model and ε-optimal policy methodology to complex reward models, model comparisons, mitigations, and proofs in the appendix.Its final sections analyze epoch-length variation and slashing-based mitigation before concluding with future work.Source: §1.4 · p. 5

2 Modeling RANDAO

The paper models RANDAO manipulation as a strategic choice over whether to propose or skip adversarial slots, with rewards that can depend on proposal patterns. It formalizes this choice as an infinite game whose state tracks the adversary’s tail and whose objective is average reward.

2.1 Background

  • RANDAO supplies randomness for Ethereum’s 32-slot proposer assignments, while a strategic adversary controlling a stake fraction α can selectively propose or skip its consecutive end-of-epoch slots.Each subset of the adversary’s tail slots yields a distinct future RANDAO value.Source: §2.1 · pp. 6–7
  • The model assumes uniformly random proposer selection with adversarial selection probability α, honest proposers always proposing, and the epoch-end RANDAO determining the next assignment.It also ignores interleaving epochs and assumes rewards reset after an honest proposer.Source: §2.1 · p. 7

2.2 RANDAO Game

  • The RANDAO game represents rewards with propose and next functions over tail and non-tail proposal strings, and maximizes long-run average reward while tracking the current tail.The two functions give expected rewards for adversarial tail proposals and non-tail proposals, respectively.Source: §2.2 · pp. 7–8

3 Solving the RANDAO Game

The solver reduces the RANDAO game to an MDP over tail lengths, then estimates transitions for general reward models through sampling and truncation. Upper and lower truncations bound the full MDP’s optimal reward, supporting an ε-approximate solution.

3 Solving the RANDAO Game

  • Sampling and truncation let the MDP handle pattern-dependent rewards whose transition probabilities are intractable to compute in closed form.The state remains tail length; sampling estimates transitions, while the truncation argument and concentration bound provide an ε-approximation guarantee.Source: §3 · p. 9

3.1 Methodology

  • The RANDAO game and its MDP have equal optimal rewards, and the solver estimates truncated transitions and rewards before computing an average-reward policy.Large tails are truncated to state T, assigning their transitions reward X for the upper model or 0 for the lower model.Source: §3.1 · pp. 9–10

3.2 Reward Guarantees

  • OPT(M−) ≤ OPT(M) ≤ OPT(M+), so lower and upper T-truncations bracket the full MDP’s optimal reward.The upper bound uses the expected duration of large-tail sequences and a per-transition reward bound.Source: §3.2 · p. 10, §3.1 · p. 10
  • With enough samples, transition probabilities and rewards can be estimated to error ε with probability at least 1−δ.The sample bound uses a Chernoff-Hoeffding bound and a union bound over transition and reward entries.Source: §3.2 · pp. 10–11

4 MEV Models and Results

The paper evaluates the solver on uniform, per-slot rollover, and multi-block reward models, focusing on stake fractions α ≤ 0.35 because the truncation bound degrades at larger fractions. The supplied passages describe the models and comparisons, but do not report table cell outcomes.

4 MEV Models and Results

  • For α ≤ 0.35, the experiments plot reward per slot against stake fraction because the truncation bound degrades as expected large-tail duration grows rapidly at larger α.The bound separating upper and lower estimates is Rmax · E[L(T, α)].Source: §4 · p. 11

4.1 Warm-up: Reproducing Uniform Reward Results

  • For uniform rewards, the solver reproduces prior results using reward equal to the number of proposed blocks, with Table 1 comparing its bounds against [2].Each table entry has an error of at most 0.0265% (ε/32).Source: §4.1 · p. 11, Table 1 · p. 12

4.2 Per-slot MEV

  • The per-slot model combines ephemeral rewards, lost when a block is missed, with rollover rewards, which accumulate across missed slots and are claimed when a block is proposed.The experiment uses 60% ephemeral and 40% rollover reward, and Table 2 compares upper and lower bounds with the honest strategy.Source: §4.2 · p. 12, Table 2 · p. 12

4.3 Multi-block MEV

  • The multi-block models assign rewards by consecutive proposed-block runs: one uses a smooth superlinear shape, while the other adds 10 when a run reaches five blocks.Both models are stylized rather than calibrated estimates; Table 3 compares their upper and lower bounds with the honest strategy.Source: §4.3 · pp. 12–13, Table 3 · p. 13

5 Improvement over Honest Strategy

The paper measures manipulation by relative average-reward improvement over honest proposing and finds that its size depends strongly on the reward model. Truncation-estimate gaps grow with stake fraction, while longer epochs reduce manipulation gains across the four MEV models.

5 Improvement over Honest Strategy

  • Manipulation incentives depend strongly on the reward model, so changes in the MEV extraction landscape may change the incentive to manipulate RANDAO.Figure 2 measures the relative improvement over the honest strategy.Source: §5 · p. 13, Figure 2 · p. 14
  • The upper- and lower-truncation estimate gap is small at low α and grows at larger α as optimal policies depend more on large tail states.Sampling is the primary source of error; more samples and a higher truncation T can improve precision.Source: §5 · p. 13, Figure 3 · p. 14
  • Across all four MEV models, manipulation incentives decay as epoch length increases, making longer epochs a partial mitigation while reward-model dependence remains.The comparison sweeps epoch length while holding α fixed.Source: §5 · p. 14

6 Tail Slashing

The section asks what tail-slot penalties would make honest behavior ε-optimal, then evaluates the minimum required penalty across reward models and stake fractions. Its illustrative scheme weights misses by their position near the epoch end and by how many misses cluster in the tail.

6 Tail Slashing

  • The authors seek the minimal slashing curve for each MEV model that makes honest behavior ε-optimal, modeling slashing as a negative reward component.They reuse their solver and use the upper truncation to certify the threshold.Source: §6 · pp. 14–15, §6.1 · p. 16

6.1 Slashing as a Reward Model

  • The proposed curve penalizes tail misses more heavily near the epoch end and increases penalties when more slots in the window are missed.For the illustrative scheme, W = 8 and the multi-miss multiplier is 1 plus the fraction of missed slots in the window.Source: §6.1 · p. 15
  • The slashing threshold κmin is the minimum κ for which honest behavior is ε-optimal in the slashed MDP.The threshold is defined relative to the honest average reward.Source: §6.1 · p. 16

6.2 Slashing Magnitudes

  • At fixed α, reward models with larger manipulation gains require larger κmin, and κmin increases monotonically with α.Figure 5 compares the minimum slashing threshold across four MEV reward models and stake fractions.Source: §6.2 · p. 16, Figure 5 · p. 16
  • The curve is gentler for solo stakers’ isolated accidental misses than a fixed per-slot penalty, because early misses carry little or no penalty and isolated misses barely raise the multiplier.The paper describes solo stakers as typically missing roughly 1–2% of assigned slots through i.i.d. accidents.Source: §6.2 · p. 17

7 Conclusion

The conclusion finds that partial reward rollover and multi-block MEV amplify RANDAO manipulation, while longer epochs partly mitigate it. Tail slashing can make honest behavior ε-optimal, and the authors identify several directions for extending the analysis.

7 Conclusion

  • Partial reward rollover and multi-block MEV amplify manipulation gains, while lengthening the epoch partially mitigates manipulation across the considered reward models.The conclusion describes these as findings across the reward models considered.Source: §7 · p. 17
  • Tail slashing, modeled as a reward function, can make honest behavior ε-optimal.Source: §7 · p. 17
  • The framework analyzes RANDAO incentives under varied reward settings and may streamline analyses for applications with complex reward models.The conclusion cites a protocol-design example that incorporates RANDAO bias analysis.Source: §7 · p. 17
  • The slashing analysis considers one curve; exploring alternative curves could reduce honest validators’ costs under the same deterrence guarantee.Source: §7 · p. 17
  • The framework is epoch-level and assumes an adversary commits to an action for the whole epoch; online adaptation remains future work.The authors also note that the empirical gap between upper and lower bounds is smaller than their sample-complexity bound predicts, motivating tighter analysis.Source: §7 · p. 17

A Proofs for Section 3 (Solving the RANDAO Game)

The proofs connect the RANDAO manipulation game to an ergodic MDP, bound its value using tail truncations, and justify estimation of transition and reward quantities with finite samples.

A Proofs for Section 3 (Solving the RANDAO Game)

  • The RANDAO manipulation game and its MDP have the same optimal average reward because strategies in either formulation can reproduce the same sequence of tails.The proof also notes that ergodicity makes the optimal average reward independent of the starting state.Source: A Proofs for Section 3 (Solving the… · p. 21
  • Always choosing the longest tail stochastically maximizes consecutive rounds above threshold T; expected duration from tail 32 is the last element of (I − P_T)^−1 1.P_T is the transition matrix over states T+1 through 32 under the longest-tail strategy.Source: A Proofs for Section 3 (Solving the… · p. 21
  • The truncated MDP values bound the original: OPT(M−) ≤ OPT(M) ≤ OPT(M+).The lower truncation gives zero reward on transitions to large tails; the upper truncation bounds their reward using the expected time spent in large tails.Source: A Proofs for Section 3 (Solving the… · p. 21
  • With N independent samples per state, Chernoff-Hoeffding and union bounds control transition and reward estimates jointly with probability at least 1−δ.The estimates are taken from the truncated MDP under a fixed policy.Source: A Proofs for Section 3 (Solving the… · p. 22

B Proofs for Section 6 (Tail Slashing)

The proof compares slashing rewards under two penalty settings for a policy optimal under the larger setting, using ergodicity to establish its average-reward properties.

B Proofs for Section 6 (Tail Slashing)

C Reward plots

The reward plot reports that one missed slot is followed by a higher consensus reward, while the accompanying bid plot is a histogram from MEV-Boost data.

C Reward plots

  • After a single missed slot, the next block earns roughly twice the consensus reward.Figure 6 excludes execution-layer rewards; its data are from [29].Source: Figure 6 · p. 23
  • Two or more consecutive missed slots show no significant further increase in consensus rewards.Source: Figure 6 · p. 23
  • Figure 7 is a histogram of bids from the MEV-Boost dataset [12].Source: Figure 7 · p. 23
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