Imperfect Commitment in Maximal Extractable Value Auctions

Abstract: Ethereum block builders run sealed auctions among searchers, but nothing in the protocol forces a builder to honor the auction outcome after observing submitted bundles. This paper studies the commitment problem. We model a builder who defects with probability $\varepsilon$ and, upon defection, replicates a type-specific fraction $γ(τ)$ of the winning MEV opportunity. Searchers anticipate this behavior and choose between a risky first-price bid and a safe deterrence bid that makes frontrunning unprofitable. The resulting equilibrium is piecewise, with the cost of imperfect commitment depending jointly on replicability and competition. Using the \texttt{libmev} dataset, we estimate $γ(τ)$ from right-tail bribe plateaus and decompose observed auction revenue against the surplus a defecting builder could capture. The results show sharp heterogeneity across MEV types: sandwich opportunities are already highly competitive, while naked arbitrage and liquidations leave substantially more surplus exposed to builder defection. Credible MEV auctions, therefore, require not only an auction format, but also constraints on the builder's ability to use observed bid and payload information ex post.

• The paper introduces a formal model of imperfect commitment, capturing builder defection and its welfare cost in Ethereum’s MEV auctions.
• It derives a Bayesian Nash equilibrium that links searchers’ bid strategies to defection probability and replicability metrics for different MEV types.
• Empirical analysis using extensive transaction data reveals heterogeneous replicability across MEV types, highlighting key revenue and design implications.

Imperfect Commitment in Maximal Extractable Value Auctions: Technical Overview

Context and Problem Statement

Maximal Extractable Value (MEV) auctions are a canonical clearing mechanism in Ethereum's block-building ecosystem, with builders running sealed-bid auctions among searchers submitting transaction bundles. A core protocol vulnerability is the lack of commitment enforcement: after receiving bids and payloads, builders can ex post defect from the auction outcome, replicating high-value searcher strategies and capturing the underlying MEV without honoring the purported winner. The paper introduces a formal model of this imperfect commitment problem, quantifies its welfare cost, and empirically estimates its significance across different classes of MEV opportunities using large-scale transaction data (2605.22667).

Theoretical Model: Commitment, Replicability, and Equilibrium Bidding

The central conceptual advance is the explicit modeling of the builder's defection parameter $\varepsilon \in [0,1]$, representing the probability with which the builder covertly replaces a winning searcher's bundle after observing all bids and payloads. Builder replication is characterized by a strategy-specific fraction $\gamma(\tau)$, which quantifies how much of the original opportunity is economically and technically replicable given MEV type $\tau$. Standard MEV types—sandwiches, arbitrage, liquidations, and backruns—are treated as observables with empirically-discriminable $\gamma(\tau)$.

The paper establishes a Bayesian Nash equilibrium in which rational searchers anticipate ex post builder replication and optimize between two regimes:

• For $v_i < v^*(\varepsilon, \tau)$, searchers follow the standard affiliated-values first-price bid schedule $\beta(v_i)$, accepting the risk of builder defection.
• For $v_i \ge v^*(\varepsilon, \tau)$, searchers escalate their bids to a deterrence threshold $b = \gamma(\tau) v_i$—the minimum that makes builder replication unprofitable.

The cutoff $v^*(\varepsilon, \tau)$ is endogenously determined by the tradeoff between expected surplus under risk of defection and the cost of safe bidding. The equilibrium is thus piecewise, with transition points and welfare consequences contingent on $\varepsilon$ and the structural primitives $\gamma(\tau)$0.

A crucial analytic result is that, in the high-extractability regime (large $\gamma(\tau)$1 and thin competition), the builder's revenue-maximizing $\gamma(\tau)$2—builders optimally always defect when profitable. In contrast, when $\gamma(\tau)$3 is low or competition drives bids above builder replication value, $\gamma(\tau)$4 is optimal.

Empirical Estimation: Dataset, Parameter Recovery, and Revenue Decomposition

Using the libmev dataset covering over two million MEV bundles on Ethereum with detailed MEV-type tagging and extracted value/tip breakdowns, the study robustly estimates $\gamma(\tau)$5 from the plateau of observed bid-to-value ratios in the upper quantiles of each MEV type. Sandwich attacks are empirically near-completely replicable ($\gamma(\tau)$6), while naked arbitrage and liquidations exhibit $\gamma(\tau)$7 in the range $\gamma(\tau)$8–$\gamma(\tau)$9, indicating only partial builder replicability.

The empirical analysis reveals intense within-type heterogeneity:

• Sandwiches: Highly competitive; bids almost always approach the full MEV value. Additional builder defection offers minimal incremental gain.
• Naked Arbitrage & Liquidations: Bids closer to $\tau$0–$\tau$1\% of extracted value, with substantial gaps to the estimated $\tau$2. Builder defection here could systematically extract remaining surplus.
• Backruns: Intermediate behavior with moderate vulnerability to builder opportunism.

Revenue decomposition quantifies the foregone frontrun surplus: for naked arbitrage, the builder could potentially extract on the order of $\tau$3 percentage points more than observed tips per transaction, amounting to over $\tau$4 in the data period. Liquidations, despite their scarcity, exhibit high per-event exposure.

Implications for Auction/Protocol Design

The results underscore that credible MEV auction outcomes rest not only on format (sealed-bid, first-price, etc.), but—more fundamentally—on constraints to builder discretion. In highly-competitive, highly-replicable settings (e.g., sandwiches), market forces mitigate the defection risk directly; in low-competition, low-replicability environments (e.g., liquidations), protocol defensibility critically degrades unless ex post builder actions can be credibly restricted.

Key design levers include:

• Limiting Builder Payload Access: Reducing or aggregating bid/payload information visible to builders at allocation time to prevent profitable replication.
• Enforcing Revert Protection: Ensuring that failed searcher bundles are not executed or front-run by builders.
• Transparency and Monitoring: Making builder (non-)commitment observable and thus punishable.
• Type-Specific Mechanism Adaptation: Adjusting auction, information, and commitment structures dynamically by MEV type and competition structure.

These considerations align the auction's theoretical incentive compatibility with practical, cryptoeconomic, and technical constraints inherent in Ethereum's evolving block-builder ecosystem.

Theoretical Connections and Future Work

The model bridges auction-theoretic literature on optimal information disclosure [bergemann2022optimal], affiliated private values, and classical corruption/collusion [compte2005corruption, lengwiler2010auctions], providing a unified treatment of the commitment problem tailored to MEV. It also motivates new environments in which builder and searcher roles are integrated and selective disclosure or favoritism can exacerbate welfare losses.

Future research directions include:

• Builder-searcher joint modeling with endogenous $\tau$5 and selective defection.
• Mechanism design for robust cryptoeconomic commitment without trust in builder behavior.
• Empirical microstructure estimation of $\tau$6 at finer granularity, including identity and temporal effects.
• Systematic benchmarking of alternative configurations (e.g., delayed payload reveals, multiparty commit protocols).

Conclusion

The paper formally establishes that the welfare cost of imperfect builder commitment in MEV auctions is sharply MEV-type dependent and fundamentally shifts attention from auction format to protocol-level constraints on ex post builder action. Practical implementation in Ethereum (and similar blockchains) must be sensitive to both the strategic replicability of MEV types and to the effective competition among searchers and builders. The work sets a foundational baseline for ongoing research in cryptoeconomic mechanism design under credible commitment constraints.