Maximal Extractable Value Searchers

• Maximal Extractable Value searchers are specialized agents that strategically bid on blockchain transaction ordering to capture latent value and bolster revenue extraction.
• When full revert protection is applied, searchers bid more aggressively, ensuring complete market clearing and maximum auction revenue, while partial or no protection leads to mixed-strategy participation and reduced efficiency.
• The auction model shows that revert protection on base fees (r1) significantly improves participation, auction revenue, and blockspace efficiency across both L1 and L2 settings.

Maximal Extractable Value (MEV) searchers are specialized agents operating in blockchain systems whose primary objective is to identify, compete for, and extract latent value created by on-chain economic activity—typically by manipulating transaction sequencing within blocks. MEV searchers play pivotal roles in blockspace markets, particularly around decentralized finance (DeFi) protocols, by submitting bids or bundles for arbitrage or other profit opportunities that depend on transaction ordering. Their activities significantly shape auction outcomes, market efficiency, and blockspace utilization, and are highly sensitive to the protocol-level rules governing failed transactions—specifically, whether protocols employ revert protection.

1. Modelling the Searcher’s Strategic Environment

The searcher’s decision environment is formalized as a competitive auction for a single common-value MEV opportunity (payoff $V$, base gas fee $g$), with $N$ searchers each choosing to bid (priority gas fee $b_i$) or abstain. The critical parameterization involves "revert penalties" for failed transactions:

• $r_1$: penalty rate applied to the base gas fee on revert.
• $r_2$: penalty rate applied to the non-base (priority) portion (bid, coinbase transfer, or MEV tax).

This model is parameterized to encompass both L1 scenarios (e.g., Ethereum block builder auctions) and L2 priority ordering/sequencer auctions. Each searcher considers the expected payoff net of revert cost, facing a game-theoretic environment with binary participation and continuous bid choice.

2. Equilibrium Searcher Strategies: The Role of Revert Protection

Pure vs. Mixed-Strategy Behavior

• Full Revert Protection ($r_1 = r_2 = 0$): All searchers are incentivized to submit bids up to the breakeven value $V-g$, producing full competition and complete extraction of the MEV for the auctioneer. The expected revenue for the block builder/sequencer is $V$, with all MEV opportunities always claimed and maximally efficient blockspace usage (at most one submission on-chain).
• Partial/No Revert Protection ($r_1 > 0$ or $r_2 > 0$): No pure-strategy Nash equilibrium exists. Instead, a symmetric mixed-strategy equilibrium arises where searchers randomize both over participation (with probability to abstain $p^*$) and over bid values according to a specific bid distribution:

Abstention probability:

$$p^* = \left( \frac{r_1 g}{V-g + r_1 g} \right)^{1/(N-1)}$$

Cumulative bid distribution:

$$F^*(b) = \frac{1}{1 - p^*}\left( \frac{r_1 g + r_2 b}{V-g-b + r_1 g + r_2 b} \right)^{1/(N-1)} - p^*$$

for $b \in [0, V-g]$.

Searcher Trade-offs

• Increasing $r_1$ or $r_2$ elevates both abstention and conservative bidding, curtailing expected participation and steering searchers towards higher rates of non-competition, resulting in more unexploited opportunities and less aggressive auction dynamics.
• The bid distribution is directly shaped by $r_1$ and $r_2$, but aggregate auction revenue and participation depend only on $r_1$ (the penalty on the base fee).

3. Auction Outcomes: Revenue, Efficiency, and Blockspace Implications

Auction Revenue

• With full revert protection: $\mathbb{E}[\mathsf{Revenue}] = V$.
• Without revert protection: Expected revenue is

$\mathbb{E}[\mathsf{Revenue}] = (1 - (p^*)^N) V$

with nonzero $p^*$ reducing the likelihood of the auction “clearing.” The revenue decomposes into base fee and priority revenue components, but is independent of $r_2$—only $r_1$ matters for total expected revenue.

Market and Blockspace Efficiency

• Clearing probability: $1 - (p^*)^N$, strictly less than 1 without revert protection; MEV is frequently left unclaimed as some opportunities are skipped.
• Blockspace usage:
  • With full revert protection, all $N$ searchers may optimistically submit, but only one winning transaction is included, ensuring optimal blockspace utilization.
  • Under penalties, expected submissions drop below $N$ and all submissions are processed, wasting blockspace relative to the ideal.

Setting	$r_1$	$r_2$	Revenue	Blockspace	Efficiency
L1 Builder/Auction - No RP (priority fee)	$>0$	$>0$	lower	low	low
L1 Builder/Auction - With RP	$0$	$0$	higher	optimal	high
L2 Sequencer - No RP (priority fee)	$>0$	$>0$	lower	low	low
L2 Sequencer - With RP	$0$	$0$	higher	optimal	high
L2 Sequencer + MEV taxes (priority fee refunded)	$>0$	$0$	lower	low	low
L2 Sequencer + MEV taxes + revert protection	$0$	$0$	higher	optimal	high

Comparative Statics

• Increasing $r_1$ decreases revenue, efficiency, and submissions.
• $r_2$ affects strategic mix, but not aggregate outcomes.
• As $N \to \infty$, both revenue and submissions converge to finite limits under any revert penalty.

4. L1 and L2 Application: Generality of the Model

This model encompasses both:

• L1 builder/auction settings (e.g., Ethereum): Revert penalties are present unless mitigated (e.g., via Flashbots Protect).
• L2 sequencer auctions: These may implement revert protection or MEV taxes (priority fees refunded on revert), directly controlling $r_1$ and $r_2$.
• Across L1 and L2, the benefits of revert protection—higher expected revenue, increased efficiency, improved resource utilization—are consistent, with design guidance that applies protocol-wide.

5. Design Guidance and Practical Implications

• Auctioneers (builders/sequencers) are incentivized to implement full revert protection to maximize expected revenue and market efficiency, even if failed transaction fees offer minor immediate gain.
• Revert protection enables maximal participation and more reliable market clearing, directly benefiting DEX price discovery and ecosystem health.
• Spam risk mitigation is necessary: full revert protection increases off-chain/mempool resource usage, though on-chain usage is optimal (one transaction per MEV event; no redundant failed attempts on-chain).
• MEV tax design: Setting $r_2 = 0$ (priority fee refunded upon revert) is supported, as it neither harms aggregate auction revenue nor efficiency.

6. Summary of Closed-Form Results

Metric	Expression
Abstention probability $p^*$	$\left( \frac{r_1 g}{V-g + r_1 g} \right)^{1/(N-1)}$
Expected revenue	$\mathbb{E}[\mathsf{Revenue}] = (1 - (p^*)^N) V$
Market clearing probability	$1 - (p^*)^N$
Expected submissions	$(1 - p^*) N$

These closed-form expressions allow protocol designers and searchers to explicitly compute equilibrium metrics and understand the parameter sensitivities inherent to revert protection mechanisms.

7. Implications for MEV Searchers

Revert protection unambiguously shifts the competitive environment for MEV searchers:

• With revert protection: Searchers optimally bid at full intensity for every opportunity, ensuring all value is competitively extracted for the benefit of the auctioneer (block builder/sequencer) and eliminating the deadweight loss associated with risk of failed transaction penalties.
• Without revert protection: Rational searchers must randomize both in bidding and participation, lowering expected participation rate, reducing expected auction revenue, and increasing the probability that arbitrage and related MEV opportunities remain unclaimed—degrading market efficiency and liquidity.
• Searchers have no incentive to over-participate or submit spam if protocol-level enforcement and off-chain rate controls exist, further reinforcing efficient equilibria.

---

Revert protection transforms the strategic calculus of MEV searchers by removing the downside risk of failed transactions, thereby maximizing blockspace and market clearing efficiency. These findings, which admit closed-form, parameterized analysis, generalize across both L1 and L2 blockchains and provide explicit rationales for protocol and auction designers to adopt revert protection wherever spam can be practically managed.