MEV Strategies in Blockchain Protocols

• MEV Strategies are a set of mechanisms that exploit blockchain transaction ordering through arbitrage, sandwich, and auctioning techniques.
• They use rigorous game-theoretic models and cooperative mechanisms to balance incentives and mitigate abusive extraction behaviors.
• Formal studies certify optimal strategies and define algorithmic bounds critical for protecting protocol integrity and ensuring fair user value.

Maximal Extractable Value (MEV) Strategies encompass the set of mechanisms, game-theoretic models, and market designs by which validators, block producers, and searchers exploit transaction ordering, inclusion, bundling, or censorship to realize additional value in blockchain ecosystems beyond standard block rewards and fees. Rigorous study of MEV strategies reveals a spectrum of extractive behaviors, complex incentive structures, and advanced mitigation schemes, especially as decentralized finance has elevated the practical and theoretical significance of MEV across protocols, from automated market makers (AMMs) to combinatorial auctions for blockspace (Mazorra et al., 2023, Bartoletti et al., 16 Oct 2025, Li et al., 2023, Chi et al., 2024).

1. Formal Model of MEV Extraction

MEV arises within a system consisting of multiple agents: users holding bundles of transactions, builders/validators sequencing and ordering blocks, and (possibly) specialized searchers. The fundamental mechanism is as follows: users submit transactions into a public or private mempool. Builders select and order subsets of these transactions to maximize a value function—specifically, the difference in their utility or token holdings after block assembly, after accounting for gas costs. Mathematically,

$$\max_{B \subseteq \mathcal{C}_P}\ \Delta b(P;\ \mathrm{st} \oplus B,\, \mathrm{st})$$

for some builder $P$ with local candidate set $\mathcal{C}_P$ and state $\mathrm{st}$ (Mazorra et al., 2023). The chosen ordering and inclusion define the MEV opportunity, exploiting dependencies across user transactions, external pricing, or DEX state.

Key types of MEV strategies, systematized in high-impact surveys, include:

• Arbitrage: Cyclic swaps across DEXes or assets exploiting price discrepancies.
• Sandwich Attacks: Bracketing a victim's trade to capitalize on induced slippage.
• Back-running: Sequencing to capture post-trade arbitrage or liquidation.
• Orderflow Auctions: Setting up markets to bid for blockspace or transaction placement.
• Front-running/Displacement/Replacement: Preemptively inserting transactions to capture intended user profit (Materwala et al., 2024).

2. Mechanism Design and Cooperative Game Theory for Rebates

A rigorous approach to mitigating MEV rent-extraction and distributing value amongst honest users leverages cooperative game-theoretic solution concepts. Define $v:2^N\to\mathbb{R}_{\geq0}$ as the value generated by a coalition $S$ of players (transactions or liquidity providers). A rebate operator $\varphi$ assigns a payoff vector $\varphi(v)\in \mathbb{R}^N_+$, guided by properties such as:

• Efficiency (E): $\sum_i \varphi_i(v) = v(N)$.
• Symmetry (S): Interchangeable agents receive equal rebates.
• Sybil-proofness (SP): Identity splitting or extension does not increase aggregate rebate.
• No-deficit (ND): $\sum_i\varphi_i(v)\leq v(N)$.

The Shapley value provides the uniquely efficient, symmetric, additive solution, but fails Sybil-proofness: splitting an identity increases payout (Mazorra et al., 2023). In response, the Banzhaf value, normalized for SP-optimality, is the unique solution featuring symmetry, additivity, and strong SP, but it can violate no-deficit in pathological cases.

A worst-case optimal prior-free operator $\psi$ is constructed to maximize the minimum user rebate under Sybil-proofness and no-deficit, achieving (for $n$ players) a total rebate no less than $v(N)/2^{n-1}$, which is tight (Mazorra et al., 2023).

Operator	Efficiency	Symmetry	SP	ND	Additivity
Shapley	Yes	Yes	No	Yes	Yes
Banzhaf	No	Yes	Yes	Various	Yes
$\psi$	No	Yes	Yes	Yes	No

3. MEV Strategies in Combinatorial Auctions and AMMs

MEV extraction is particularly acute in settings of combinatorial orderflow auctions and automated market makers (AMMs), such as CFMMs:

• Orderflow Auctions: Each transaction is modeled as a single-parameter bid for blockspace; allocation via Myerson’s lemma yields truthful and individually rational mechanisms, but MEV-aware allocations that include the builder's MEV cannot guarantee Sybil-proofness with positive worst-case welfare when conflicts arise (Mazorra et al., 2023).
• AMMs (CFMMs): Arbitrage opportunities across pool states are modeled as cooperative games among liquidity providers (LPs). If the AMM trading function is 1-homogeneous, then the Shapley value coincides with a pro-rata split of arbitrage value, but again Sybil-proofness fails without a strongly robust operator such as $\psi$ (Mazorra et al., 2023).

4. Optimality, Sybil Attacks, and Complexity

The core impossibility theorem is a Sybil/Collusion/Symmetry trilemma: no nontrivial operator can be symmetric, fully collusion-proof, and generally Sybil-resistant. Specifically, the Shapley value is not Sybil-proof. Upper bounds show that symmetric Sybil-proof operators pay at most $n/2^{n-1}$ fractions of the joint value. The Banzhaf value is characterized as the unique symmetric, additive, Sybil-proof optimal operator, and the $\psi$ operator is worst-case prior-free optimal among all SP, ND, symmetric, monotonic operators (Mazorra et al., 2023).

Computing MEV optimally (even for local bundle maximization) is generally NP-hard due to the combinatorial interaction among transaction effects.

5. Formal Certification and Algorithmic Bounds

Recently, formal methods have been employed to not only specify but certify the optimality of concrete MEV strategies. “Certifying optimal MEV strategies with Lean” (Bartoletti et al., 16 Oct 2025) introduces a mechanized, theorem-proving framework to verify upper bounds (and tightness) of MEV extraction for DeFi protocols, notably sandwich attacks on AMMs.

• Invariant/Guess Pattern: One defines an invariant over system state and a guess for extractable MEV, then proves coherence (constructing an explicit trace achieving the guess) and a soundness lemma (no single adversarial move can exceed the guess).
• Case Study: Proves, machine-verified, that the canonical front-run–victim–back-run sequence in an AMM is optimal for the adversary when mempool holds only one honest swap.

This approach allows protocol designers to rigorously check and evolve design rules (e.g., restrict mempool, impose swap fees) and certify their impact on MEV bounds.

6. Sequencing Rules, User Impact, and Welfare Results

Sequencing rules—such as the Greedy Sequencing Rule (GSR)—drastically affect the possible MEV. Under GSR, which enforces that the execution price in a block alternates around the initial price, classical sandwich attacks are obviated because an attacker cannot perform both legs (front and back-run) around a user transaction. In zero-fee regimes, miner-optimal MEV extraction strategies can be computed in polynomial time and benefit all users: every user transaction is executed, and each user receives at least their single-block baseline profit. With a nonzero fee, however, the block MEV maximization becomes NP-hard (Li et al., 2023).

7. Strategic and Protocol Implications

The formalization and analysis of MEV strategies highlight a set of core protocol and economic implications:

• Sybil-robustness and Fair Rebates: No symmetric, efficient, additive, and Sybil-proof rebate exists; thus, robust mechanisms must accept a trade-off between efficiency and Sybil-robustness.
• Auction Design Limits: In blockspace and AMM allocation, Sybil-proofness fundamentally restricts worst-case user welfare, and full truthfulness cannot be achieved when conflicting bundles are present.
• Computational Tractability: Only in certain cases (e.g., no-fee GSR) can optimal MEV extraction be computed efficiently; otherwise, searchers and protocols must rely on approximation or heuristic mechanisms.
• Tight Protocol Analyses: Certified upper bounds on MEV make it possible to claim that a protocol is “tight,” i.e., that no adversary can do better than the known optimal attack (Bartoletti et al., 16 Oct 2025).
• Design Guidance: Restricting adversarial transaction insertion, minimizing mempool size, or using robust fee and commitment schemes allows protocols to raise provable soundness bounds against MEV attacks.

• (Mazorra et al., 2023) Towards Optimal Prior-Free Permissionless Rebate Mechanisms, with applications to Automated Market Makers & Combinatorial Orderflow Auctions
• (Bartoletti et al., 16 Oct 2025) Certifying optimal MEV strategies with Lean
• (Li et al., 2023) MEV Makes Everyone Happy under Greedy Sequencing Rule
• (Chi et al., 2024) Remeasuring the Arbitrage and Sandwich Attacks of Maximal Extractable Value in Ethereum