Maximal Extractable Value (MEV) in DeFi

• Maximal Extractable Value (MEV) is defined as the additional profit privileged blockchain actors extract by strategically reordering, inserting, or censoring transactions.
• MEV encompasses various strategies including sandwich attacks, front-running, and arbitrage, highlighting its deep roots in game-theoretic models.
• Current research focuses on mitigation techniques such as fair ordering, encrypted mempools, and proposer-builder separation to balance efficiency and decentralization.

Maximal Extractable Value (MEV) is a central concept in understanding the power and incentive structure of contemporary blockchain and decentralized finance (DeFi) systems. MEV describes the maximum profit attainable by privileged actors—including miners, validators, block builders, and searchers—through strategic manipulation of transaction ordering, inclusion, and censorship within a block. This extractable value is not limited to transaction fees, but extends to profits from front-running, back-running, sandwich attacks, and a range of inter-transaction market manipulations. The theoretical foundations, game-theoretic properties, detection approaches, and mitigation techniques of MEV are the subject of active inquiry and formalization in decentralized finance research.

1. Formal Definition and Modeling of MEV

MEV is defined as the surplus value, above standard block rewards or transaction fees, that an agent with transaction ordering control can capture by reordering, inserting, or censoring transactions within a block. In rigorous terms, given a blockchain state $st$, a set of candidate transactions, and a privileged player $P$, the maximal extractable value is:

$$\text{MEV}(P, st) = \max \left\{ b(P, st') - b(P, st) \mid st' = \mathcal{O}(st, \mathcal{T}) \right\}$$

where $b(P, st)$ is the balance of $P$ in state $st$, $\mathcal{T}$ is a set of transactions, and $\mathcal{O}$ denotes all possible execution orderings/permutations of those transactions (Mazorra et al., 2022, Guo, 2023, Hughes, 2023).

This definition is embedded in algorithmic and market-theoretic frameworks: for example, profit-maximizing strategies of MEV searchers can be formally posed as combinatorial or knapsack optimization problems, subject to block resource constraints and transaction dependencies (Mazorra et al., 2022, Mohan et al., 28 Mar 2024).

In the context of constant function market makers (CFMMs), including Uniswap-like AMMs, the MEV extractable via “sandwich attacks” or arbitrage is expressed by the profit function using the CFMM’s forward exchange function $G(\Delta)$ and related slippage and reserve parameters (Kulkarni et al., 2022):

$$G(\Delta + \Delta^{\text{sand}}) - G(\Delta^{\text{sand}}) = (1 - \eta) G(\Delta)$$

where $\Delta$ is the trade size and $\eta$ is the user's slippage limit.

2. Game-Theoretic Analysis and Systemic Metrics

Extracting MEV is inherently game-theoretic, involving the interplay between block producers, searchers, users, and sometimes complex auction or market-building mechanisms. Two principal dimensions of MEV are:

• Routing MEV: Arising when trades are routed through a network of CFMMs; comparison is made between optimal (planner-driven) and Nash (selfish agent-driven) routing. Sandwich attacks can alter equilibrium properties, sometimes counterintuitively improving aggregate outputs due to congestion reallocation (Kulkarni et al., 2022).
• Reordering MEV: Emerges from permutations of user trade orderings within a block. The "cost of feudalism" (CoF) metric is defined as:

$$\text{CoF}(T_n) = \frac{\max_{\pi \in S_n} \max_i |\text{PNL}_{\pi(i)} - \text{PNL}_i|}{\operatorname{avg}_i |\text{PNL}_i|},$$

where $\text{PNL}_i$ is the unexpected profit/loss extracted by the attacker via trade $i$ under permutation $\pi$. Under locality assumptions for sandwich attacks, the worst-case CoF scales as $O(\log n)$ in the number of user trades.

A closely related systemic efficiency metric is the Price of Anarchy (PoA) or, in MEV-specific literature, the Price of MEV (PoMEV) (Mazorra et al., 2022):

$$\text{PoA} = \frac{\text{Optimal Routing Output (with sandwiching)}}{\text{Selfish Nash Routing Output (with sandwiching)}}$$

$$\text{PoMEV} = \frac{\max_{S \in SNE(\mathcal{G})} C(S)}{\min_{S \in NS_C} C(S)}$$

where $SNE(\mathcal{G})$ is the set of Sybil-resistant Nash equilibria and $C(S)$ captures blockspace or resource cost.

Significantly, if sandwich attack impacts are localized, the PoA in CFMM routing remains constant independent of network size, providing a theoretical bound on the social inefficiency introduced by MEV-extracting strategies (Kulkarni et al., 2022).

3. Invariance, Structural Properties, and Limitations

Rigorous formal modeling has established that, under certain natural conditions for AMMs (frictionlessness, path-independence, and efficient liquidity), the total MEV—specifically arbitrage MEV—is invariant under changes to both the transaction ordering mechanism and block times (Guo, 2023). For each block, this means:

$$\text{MEV}_{path}(B) = \sup_{S \text{ competitive}} \text{PNL}(S) = \text{PNL}^*(S_0)$$

where $S_0$ is the simple arbitrage strategy that always brings the pool back to its no-arbitrage state, and the result holds for both deterministic and subdivided block intervals.

A critical implication is that MEV cannot be fundamentally “increased” or “decreased” by modifying transaction sequencing or block frequency; such changes only redistribute MEV among agents or affect its realization timing. Protocol designers cannot reduce the total extractable value inherent in on-chain liquidity solely via reordering constraints—they must instead address the mechanisms that enable harmful MEV manifestations (Guo, 2023, Chitra, 2023).

4. Detection and Classification in DeFi Systems

Recognizing concrete MEV activities is technically challenging because attacks (e.g., sandwich, front/back-running, time-bandit) are often subtle and involve complex transaction interleaving. Recent detection approaches include:

• Heuristic methods: These scan for transaction patterns (e.g., cyclic swaps, token transfers, sequencings indicative of front/back-running) and use transaction window analyses, graph search algorithms, and comparison of input/output values (Chi et al., 28 May 2024, Materwala et al., 22 Oct 2024).
• Machine Learning/GNN approaches: ABI-free graph neural network classifiers have been introduced—such as ArbiNet—which leverage only transfer graphs and structural features, bypassing the need for purpose-built ABI decoding (Park et al., 2023). These increase detection recall and adapt to evolving DeFi protocols.

MEV transaction taxonomies now distinguish between value-diverting (e.g., suppression, replacement front-running, sandwich) and value-creating (e.g., arbitrage, beneficial liquidations) transactions, with further subcategories for burger sandwiches, dagwood attacks, burn-and-mint arbitrages, and cyclic multi-address arbitrages (Materwala et al., 22 Oct 2024).

No single detection scheme is universally effective. Heuristic detection is limited by evolving attack patterns, while ML models may struggle to generalize across fast-changing DeFi environments, rendering MEV incidence estimates as lower bounds (Materwala et al., 22 Oct 2024).

5. Mitigation, Protocol Design, and Ongoing Countermeasures

A spectrum of MEV mitigation strategies has been systematically surveyed:

Transaction Sequencing Approaches

• Fair Ordering: Techniques such as receive-order fairness (e.g., Aequitas, Themis, Wendy), TimeBoost scoring ($S(t_i, b_i) = \pi(b_i) - t_i$), and batch auctions constrain sequencing to reduce reordering and front-running. Both single sequencer and decentralized (committee-based) variants exist, with accompanying communication and complexity trade-offs (Yang et al., 2022, Alipanahloo et al., 28 Jul 2024).
• Encrypted Mempools and Commit–Reveal: Transaction content is hidden from block builders/sequencers until the order is fixed via threshold encryption, TEEs, or time-lock puzzles. Networks like Fino on DAG-based BFT and systems leveraging BlindPerm for shuffling provide examples (Malkhi et al., 2022, Alipanahloo et al., 28 Jul 2024).

Application-level and DApp Design

• Batch Auctions and Commit–Reveal Protocols: DeFi applications may shift to batch auctions (e.g., CowSwap, FairTraDEX, FairMM) or encrypted commit–reveal order matching to reduce exposure to sandwich and front-running attacks (Yang et al., 2022, Alipanahloo et al., 28 Jul 2024).

Proposer-Builder Separation (PBS)

• PBS decouples block proposal and construction (as with MEV-Boost), reducing direct validator extraction but potentially reintroducing centralization via dominant block builders or relays (Ramos et al., 2023, Yang et al., 2022, Alipanahloo et al., 28 Jul 2024).

Cryptoeconomic and Auction Mechanisms

• Knapsack Auctions: Block builders solve variants of the knapsack problem, sometimes using greedy or second/third price auctions for block inclusion. The challenge lies in reconciling revenue maximization with allocative efficiency and truthfulness, particularly in the presence of positional/ordering effects (Mohan et al., 28 Mar 2024).
• MEV-Sharing and Rebates: Dynamic MEV extraction rates (e.g., via EIP-1559 analogs) have been proposed to balance block producer and user incentives. Formal Shapley-value-based rebates or Sybil-resistant distributions may be implemented for LPs or DApp users (Mazorra et al., 2023, Braga et al., 24 Feb 2024).
• Execution Tickets: Advanced protocols such as Ethereum Execution Tickets internalize MEV as a protocol asset, making it claimable via auctioned, transferable tickets whose market cap represents the present value of future execution layer rewards (Burian, 5 Mar 2024).

6. Fundamental Limitations and Theoretical Boundaries

Recent formalism introduces information-theoretic and Fourier-analytic perspectives:

• Information-theoretic MEV: Any non-trivial blockchain that supports expressive user transactions creates entropy (“disorder”), which is reduced (good MEV) or increased (bad MEV) by agents. Controlling MEV thus trades off with limiting user expressibility (Hughes, 2023).
• Uncertainty Principles for MEV: The complexity (“degree”) of payoff functions (e.g., for liquidations, which are highly non-smooth) is fundamentally at odds with the restrictiveness of ordering mechanisms. A Nyquist–Shannon-style tradeoff quantifies how no single sequencing rule can simultaneously prevent MEV for all types of payoffs—application specificity in sequencing rules is required (Chitra, 2023).

7. Research Directions and Open Problems

Despite a rich variety of countermeasures, no approach singularly eliminates MEV for all attack surfaces or transaction classes (Materwala et al., 22 Oct 2024, Yang et al., 2022). The space is characterized by fundamental trilemmas—involving trade-offs between efficiency, decentralization, expressibility, and exploitability. New forms of MEV (emerging in Layer-2/rollup ecosystems and through increasingly complex DeFi strategies) require generalized, adaptive mitigation protocols and continuous surveillance.

A neutral assessment is that systemic improvements—spanning protocol-level, application-level, and cryptoeconomic layers—are needed to curb the most harmful aspects of MEV while preserving legitimate value-creating activities and network decentralization. Ongoing research emphasizes hybrid and standardized approaches, detailed auditing and monitoring systems, and robust auction and incentive designs that promote fairness without sacrificing performance.

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Table: Summary of Major MEV Mitigation Approaches

Approach	Principle	Limitations
Fair Ordering	Enforce arrival- or batch-based sequencing; mitigate reordering attacks	Vulnerable to timestamp manipulation; may increase latency (Yang et al., 2022, Alipanahloo et al., 28 Jul 2024)
Encrypted/Commit–Reveal Pools	Hide transaction content with threshold or time-lock encryption, TEEs	High complexity, latency, or centralization risk (Malkhi et al., 2022, Alipanahloo et al., 28 Jul 2024)
Proposer-Builder Separation	Separate block proposal/construction, introduce marketplace of builders	Risk of builder or relay centralization (Ramos et al., 2023, Yang et al., 2022)
Application Layer Redesign	Use batch auctions, commit–reveal, or ticketing in DApps	Requires contract updates, not always feasible (Yang et al., 2022, Alipanahloo et al., 28 Jul 2024)
MEV Rebates/Auction Mechanisms	Redistribute extracted MEV via Sybil-proof or dynamic allocations and ticket systems	Complexity, exploitation by sybil identities, new incentive balance required (Mazorra et al., 2023, Braga et al., 24 Feb 2024, Burian, 5 Mar 2024)

References here denote arXiv identifiers for the most central underlying source material: (Kulkarni et al., 2022, Mazorra et al., 2022, Guo, 2023, Park et al., 2023, Mazorra et al., 2023, Yang et al., 2022, Chitra, 2023, Hughes, 2023, Materwala et al., 22 Oct 2024, Braga et al., 24 Feb 2024, Mohan et al., 28 Mar 2024, Burian, 5 Mar 2024, Alipanahloo et al., 28 Jul 2024).

This construction reflects the current state of research on MEV, its detection and mitigation challenges, and foundational theoretical properties in decentralized finance systems.