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Enrich M3 sim sub-specs with 11 discovered frameworks and 360:1 minimum speed
- M3 hub: add L3 invariant (360:1 minimum sim speed), six-horizon time table - M3a: add Heston stochastic vol, rough volatility (fBM), HMM regime detection, DCC-GARCH copula, jump-diffusion; six-horizon mapping - M3b: add Hegselmann-Krause bounded confidence, complex contagion, bandit- replicator hybrid, MFG (HJB+FP), pump-and-dump 3-type ABM; six-horizon mapping - M3c: add six-horizon time table - M3d: add Kolokoltsov adversarial (non-linear FP + WENO), DSMFG bilevel optimization, cross-chain adversarial arbitrage; six-horizon mapping - M3e: add kinked lending rate model, DeXposure inter-protocol credit network, composable yield optimizer; six-horizon mapping - M3f: add MFG for validator populations, six-horizon time table - M3g: add Almgren-Chriss optimal execution, six-horizon mapping - CLAUDE.md: add subagent productivity note Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
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Claude
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# M3d — MEV & adversarial extraction sims
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## 1. Component
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Maximal Extractable Value simulation: models **transaction ordering as an optimization problem**,
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**Priority Gas Auctions (PGA) as all-pay auctions**, and **block building as a multidimensional
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knapsack problem**. Pops here are **searcher bots, block builders, and validators** competing for
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extractable value. Grounded in ACM MEV game theory [3] and knapsack auction literature [4,5].
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Maximal Extractable Value and adversarial simulation: models **transaction ordering as an
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optimization problem**, **Priority Gas Auctions (PGA) as all-pay auctions**, **block building as a
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multidimensional knapsack problem**, **cross-chain adversarial arbitrage**, and **Dynamic
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Stackelberg Mean-Field Games (DSMFG) for protocol-level adversarial policy**. Pops here are
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**searcher bots, block builders, validators, cross-chain arbitrageurs, and adversarial
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manipulators** competing for extractable value across **six concurrent time horizons**.
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Grounded in ACM MEV game theory [3], knapsack auction literature [4,5], Kolokoltsov adversarial
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dynamics (non-linear Fokker-Planck with WENO shock capturing), and DSMFG bilevel optimization
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(leader policy + follower MFG equilibrium).
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## 2. Status / certainty
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DESIGN-FIRST · ABSENT. PGA-as-all-pay-auction model C4 (ACM [3]); knapsack formulation C4
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(Cornell [4,5]); simulation parameterization C1.
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DESIGN-FIRST · ABSENT. PGA-as-all-pay-auction C4 (ACM [3]); knapsack formulation C4 (Cornell
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[4,5]); cross-chain arbitrage C4 (ACM SIGMETRICS 2025, 5.5x growth since Dencun); DSMFG bilevel
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optimization C3 (emerging — SMFRL solvers); Kolokoltsov adversarial C3 (non-linear Fokker-Planck;
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WENO discretization established but crypto application novel). Parameterization C1.
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## 3. Language & location
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TBD · `src/economy/sims/mev/`. Needs combinatorial optimization (for knapsack) and continuous-time
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auction modeling. Python (PuLP/OR-Tools for optimization), Rust, or Julia.
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TBD · `src/economy/sims/mev/`. Needs combinatorial optimization (PuLP/OR-Tools for knapsack),
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continuous-time auction modeling, PDE solvers (WENO for shock-capturing in adversarial dynamics),
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and bilevel optimization (DSMFG). Python, Rust, or Julia.
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## 4. Does / does-not
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- **Does:** simulate Priority Gas Auctions where multiple searcher bots compete for the same
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arbitrage opportunity $V$ by bidding gas fees $g$ in a continuous-time all-pay auction; model
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block building as a multidimensional knapsack problem (scarce block space, heterogeneous
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transaction values/sizes); simulate endogenous selection cutoffs under paid-priority ordering;
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predict MEV exposure for proposed trades; produce bounded predictions on extraction risk and
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optimal gas strategies.
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- **Does-not:** extract MEV itself (this is a simulator, not a searcher); model AMM mechanics
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(M3c handles pool math); model social dynamics (M3b).
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model **cross-chain adversarial arbitrage** with inventory vs. bridge execution trade-off:
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$\pi_{\text{inv}} = (P_{\text{src}} - P_{\text{dst}} - \text{slippage} - \text{gas}) \times q$
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vs. $\pi_{\text{bridge}} = (P_{\text{src}} - P_{\text{dst}} - \text{fee} -
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\text{depreciation}(\Delta t)) \times q$ where bridge latency $\Delta t \approx 242$s vs.
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inventory $\Delta t \approx 9$s; solve **Dynamic Stackelberg MFG** for adversarial policy
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design — bilevel optimization where a leader (protocol/regulator) sets policy and followers
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(searchers) respond as an MFG equilibrium: the leader solves
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$\min_\alpha J_L(\alpha, m^*(\alpha))$ subject to $m^*(\alpha)$ being the MFG Nash equilibrium
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of followers under policy $\alpha$; model **Kolokoltsov adversarial dynamics** via non-linear
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Fokker-Planck: $\partial_t m + \nabla \cdot (b(x,m)m) = \frac{1}{2}\nabla^2(\sigma^2 m)$
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with WENO shock-capturing for discontinuous adversarial strategies; predict MEV exposure for
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proposed trades; produce bounded predictions on extraction risk across all six time horizons.
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- **Does-not:** extract MEV itself (simulator, not a searcher); model AMM pool math (M3c);
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model social dynamics (M3b); execute cross-chain bridges (Marketplace does).
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## 5. Interface contract
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- Implements `query(PredictionQuery) -> BoundedPrediction` per M3 hub.
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- **Output bounds:** extraction probability ranges and gas cost intervals.
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Example: `{ value: 0.23, lower_bound: 0.11, upper_bound: 0.38, confidence: 0.80,
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time_horizon: "next_block", sim_type: "mev_adversarial" }` — probability this trade gets
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sandwiched.
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Example: `{ value: 14.7, lower_bound: 8.2, upper_bound: 22.5, confidence: 0.75,
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time_horizon: "next_block", sim_type: "mev_adversarial" }` — optimal gas bid (gwei) for
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a given opportunity.
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- **Output bounds:** extraction probability ranges, gas cost intervals, cross-chain profit
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bounds, DSMFG equilibrium stability ranges.
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- **Time-horizon mapping** (all run concurrently, ≥ 360:1 speed):
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| Horizon | Primary models | Update cadence |
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|---------|---------------|----------------|
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| Tick–hourly | PGA auctions, sandwich detection, cross-chain arb | Every block |
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| Daily | Knapsack builder strategies, MEV landscape | Hourly roll |
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| Weekly | Searcher population dynamics, cross-chain flow patterns | Daily roll |
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| Monthly | DSMFG policy equilibria, adversarial strategy evolution | Weekly roll |
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| Annual | Kolokoltsov adversarial long-run dynamics | Monthly roll |
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| 5-year | Structural MEV regime shifts, protocol-level policy effects | Quarterly roll |
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- Examples:
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`{ value: 0.23, lower_bound: 0.11, upper_bound: 0.38, confidence: 0.80,
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time_horizon: "next_block", sim_type: "mev_adversarial" }` — sandwich probability.
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`{ value: 14.7, lower_bound: 8.2, upper_bound: 22.5, confidence: 0.75,
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time_horizon: "next_block", sim_type: "mev_adversarial" }` — optimal gas bid (gwei).
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`{ value: 0.034, lower_bound: 0.018, upper_bound: 0.052, confidence: 0.82,
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time_horizon: "1h", sim_type: "mev_adversarial" }` — cross-chain arb profit (ETH).
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- **Prediction types:** `sandwich_probability`, `frontrun_risk`, `optimal_gas_bid`,
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`block_inclusion_probability`, `mev_exposure`.
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- Calibration: ingests `on_chain_event` (mempool-like data) and `price_tick` from M2.
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`block_inclusion_probability`, `mev_exposure`, `cross_chain_arb_profit`,
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`adversarial_policy_stability`, `searcher_population_shift`.
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- Calibration: ingests `on_chain_event` (mempool-like data), `price_tick`, and cross-chain
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bridge state from M2.
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## 6. Dependencies & stubs
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- M2 Data Feeds — on-chain events and gas data; *stub:* canned mempool snapshots.
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- M2 Data Feeds — on-chain events, gas data, cross-chain state; *stub:* canned snapshots.
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- M3 Sims hub — lifecycle management; *stub:* manual init.
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- M3c AMM sims — pool state for arbitrage opportunity detection; *stub:* fixed pool state.
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## 7. Invariants / laws
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- **L1 (C4):** PGA is modeled as an **all-pay auction** — all bidders pay their gas whether they
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- **L1 (C5):** PGA is modeled as an **all-pay auction** — all bidders pay their gas whether they
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win or not. The sim must capture this cost structure (not winner-pays-only).
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- **L2 (C4):** block building is a **knapsack problem, not a queue** — builders optimize for
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- **L2 (C5):** block building is a **knapsack problem, not a queue** — builders optimize for
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total extracted value subject to gas limit constraints, not first-come-first-served.
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- **L3 (C3):** MEV exposure predictions are **pre-trade** — traders query this sim *before*
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- **L3 (C4):** MEV exposure predictions are **pre-trade** — traders query this sim *before*
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submitting to the Marketplace to understand their extraction risk.
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- **L4 (C4):** cross-chain arb models **both execution paths** — inventory (fast, capital-
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intensive) and bridge (slow, capital-light) — never assumes one dominates.
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- **L5 (C3):** DSMFG solutions are **bilevel** — the leader's optimal policy depends on the
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followers' MFG equilibrium, which itself depends on the leader's policy. Fixed-point iteration
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or SMFRL solvers required.
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## 8. Build steps
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1. Implement the PGA all-pay auction model (N searchers, opportunity value V, gas bids).
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2. Implement the block-building knapsack solver.
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3. Add sandwich/frontrun detection heuristics.
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4. Wire M2 on-chain data → calibration of searcher population and gas dynamics.
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5. Wire pre-trade query interface for Traders.
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4. Implement cross-chain arb model (inventory vs. bridge, latency, MEV exposure).
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5. Implement Kolokoltsov non-linear Fokker-Planck with WENO discretization.
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6. Implement DSMFG bilevel solver (leader policy + follower MFG equilibrium).
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7. Wire M2 on-chain + cross-chain data → calibration.
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8. Wire pre-trade query interface for Traders.
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## 9. Tests
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All-pay: losing bidders still pay gas cost. Knapsack: builder selects optimal transaction set
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under gas limit. Sandwich: known sandwich-vulnerable trade flagged; non-vulnerable trade clear.
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Bounds: all outputs bounded. Pre-trade: query does not submit any transaction.
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Cross-chain: inventory path preferred when latency advantage exceeds capital cost. DSMFG: leader
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policy converges to fixed point with follower equilibrium. Kolokoltsov: WENO captures shock
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discontinuities in adversarial strategy distribution. Bounds: all outputs bounded. Pre-trade:
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query does not submit any transaction. Speed: sim advances ≥ 360:1.
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## 10. Open items
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- Mempool data access (public mempool? private order flow?).
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- Which MEV types to model initially (sandwich, backrun, liquidation, JIT?).
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- Multi-block MEV (cross-block extraction strategies).
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- Integration with M3c (arbitrage opportunities arise from AMM pool state).
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- DSMFG solver choice (SMFRL? fictitious play? direct bilevel optimization?).
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- WENO order for Kolokoltsov (3rd? 5th? tradeoff with compute budget).
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- Which L2s/bridges to model for cross-chain (Arbitrum? Optimism? Base?).
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