sica-fondt/core/docs/plans/M3d-mev-adversarial-sims.md

M3d — MEV & adversarial extraction sims

1. Component

Maximal Extractable Value and adversarial simulation: models transaction ordering as an optimization problem, Priority Gas Auctions (PGA) as all-pay auctions, block building as a multidimensional knapsack problem, cross-chain adversarial arbitrage, and Dynamic Stackelberg Mean-Field Games (DSMFG) for protocol-level adversarial policy. Pops here are searcher bots, block builders, validators, cross-chain arbitrageurs, and adversarial manipulators competing for extractable value across six concurrent time horizons.

Grounded in ACM MEV game theory [3], knapsack auction literature [4,5], Kolokoltsov adversarial dynamics (non-linear Fokker-Planck with WENO shock capturing), and DSMFG bilevel optimization (leader policy + follower MFG equilibrium).

2. Status / certainty

DESIGN-FIRST · ABSENT. PGA-as-all-pay-auction C4 (ACM [3]); knapsack formulation C4 (Cornell [4,5]); cross-chain arbitrage C4 (ACM SIGMETRICS 2025, 5.5x growth since Dencun); DSMFG bilevel optimization C3 (emerging — SMFRL solvers); Kolokoltsov adversarial C3 (non-linear Fokker-Planck; WENO discretization established but crypto application novel). Parameterization C1.

3. Language & location

TBD · src/economy/sims/mev/. Needs combinatorial optimization (OR-Tools for knapsack), continuous-time auction modeling, PDE solvers (WENO for shock-capturing in adversarial dynamics), and bilevel optimization (DSMFG). Julia, Fortran, Octave, or Zig.

4. Does / does-not

• Does: simulate Priority Gas Auctions where multiple searcher bots compete for the same arbitrage opportunity V by bidding gas fees g in a continuous-time all-pay auction; model block building as a multidimensional knapsack problem (scarce block space, heterogeneous transaction values/sizes); simulate endogenous selection cutoffs under paid-priority ordering; model cross-chain adversarial arbitrage with inventory vs. bridge execution trade-off: \pi_{\text{inv}} = (P_{\text{src}} - P_{\text{dst}} - \text{slippage} - \text{gas}) \times q vs. $\pi_{\text{bridge}} = (P_{\text{src}} - P_{\text{dst}} - \text{fee} - \text{depreciation}(\Delta t)) \times q$ where bridge latency $\Delta t \approx 242$s vs. inventory $\Delta t \approx 9$s; solve Dynamic Stackelberg MFG for adversarial policy design — bilevel optimization where a leader (protocol/regulator) sets policy and followers (searchers) respond as an MFG equilibrium: the leader solves \min_\alpha J_L(\alpha, m^*(\alpha)) subject to m^*(\alpha) being the MFG Nash equilibrium of followers under policy \alpha; model Kolokoltsov adversarial dynamics via non-linear Fokker-Planck: \partial_t m + \nabla \cdot (b(x,m)m) = \frac{1}{2}\nabla^2(\sigma^2 m) with WENO shock-capturing for discontinuous adversarial strategies; predict MEV exposure for proposed trades; produce bounded predictions on extraction risk across all six time horizons.
• Does-not: extract MEV itself (simulator, not a searcher); model AMM pool math (M3c); model social dynamics (M3b); execute cross-chain bridges (Marketplace does).

5. Interface contract

• Implements query(PredictionQuery) -> BoundedPrediction per M3 hub.
• Output bounds: extraction probability ranges, gas cost intervals, cross-chain profit bounds, DSMFG equilibrium stability ranges.
• Time-horizon mapping (all run concurrently, tick-advanced, 90:1 (1s wall = 90s sim)):

  Horizon	Primary models	Update cadence
  Tick–hourly	PGA auctions, sandwich detection, cross-chain arb	Every block
  Daily	Knapsack builder strategies, MEV landscape	Hourly roll
  Weekly	Searcher population dynamics, cross-chain flow patterns	Daily roll
  Monthly	DSMFG policy equilibria, adversarial strategy evolution	Weekly roll
  Annual	Kolokoltsov adversarial long-run dynamics	Monthly roll
  5-year	Structural MEV regime shifts, protocol-level policy effects	Quarterly roll

• Examples: { value: 0.23, lower_bound: 0.11, upper_bound: 0.38, confidence: 8.00, time_horizon: "next_block", sim_type: "mev_adversarial" } — sandwich probability. { value: 14.7, lower_bound: 8.2, upper_bound: 22.5, confidence: 7.50, time_horizon: "next_block", sim_type: "mev_adversarial" } — optimal gas bid (gwei). { value: 0.034, lower_bound: 0.018, upper_bound: 0.052, confidence: 8.20, time_horizon: "1h", sim_type: "mev_adversarial" } — cross-chain arb profit (ETH).
• Prediction types: sandwich_probability, frontrun_risk, optimal_gas_bid, block_inclusion_probability, mev_exposure, cross_chain_arb_profit, adversarial_policy_stability, searcher_population_shift.
• Calibration: ingests on_chain_event (mempool-like data), price_tick, and cross-chain bridge state from M2.

6. Dependencies & stubs

• M2 Data Feeds — on-chain events, gas data, cross-chain state; stub: canned snapshots.
• M3 Sims hub — lifecycle management; stub: manual init.
• M3c AMM sims — pool state for arbitrage opportunity detection; stub: fixed pool state.

7. Invariants / laws

• L1 (C5): PGA is modeled as an all-pay auction — all bidders pay their gas whether they win or not. The sim must capture this cost structure (not winner-pays-only).
• L2 (C5): block building is a knapsack problem, not a queue — builders optimize for total extracted value subject to gas limit constraints, not first-come-first-served.
• L3 (C4): MEV exposure predictions are pre-trade — traders query this sim before submitting to the Marketplace to understand their extraction risk.
• L4 (C4): cross-chain arb models both execution paths — inventory (fast, capital- intensive) and bridge (slow, capital-light) — never assumes one dominates.
• L5 (C3): DSMFG solutions are bilevel — the leader's optimal policy depends on the followers' MFG equilibrium, which itself depends on the leader's policy. Fixed-point iteration or SMFRL solvers required.

8. Build steps

1. Implement the PGA all-pay auction model (N searchers, opportunity value V, gas bids).
2. Implement the block-building knapsack solver.
3. Add sandwich/frontrun detection heuristics.
4. Implement cross-chain arb model (inventory vs. bridge, latency, MEV exposure).
5. Implement Kolokoltsov non-linear Fokker-Planck with WENO discretization.
6. Implement DSMFG bilevel solver (leader policy + follower MFG equilibrium).
7. Wire M2 on-chain + cross-chain data → calibration.
8. Wire pre-trade query interface for Traders.

9. Tests

All-pay: losing bidders still pay gas cost. Knapsack: builder selects optimal transaction set under gas limit. Sandwich: known sandwich-vulnerable trade flagged; non-vulnerable trade clear. Cross-chain: inventory path preferred when latency advantage exceeds capital cost. DSMFG: leader policy converges to fixed point with follower equilibrium. Kolokoltsov: WENO captures shock discontinuities in adversarial strategy distribution. Bounds: all outputs bounded. Pre-trade: query does not submit any transaction. Speed: sim tick-advances at 90:1.

10. Open items

• Mempool data access (public mempool? private order flow?).
• Which MEV types to model initially (sandwich, backrun, liquidation, JIT?).
• Multi-block MEV (cross-block extraction strategies).
• DSMFG solver choice (SMFRL? fictitious play? direct bilevel optimization?).
• WENO order for Kolokoltsov (3rd? 5th? tradeoff with compute budget).
• Which L2s/bridges to model for cross-chain (Arbitrum? Optimism? Base?).