sica-fondt/core/docs/plans/M3e-tokenomics-macro-sims.md

M3e — Tokenomics & macro-state sims

1. Component

Macro-level token economy simulation: models token supply dynamics, monetary policy (halvings, burns, inflation), lending protocol dynamics, DeFi systemic risk, and stock-flow balances using stochastic differential equations (SDEs), state-space models, kinked interest rate curves, and inter-protocol credit exposure networks. Pops here are aggregate behavioral cohorts (miners/validators, holders, speculators, protocol treasuries, borrowers/lenders) whose collective behavior drives token-level dynamics across six concurrent time horizons at tick-advanced, 90:1 (1s wall = 90s sim).

Grounded in Vienna complex-systems token modeling [7], ResearchGate engineering token economy frameworks [6], Aave/Compound kinked interest rate models (industry standard), and DeXposure inter-protocol credit propagation (Matzakos et al. 2025).

2. Status / certainty

DESIGN-FIRST · ABSENT. SDE state-space framework C4 (Vienna [7]); stock-flow modeling C4 (ResearchGate [6]); kinked interest rate model C5 (Aave/Compound production standard); DeXposure inter-protocol credit propagation C3 (emerging, 2025 — high DeFi specificity); composable yield optimization C4 (Yearn v3, Beefy, production-validated). Specific parameters C1.

3. Language & location

TBD · src/economy/sims/tokenomics/. Needs SDE solvers (Euler-Maruyama, Milstein), state-space estimation, and VAR (vector autoregression) for credit exposure impulse responses. Julia (DifferentialEquations.jl) or Octave.

4. Does / does-not

• Does: simulate token state dynamics via the SDE framework: dX_t = f(X_t, u(X_t, t), t)dt + \sigma(X_t, t)dW_t where X_t is the system state vector, u is the behavioral policy function, deterministic drift captures programmatic parameters (halvings, burns), and Brownian motion \sigma dW_t captures stochastic behavioral shocks; model stock-flow balances (circulating supply, staked, locked, burned); simulate monetary policy impacts (halving events, fee burns, treasury emissions); model lending protocol dynamics via kinked interest rate curves: R = R_0 + R_{\text{slope1}} \times U if U \leq U_{\text{opt}}, $R = R_0 + R_{\text{slope1}} \times U_{\text{opt}} + R_{\text{slope2}} \times (U - U_{\text{opt}})$ if U > U_{\text{opt}} where $U = \text{Borrowed}/(\text{Supplied} + \text{Borrowed})$, U_{\text{opt}} \approx 0.8 — cascade liquidations when \text{collateral} \times \text{LTV} < \text{borrowed}; model DeFi systemic risk via DeXposure inter-protocol credit propagation: $E_{ij}(t) = \sum_{\text{tokens}} [\text{TVL}_j(\text{token}) \times \text{ownership}_i(\text{token})]$ with VAR impulse responses for shock contagion across protocols sharing collateral; model composable yield optimization: \max \sum_i w_i(t) \cdot \text{APY}_i(t) - \lambda \sum_i w_i(t)^2 \sigma_i^2(t) subject to \sum_i w_i = 1 — dynamic rebalancing across lending, LP, and staking strategies; produce bounded predictions on token supply, protocol health, yield, and systemic risk.
• Does-not: model individual transactions (M3c/M3d); model social sentiment (M3b); model consensus mechanics (M3f); execute yield strategies (Traders/Marketplace do).

5. Interface contract

• Implements query(PredictionQuery) -> BoundedPrediction per M3 hub.
• Output bounds: SDE confidence bands, utilization rate ranges, contagion impact intervals.
• Time-horizon mapping (all run concurrently, tick-advanced, 90:1 (1s wall = 90s sim)):

  Horizon	Primary models	Update cadence
  Hourly	Lending rates, utilization, liquidation risk	Every block
  Daily	Yield optimization, protocol TVL flows	Hourly roll
  Weekly	SDE supply trajectory, stock-flow balances	Daily roll
  Monthly	DeXposure credit contagion, systemic risk	Weekly roll
  Annual	Halving/burn policy impacts, inflation trajectory	Monthly roll
  5-year	Token supply long-run equilibrium, protocol lifecycle	Quarterly roll

• Examples: { value: 2.1, lower_bound: 1.4, upper_bound: 3.2, confidence: 9.00, time_horizon: "90d", sim_type: "tokenomics_macro" } — annualized inflation rate (%). { value: 0.67, lower_bound: 0.58, upper_bound: 0.74, confidence: 8.50, time_horizon: "30d", sim_type: "tokenomics_macro" } — staking ratio. { value: 0.83, lower_bound: 0.78, upper_bound: 0.91, confidence: 8.80, time_horizon: "1h", sim_type: "tokenomics_macro" } — Aave ETH utilization rate. { value: 0.12, lower_bound: 0.04, upper_bound: 0.25, confidence: 7.20, time_horizon: "7d", sim_type: "tokenomics_macro" } — systemic contagion risk index.
• Prediction types: supply_trajectory, inflation_rate, staking_ratio, velocity_estimate, halving_impact, treasury_runway, utilization_rate, liquidation_cascade_risk, systemic_contagion_index, optimal_yield_allocation.
• Calibration: ingests on_chain_event (supply metrics, staking data, lending protocol state, TVL) from M2.

6. Dependencies & stubs

• M2 Data Feeds — on-chain supply/staking/lending data; stub: canned supply snapshots.
• M3 Sims hub — lifecycle management; stub: manual init.

7. Invariants / laws

• L1 (C5): the SDE framework is the canonical representation — all token dynamics are expressed as drift + diffusion. Deterministic policy (halvings, burns) lives in the drift f; behavioral uncertainty lives in the diffusion \sigma dW_t.
• L2 (C5): stock-flow conservation — tokens are never created or destroyed outside the protocol's defined mechanisms. circulating + staked + locked + burned = total ever minted.
• L3 (C5): lending rate curves are kinked at $U_{\text{opt}}$ — the steep slope above optimal utilization is a design invariant of Aave/Compound, not a parameter to smooth.
• L4 (C4): macro sims operate on aggregate cohorts, not individuals — the state vector X_t tracks population-level quantities (total staked, total circulating), not per-wallet.
• L5 (C4): DeXposure contagion is directional — protocol A's exposure to protocol B is not symmetric. The exposure matrix E_{ij} is not assumed symmetric.

8. Build steps

1. Implement Euler-Maruyama SDE solver for a simple token model (supply + staking).
2. Define the state vector X_t and drift/diffusion functions for a reference token.
3. Add stock-flow accounting (verify conservation).
4. Implement kinked lending rate model (Aave-style) with liquidation cascade simulation.
5. Implement DeXposure credit propagation network with VAR impulse responses.
6. Implement composable yield optimizer (risk-adjusted return maximization).
7. Wire M2 on-chain data → state estimation / calibration.
8. Add monetary policy events (halving, burn) as drift discontinuities.

9. Tests

SDE: sample paths have correct mean (matches drift) and variance (matches diffusion). Stock-flow: conservation holds across all time steps. Halving: supply growth rate drops at halving event. Lending: rate curve exhibits kink at U_{\text{opt}}; liquidation cascades triggered when collateral ratio breached. DeXposure: shock to protocol A propagates to protocol B through shared collateral; isolated protocols unaffected. Yield: optimizer rebalances toward highest risk-adjusted APY. Calibration: state estimate converges to observed data. Bounds: SDE confidence bands cover realized paths on backtest. Speed: sim tick-advances at 90:1.

10. Open items

• Which tokens to model initially (ETH? BTC? a specific alt?).
• State vector dimensionality (how many state variables per token model?).
• Behavioral policy function u(X_t, t) — how to parameterize aggregate cohort behavior.
• Multi-token interactions (correlated diffusions across tokens?).
• DeXposure graph granularity (how many protocols? top-10 by TVL?).
• Lending model extensions (Morpho AdaptiveCurveIRM? variable kink parameters?).