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All sims advance every tick continuously. The 360:1 floor means the slowest system produces 1 simulated hour per 1 wall-clock second. Updated hub cadence table and all sub-spec references. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
89 lines
5.4 KiB
Markdown
89 lines
5.4 KiB
Markdown
# M3f — Consensus & staking game sims
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## 1. Component
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Consensus-layer simulation: models **Proof-of-Stake validation dynamics, staking pool game theory,
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and Byzantine fault tolerance** using evolutionary games and Markov chains. Pops here are
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**validators and staking pool operators** whose honesty is a dynamic, evolving strategy under
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financial incentives. Grounded in Cornell evolutionary consensus [8,9], ACM staking pool risk
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theorems [10], and Monash dynamic PBFT modeling [11].
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## 2. Status / certainty
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DESIGN-FIRST · ABSENT. Evolutionary PoS game theory C4 (Cornell [8]); staking pool Nash
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equilibrium proofs C4 (ACM [10]); Markov chain throughput models C4 (Monash [11]); MFG for
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validator populations C4 (Lasry & Lions 2007; validator-specific application C3);
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simulation parameterization C1.
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## 3. Language & location
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TBD · `src/economy/sims/consensus/`. Needs Markov chain solvers and game-theoretic equilibrium
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computation. Python, Julia, or R.
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## 4. Does / does-not
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- **Does:** simulate validator populations where honesty evolves via **evolutionary game theory**
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under bounded rationality [8]; model staking pool delegation as a game with proven reward-
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parameter thresholds enforcing subgame-perfect Nash equilibria favoring honest validation over
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malicious slashing [10]; simulate **throughput stability under shifting validator states** via
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Markov chains [11]; solve **Mean-Field Game equilibria for large validator populations** —
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coupled HJB (individual validator optimization) + Fokker-Planck (population density):
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$-\partial_t u + H(x, \nabla u) = F(x, m)$, $\partial_t m - \nabla \cdot (m \nabla_p H) = 0$
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— captures emergent staking coordination without enumerating every validator; predict slashing
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risk, validator set stability, and staking yield across **six concurrent time horizons** at
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tick-advanced, ≥ 360:1 (1s wall = 1h sim); produce bounded predictions on consensus health and staking returns.
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- **Does-not:** validate blocks (this is a simulator); model AMM pools (M3c); model token supply
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(M3e — but consumes staking ratio from M3e as input).
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## 5. Interface contract
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- Implements `query(PredictionQuery) -> BoundedPrediction` per M3 hub.
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- **Output bounds:** equilibrium stability ranges and yield intervals.
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Example: `{ value: 0.89, lower_bound: 0.82, upper_bound: 0.94, confidence: 0.88,
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time_horizon: "7d", sim_type: "consensus_staking" }` — fraction of validators honest in
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equilibrium.
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Example: `{ value: 4.2, lower_bound: 3.6, upper_bound: 5.1, confidence: 0.82,
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time_horizon: "30d", sim_type: "consensus_staking" }` — annualized staking yield (%).
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- **Time-horizon mapping** (all run concurrently, tick-advanced, ≥ 360:1 (1s wall = 1h sim)):
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| Horizon | Primary models | Update cadence |
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|---------|---------------|----------------|
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| Hourly | Markov chain validator state transitions | Every epoch |
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| Daily | Replicator dynamics strategy shifts, slashing events | Hourly roll |
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| Weekly | Staking pool Nash equilibrium recalculation | Daily roll |
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| Monthly | MFG equilibrium for validator population | Weekly roll |
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| Annual | Evolutionary stable strategies, yield trajectory | Monthly roll |
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| 5-year | Consensus mechanism structural evolution | Quarterly roll |
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- **Prediction types:** `validator_honesty_fraction`, `slashing_probability`, `staking_yield`,
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`pool_delegation_equilibrium`, `throughput_stability`, `consensus_liveness`,
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`mfg_validator_equilibrium`.
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- Calibration: ingests `on_chain_event` (validator set changes, slashing events) from M2.
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## 6. Dependencies & stubs
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- M2 Data Feeds — validator/staking on-chain data; *stub:* canned validator snapshots.
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- M3e Tokenomics — staking ratio as macro input; *stub:* fixed ratio.
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- M3 Sims hub — lifecycle management; *stub:* manual init.
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## 7. Invariants / laws
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- **L1 (C4):** validator honesty is a **dynamic equilibrium, not a fixed parameter** — it evolves
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via replicator dynamics as payoffs change. The sim must not assume fixed honesty rates.
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- **L2 (C4):** the staking pool reward threshold is **mathematically derived** — the sim must
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reproduce the subgame-perfect Nash equilibrium from the ACM proofs [10], not use ad-hoc
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thresholds.
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- **L3 (C4):** throughput is modeled as a **Markov chain** over validator states (active, pending,
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slashed, exited) — transitions are stochastic with rates calibrated from on-chain data [11].
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## 8. Build steps
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1. Implement the evolutionary honesty game (replicator dynamics, bounded rationality).
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2. Implement the Markov chain validator-state model.
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3. Reproduce the staking pool Nash equilibrium reward threshold from [10].
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4. Implement MFG solver (HJB + Fokker-Planck) for large validator populations.
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5. Wire M2 validator data → calibration of transition rates.
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6. Wire M3e staking ratio input.
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## 9. Tests
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Equilibrium: honesty fraction converges to Nash equilibrium under stable payoffs. Markov:
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stationary distribution matches expected validator state proportions. Threshold: pool delegation
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equilibrium matches the ACM proof for test parameters. Bounds: all outputs bounded. Liveness:
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throughput degrades when honest fraction drops below threshold.
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## 10. Open items
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- Which PoS protocol to model initially (Ethereum? a specific L2?).
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- Bounded rationality implementation (noisy best-response? epsilon-greedy? logit?).
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- Slashing severity parameterization.
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- Cross-sim: does consensus instability feed into M3b sociological panic signals?
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