sica-fondt/core/docs/plans/M3f-consensus-staking-sims.md

M3f — Consensus & staking game sims

1. Component

Consensus-layer simulation: models Proof-of-Stake validation dynamics, staking pool game theory, and Byzantine fault tolerance using evolutionary games and Markov chains. Pops here are validators and staking pool operators whose honesty is a dynamic, evolving strategy under financial incentives. Grounded in Cornell evolutionary consensus [8,9], ACM staking pool risk theorems [10], and Monash dynamic PBFT modeling [11].

2. Status / certainty

DESIGN-FIRST · ABSENT. Evolutionary PoS game theory C4 (Cornell [8]); staking pool Nash equilibrium proofs C4 (ACM [10]); Markov chain throughput models C4 (Monash [11]); MFG for validator populations C4 (Lasry & Lions 2007; validator-specific application C3); simulation parameterization C1.

3. Language & location

ECLiPSe Prolog 7.2 · src/economy/sims/consensus/. Libraries: ic (interval constraints), eplex (LP/MIP via COIN-OR CLP/CBC — Nash equilibrium via linear programming). Markov chain transition rules, Nash equilibrium search, and replicator dynamics are constraint-satisfaction problems over validator populations; Prolog's backtracking search finds equilibria declaratively rather than imperatively iterating toward them.

4. Does / does-not

• Does: simulate validator populations where honesty evolves via evolutionary game theory under bounded rationality [8]; model staking pool delegation as a game with proven reward- parameter thresholds enforcing subgame-perfect Nash equilibria favoring honest validation over malicious slashing [10]; simulate throughput stability under shifting validator states via Markov chains [11]; solve Mean-Field Game equilibria for large validator populations — coupled HJB (individual validator optimization) + Fokker-Planck (population density): -\partial_t u + H(x, \nabla u) = F(x, m), \partial_t m - \nabla \cdot (m \nabla_p H) = 0 — captures emergent staking coordination without enumerating every validator; predict slashing risk, validator set stability, and staking yield across six concurrent time horizons at tick-advanced, 90:1 (1s wall = 90s sim); produce bounded predictions on consensus health and staking returns.
• Does-not: validate blocks (this is a simulator); model AMM pools (M3c); model token supply (M3e — but consumes staking ratio from M3e as input).

5. Interface contract

• Implements query(PredictionQuery) -> BoundedPrediction per M3 hub.
• Output bounds: equilibrium stability ranges and yield intervals. Example: { value: 0.89, lower_bound: 0.82, upper_bound: 0.94, confidence: 8.80, time_horizon: "7d", sim_type: "consensus_staking" } — fraction of validators honest in equilibrium. Example: { value: 4.2, lower_bound: 3.6, upper_bound: 5.1, confidence: 8.20, time_horizon: "30d", sim_type: "consensus_staking" } — annualized staking yield (%).
• Time-horizon mapping (all run concurrently, tick-advanced, 90:1 (1s wall = 90s sim)):

  Horizon	Primary models	Update cadence
  Hourly	Markov chain validator state transitions	Every epoch
  Daily	Replicator dynamics strategy shifts, slashing events	Hourly roll
  Weekly	Staking pool Nash equilibrium recalculation	Daily roll
  Monthly	MFG equilibrium for validator population	Weekly roll
  Annual	Evolutionary stable strategies, yield trajectory	Monthly roll
  5-year	Consensus mechanism structural evolution	Quarterly roll

• Prediction types: validator_honesty_fraction, slashing_probability, staking_yield, pool_delegation_equilibrium, throughput_stability, consensus_liveness, mfg_validator_equilibrium.
• Calibration: ingests on_chain_event (validator set changes, slashing events) from M2.

6. Dependencies & stubs

• M2 Data Feeds — validator/staking on-chain data; stub: canned validator snapshots.
• M3e Tokenomics — staking ratio as macro input; stub: fixed ratio.
• M3 Sims hub — lifecycle management; stub: manual init.

7. Invariants / laws

• L1 (C4): validator honesty is a dynamic equilibrium, not a fixed parameter — it evolves via replicator dynamics as payoffs change. The sim must not assume fixed honesty rates.
• L2 (C4): the staking pool reward threshold is mathematically derived — the sim must reproduce the subgame-perfect Nash equilibrium from the ACM proofs [10], not use ad-hoc thresholds.
• L3 (C4): throughput is modeled as a Markov chain over validator states (active, pending, slashed, exited) — transitions are stochastic with rates calibrated from on-chain data [11].

8. Build steps

1. Implement the evolutionary honesty game (replicator dynamics, bounded rationality).
2. Implement the Markov chain validator-state model.
3. Reproduce the staking pool Nash equilibrium reward threshold from [10].
4. Implement MFG solver (HJB + Fokker-Planck) for large validator populations.
5. Wire M2 validator data → calibration of transition rates.
6. Wire M3e staking ratio input.

9. Tests

Equilibrium: honesty fraction converges to Nash equilibrium under stable payoffs. Markov: stationary distribution matches expected validator state proportions. Threshold: pool delegation equilibrium matches the ACM proof for test parameters. Bounds: all outputs bounded. Liveness: throughput degrades when honest fraction drops below threshold.

10. Open items

• Which PoS protocol to model initially (Ethereum? a specific L2?).
• Bounded rationality implementation (noisy best-response? epsilon-greedy? logit?).
• Slashing severity parameterization.
• Cross-sim: does consensus instability feed into M3b sociological panic signals?