Nash Strategy Layer (IP-Restricted)

Nash provided the existence condition for equilibrium.
NashMarkAI defines the inevitability, stability, and ethical governance of equilibrium across legal, cognitive, ecological, and strategic systems.

The Nash Strategy Layer is the equilibrium decision core within the NashMark-AI stack. It transforms Markov state distributions and risk signals into stable multi-party strategies. All payoff structures, jurisdictional coefficients and allocation rules are IP-restricted.

IP-Restricted Component. Only the abstract shell, interfaces and high-level equations are disclosed. Full payoff matrices, harm weights and jurisdiction-specific mappings are withheld.

1. Role in the Architecture

• Receives system distributions and risk tiers from the Markov Engine.
• Computes stable strategy profiles under Nash–Markov equilibrium constraints.
• Exports equilibrium strategies, sanctions and allocations to Sansana / PHM.
• Feeds Sentinel, Breach Cascade Engine and Equilibrium Enforcement Engine with equilibrium-consistent strategy recommendations.

2. Equilibrium Strategy Shell (Public)

$ A_i = \{ a_{i1}, a_{i2}, \dots, a_{ik_i} \}, \quad i = 1, \dots, N $

$ \sigma = (\sigma_1, \dots, \sigma_N), \quad \sigma_i \in \Delta(A_i) $

$ U_i(\sigma) \ge U_i(a_i, \sigma_{-i}), \quad \forall i,\; \forall a_i \in A_i $

• $ A_i $ — action set for party or agent $ i $.
• $ \sigma_i $ — mixed strategy for $ i $ over $ A_i $.
• $ U_i $ — utility/harm function (full form withheld).
• Equilibrium strategy profile $ \sigma^{*} $ satisfies the inequality above for all parties.

3. Mapping from Markov State to Strategy

$ \pi_t \in \Delta^{n} $ — Markov state distribution at iteration $ t $.

$ \sigma_t = \Phi(\pi_t, \theta) $

• $ \pi_t $ — current ethical / systemic state distribution from the Markov Engine.
• $ \theta $ — parameter vector (harm weights, jurisdictional factors, escalation bands) — withheld.
• $ \Phi(\cdot) $ — proprietary mapping from state distribution to equilibrium strategy profile.

4. Integration Contract

5. Public Pseudocode Shell

def nash_strategy_layer(pi_t, eq_signal, volatility, risk_tier):
    """
    Inputs:
        pi_t        - Markov state distribution
        eq_signal   - equilibrium proximity index
        volatility  - volatility index
        risk_tier   - risk band (0–n) for legal / governance engines
    Outputs:
        sigma_t     - equilibrium strategy profile
        actions     - recommended action set
        sanction    - sanction / remedy band
    """
    # Internal mapping and payoffs are IP-restricted and redacted.

    # 1. Project state distribution into payoff space (redacted)
    payoff_tensor = project_to_payoffs(pi_t, risk_tier)

    # 2. Compute equilibrium profile (solver details redacted)
    sigma_t = compute_nash_equilibrium(payoff_tensor, eq_signal, volatility)

    # 3. Derive concrete actions and sanction band (redacted)
    actions = derive_actions(sigma_t)
    sanction = classify_sanction_band(sigma_t, risk_tier)

    return sigma_t, actions, sanction
        

6. Deployment Notes

• Deployed only behind secured APIs or compiled service boundaries.
• No direct access to payoff tensors, coefficients or harm functions.
• External systems receive strategies, not internal score functions.
• Research versions expose simplified payoff structures that are not suitable for live legal or regulatory use.

© 2025 Truthfarian · Nash Strategy Layer · IP-Restricted Component