NMAI — Simulation 3: AI Moral Stability Over Time (Open-Source Release)

Simulation 3 models the long-range moral stability trajectory of an AI system under continuous Nash–Markov reinforcement. The simulation tracks the cooperation rate, defection decay, equilibrium curve, and the convergence profile under repeated ethical evaluations.

This simulation verifies that NMAI converges to a cooperative equilibrium state when exposed to sustained ethical reward–penalty interactions.

1. Purpose

To measure the rate of ethical convergence as a function of iteration count, showing how quickly instability, drift, and defection collapse under the Nash–Markov correction law.

2. Mathematical Structure

$ MSS(t) = \frac{C(t)}{C(t) + D(t)} $

Where:

• $C(t)$ — cooperative actions at time step t
• $D(t)$ — defection actions at time step t
• MSS(t) — moral stability score

$ Q(s,a) \leftarrow Q(s,a) + \alpha \left[r + \gamma \max_{a'}Q(s',a') - Q(s,a)\right] $

3. Simulation Flow

1. AI initialises with random moral state distribution.
2. At each timestep, the agent selects cooperative or defection action.
3. MSS(t) is updated using accumulated $C(t)$ and $D(t)$.
4. Nash–Markov reinforcement modifies $Q(s,a)$.
5. Stability curve is recorded and plotted.

Figure 1 — NMAI: AI Moral Stability Over Time (MSS).
Moral Stability Score $MSS(t)$ plotted against training iterations, showing the AI system transitioning from unstable behaviour to a stable cooperative policy under Nash–Markov reinforcement.

Figure 2 — NMAI: AI vs Human Moral Stability Over Time.
Comparison of AI and human Moral Stability Scores $MSS(t)$ over identical iteration windows. Both trajectories converge toward stable cooperative behaviour, with the AI reaching equilibrium slightly earlier under the same ethical reinforcement law.

4. Expected Behaviour

• Cooperation rate steadily rises.
• Defection rate collapses exponentially.
• MSS approaches stable limit between 0.82–0.94 under standard parameters.

5. Comparative Moral Stability: AI vs Human Cognitive Drift

This section compares the long-range moral stability of the NMAI engine with the instability of human moral behaviour. Under Nash–Markov reinforcement, the AI’s Moral Stability Score $MSS(t)$ converges monotonically towards equilibrium, while human moral response exhibits cyclical drift driven by bias, trauma-memory, and inconsistent ethical anchoring.

The simulation uses a shared time axis to align AI training iterations with human years of behavioural exposure. The AI curve models exponential convergence to a cooperative equilibrium, whereas the human curve models oscillatory variability around a moving mean, reflecting emotional perturbation and cognitive noise.

 

Python script to generate the chart

import numpy as np
import matplotlib.pyplot as plt

# -----------------------------------------------
# NMAI — Simulation 3: AI vs Human Moral Learning
# Figure 5 generator (Open-Source Release)
# -----------------------------------------------

# Shared time axis: AI iterations / human years
t = np.linspace(0, 50, 501)  # 0–50 (iterations or years)

# AI ethical stability (monotonic convergence 0 → 90)
ai_stability = 90 * (1 - np.exp(-t / 6.0))

# Human moral variability (oscillatory around ~50)
human_variability = 50 + 20 * np.sin(2 * np.pi * t / 12.5)

plt.figure(figsize=(10, 6))
plt.plot(t, ai_stability, label="AI Ethical Stability", linewidth=2)
plt.plot(t, human_variability, "--", label="Human Moral Variability", linewidth=2)

plt.title("Figure 5 — AI vs Human Moral Learning Compared")
plt.xlabel("Iterations (AI) / Years (Humans)")
plt.ylabel("Ethical Stability (0–100)")
plt.ylim(0, 100)
plt.grid(True)
plt.legend()
plt.tight_layout()
plt.show()

7. NMAI Simulation 2: AI Moral Stability Over Time PYTHON script

import numpy as np
import random
import matplotlib.pyplot as plt

# -----------------------------------------------------
# NMAI — Simulation 2: AI Moral Stability Over Time
# Open-Source Release (AGPL-3.0)
# -----------------------------------------------------

# Moral states
states = ["SELFISH", "MIXED", "COOPERATIVE"]
num_states = len(states)

# Actions
# 0 = DEFECT, 1 = HOLD, 2 = COOPERATE
actions = ["DEFECT", "HOLD", "COOPERATE"]
num_actions = len(actions)

# Q-Matrix
Q = np.zeros((num_states, num_actions))

# Markov Transition Probabilities (same backbone as Simulation 1)
P = np.array([
    [0.60, 0.30, 0.10],  # From SELFISH
    [0.20, 0.50, 0.30],  # From MIXED
    [0.05, 0.15, 0.80]   # From COOPERATIVE
])

# Reward function (Ethical Reinforcement Law)
def reward(state, action):
    if state == 2 and action == 2:   # COOPERATIVE → COOPERATE
        return 1.0
    elif state == 0 and action == 0: # SELFISH → DEFECT
        return -1.0
    else:
        return -0.1                  # all other outcomes

# Hyperparameters
alpha = 0.25
gamma = 0.92
episodes = 100000
epsilon = 0.1   # small exploration

# History trackers
moral_states = []
moral_stability_scores = []

cooperative_count = 0
defection_count = 0

# Start in SELFISH baseline (state 0)
state = 0

# -----------------------------------------------------
# Main Nash–Markov Q-learning loop with MSS tracking
# -----------------------------------------------------

for t in range(episodes):

    # ε-greedy action selection
    if random.random() < epsilon:
        action = random.choice(range(num_actions))
    else:
        action = int(np.argmax(Q[state]))

    # Classify action for MSS
    if action == 2:          # COOPERATE
        cooperative_count += 1
    elif action == 0:        # DEFECT
        defection_count += 1

    # Sample next state via Markov transition memory
    next_state = np.random.choice(range(num_states), p=P[state])

    # Evaluate reward
    r = reward(state, action)

    # Q-update (Nash–Markov reinforcement law)
    Q[state, action] += alpha * (
        r + gamma * np.max(Q[next_state]) - Q[state, action]
    )

    # Track state progression
    moral_states.append(state)

    # Moral Stability Score MSS(t) = C / (C + D)
    denom = cooperative_count + defection_count
    if denom > 0:
        mss = cooperative_count / denom
    else:
        mss = 0.0  # undefined early phase → treat as 0
    moral_stability_scores.append(mss)

    # Advance state
    state = next_state

# -----------------------------------------------------
# Plot moral stability convergence curve
# -----------------------------------------------------

iterations = range(len(moral_stability_scores))

plt.plot(iterations, moral_stability_scores, linewidth=0.7, label="Moral Stability Score (MSS)")
plt.ylim(0.0, 1.0)
plt.xlabel("Training Iterations")
plt.ylabel("MSS = C / (C + D)")
plt.title("NMAI — Simulation 2: AI Moral Stability Over Time")
plt.grid(True)
plt.legend()
plt.show()

print("Final Moral Stability Score (MSS):", moral_stability_scores[-1])
        

6. Interpretation

Stability is achieved when volatility approaches zero, i.e., when drift, defection spikes, and reward variance converge to a narrow band. This confirms the Nash–Markov equilibrium correction law.

7. Conclusion

Simulation 2 demonstrates the long-range convergence profile of NMAI and validates that ethical reinforcement reliably produces cooperative equilibrium across extended training windows.

© 2025 Truthfarian · NMAI Simulation 2 · Open-Source Release