fix: correct COI formulation to measure price erosion over time

The fundamental error was treating COI as instantaneous margin × alpha.
The corrected formulation is:

    COI = E[p_start] - p_transaction

This measures price erosion over time, capturing how agents using
multiple sessions gather information and drive prices down.

Key changes:
- Add coi.py with COIWindow, COITracker, and compute_multi_session_coi
- Add separability.py with KL-divergence behavioral classification
- Update simplified_env.py to track initial prices and compute windowed COI
- Add corrected COI metrics (coi_*_corrected) alongside legacy metrics

The new approach:
1. Tracks prices at episode start as E[p] (expected price)
2. Computes transaction prices as p (actual sale price)
3. Measures leak as the difference (price erosion)
4. Includes order statistic erosion (Theorem 1: N agents -> min price)

lab/case/thesis/coi.py

@@ -0,0 +1,378 @@
+"""Cost of Information (COI) computation for thesis pricing simulation.
+
+Implements the corrected COI formulation:
+
+    COI = E[p] - p
+
+where:
+- E[p] = expected price BEFORE information revelation (window start price)
+- p = actual transaction price (price at which sales occur)
+
+The fundamental insight is that COI should measure PRICE EROSION over time,
+not instantaneous margin leakage. When agents explore across sessions:
+1. They reveal demand signals that drive platform price adjustments
+2. Coordinated agents can find the minimum price across their session pool
+3. The price path from window start to transaction captures information leakage
+
+Key components:
+- COIWindow: Windowed price erosion measurement over K steps
+- compute_coi_window: Per-episode COI from session-level transactions
+- coi_erosion: Order statistic erosion (Theorem 1: N agents -> min price)
+
+This fixes the fundamental error of treating COI as instantaneous margin × alpha.
+"""
+from __future__ import annotations
+from dataclasses import dataclass, field
+from typing import Dict, List, TYPE_CHECKING
+import numpy as np
+
+if TYPE_CHECKING:
+    from .simplified import Session
+
+EPS = 1e-10
+
+
+@dataclass
+class COIWindow:
+    """Windowed COI measurement capturing price erosion over time.
+
+    Attributes:
+        policy: Platform's intended COI (prices at window start - cost)
+        agent: Realized COI for agents (prices at transaction - cost)
+        leak: COI leakage = policy - agent (price erosion due to exploration)
+        survival_ratio: Fraction of intended COI that survives (agent/policy)
+        policy_by_product: Per-product policy COI
+        agent_by_product: Per-product agent COI
+        demand_weights: Demand weights used for aggregation
+    """
+    policy: float = 0.0          # E[p] - c at window start
+    agent: float = 0.0           # p_transaction - c
+    leak: float = 0.0            # policy - agent = price erosion
+    survival_ratio: float = 1.0  # agent / policy
+    policy_by_product: np.ndarray = field(default_factory=lambda: np.zeros(1))
+    agent_by_product: np.ndarray = field(default_factory=lambda: np.zeros(1))
+    demand_weights: np.ndarray = field(default_factory=lambda: np.zeros(1))
+
+    def to_dict(self) -> Dict[str, float]:
+        return {
+            'coi_policy': self.policy,
+            'coi_agent': self.agent,
+            'coi_leak': self.leak,
+            'coi_survival': self.survival_ratio,
+        }
+
+
+def compute_coi_window(
+    sessions: List["Session"],
+    costs: np.ndarray,
+    demand_mapping: Dict[str, float] = None,
+    window_prices: np.ndarray = None,
+) -> COIWindow:
+    """Compute COI from session data using the corrected formulation.
+
+    COI = E[p_start] - p_transaction
+
+    This measures how much the platform's pricing power eroded during the window.
+    Price at window start represents E[p] (what we expected to charge).
+    Transaction prices represent p (what we actually charged).
+
+    Args:
+        sessions: List of sessions with events containing price_seen and purchases
+        costs: Product costs array
+        demand_mapping: Optional session_id -> demand proxy mapping
+        window_prices: Optional explicit window start prices (otherwise use first seen)
+
+    Returns:
+        COIWindow with erosion metrics
+    """
+    if not sessions:
+        n = len(costs)
+        zeros = np.zeros(n)
+        return COIWindow(policy=0.0, agent=0.0, leak=0.0, survival_ratio=1.0,
+                        policy_by_product=zeros, agent_by_product=zeros, demand_weights=zeros)
+
+    n = len(costs)
+    demand_mapping = demand_mapping or {}
+
+    # Track prices seen at start (E[p]) and transaction prices (p)
+    first_prices = np.zeros(n)  # first price seen per product (window start proxy)
+    transaction_prices = np.zeros(n)  # prices at which purchases occurred
+    transaction_counts = np.zeros(n)
+    view_counts = np.zeros(n)
+    demand_weights = np.zeros(n)
+
+    for sess in sessions:
+        sid = sess.sid
+        sess_demand = demand_mapping.get(sid, 1.0)
+
+        for e in sess.events:
+            pidx = e.product_idx
+            if pidx < 0 or pidx >= n:
+                continue
+
+            price_seen = float(e.price_seen)
+
+            # Track first price seen (proxy for E[p] at window start)
+            if view_counts[pidx] == 0:
+                first_prices[pidx] = price_seen
+            view_counts[pidx] += 1
+
+            # Track transaction prices
+            if e.action == "purchase":
+                transaction_prices[pidx] += price_seen
+                transaction_counts[pidx] += 1
+                demand_weights[pidx] += sess_demand
+
+    # Compute per-product COI
+    # Policy COI: what we intended to charge (first seen price - cost)
+    policy_by_product = np.zeros(n)
+    agent_by_product = np.zeros(n)
+
+    for i in range(n):
+        if view_counts[i] > 0:
+            # Use explicit window prices if provided, else first seen
+            start_price = window_prices[i] if window_prices is not None else first_prices[i]
+            policy_by_product[i] = max(0, start_price - costs[i])
+
+        if transaction_counts[i] > 0:
+            avg_transaction = transaction_prices[i] / transaction_counts[i]
+            agent_by_product[i] = max(0, avg_transaction - costs[i])
+
+    # Aggregate with demand weighting
+    total_demand = np.sum(demand_weights) + EPS
+    weights = demand_weights / total_demand
+
+    # Only count products with transactions for fair comparison
+    active_mask = transaction_counts > 0
+    if np.any(active_mask):
+        policy = float(np.sum(policy_by_product[active_mask] * weights[active_mask]) /
+                      (np.sum(weights[active_mask]) + EPS))
+        agent = float(np.sum(agent_by_product[active_mask] * weights[active_mask]) /
+                     (np.sum(weights[active_mask]) + EPS))
+    else:
+        # No transactions - use view-weighted policy COI
+        view_weights = view_counts / (np.sum(view_counts) + EPS)
+        policy = float(np.sum(policy_by_product * view_weights))
+        agent = policy  # No erosion without transactions
+
+    # Leak = price erosion due to information revelation
+    leak = max(0, policy - agent)
+    survival = agent / (policy + EPS) if policy > EPS else 1.0
+
+    return COIWindow(
+        policy=policy,
+        agent=agent,
+        leak=leak,
+        survival_ratio=float(np.clip(survival, 0, 1)),
+        policy_by_product=policy_by_product,
+        agent_by_product=agent_by_product,
+        demand_weights=demand_weights,
+    )
+
+
+def coi_erosion(policy_coi: float, agent_coi: float) -> float:
+    """Compute COI erosion rate: (policy - agent) / policy.
+
+    Returns the fraction of intended COI that was lost to information leakage.
+    0 = no erosion, 1 = complete erosion.
+    """
+    if policy_coi < EPS:
+        return 0.0
+    return float(np.clip((policy_coi - agent_coi) / policy_coi, 0, 1))
+
+
+def order_statistic_erosion(n_agents: int, price_std: float, base_margin: float = 1.0) -> float:
+    """Compute COI erosion from order statistic effect (Theorem 1).
+
+    When N agents independently query prices:
+    - Each sees a price p_i ~ N(μ, σ²)
+    - They coordinate to buy at min(p_1, ..., p_N)
+    - Expected minimum: μ - σ * E[order_stat]
+
+    As N -> ∞, E[min] -> p_min, so COI -> 0.
+
+    This quantifies the price discovery benefit of multiple sessions.
+
+    Args:
+        n_agents: Number of independent agent sessions
+        price_std: Standard deviation of price distribution
+        base_margin: Expected margin (μ - cost)
+
+    Returns:
+        Erosion rate in [0, 1]
+    """
+    if n_agents <= 1 or price_std < EPS:
+        return 0.0
+
+    # For standard normal order statistics, E[min of N] ≈ -Φ^{-1}(1/(N+1))
+    # For large N, this grows like sqrt(2 * log(N))
+    log_n = np.log(n_agents)
+    if log_n < 0.1:
+        return 0.0
+
+    # Extreme value theory: expected min shift
+    shift = price_std * (np.sqrt(2 * log_n) -
+                        (np.log(log_n) + np.log(4 * np.pi)) / (2 * np.sqrt(2 * log_n) + EPS))
+
+    # Erosion = shift / base_margin, capped at 1
+    return float(np.clip(shift / (base_margin + EPS), 0, 1))
+
+
+@dataclass
+class COITracker:
+    """Track COI over multiple windows for temporal analysis.
+
+    This addresses the user's insight: compute COI over K episodes to see
+    how prices change from window start to end.
+
+    If at start of window price is A and by end it's B, the difference
+    A - B represents COI leakage from exploratory sessions.
+    """
+    window_size: int = 10  # K episodes per window
+    _price_history: List[np.ndarray] = field(default_factory=list)
+    _transaction_history: List[np.ndarray] = field(default_factory=list)
+    _coi_history: List[float] = field(default_factory=list)
+
+    def add_step(self, prices: np.ndarray, transactions: np.ndarray = None):
+        """Record price observation for current step."""
+        self._price_history.append(prices.copy())
+        if transactions is not None:
+            self._transaction_history.append(transactions.copy())
+
+    def compute_window_coi(self, costs: np.ndarray) -> float:
+        """Compute COI over the current window.
+
+        COI = E[p_start] - E[p_end] for the window.
+        This captures price erosion due to information revelation.
+        """
+        if len(self._price_history) < 2:
+            return 0.0
+
+        # Get prices at window boundaries
+        window_start = max(0, len(self._price_history) - self.window_size)
+        start_prices = self._price_history[window_start]
+        end_prices = self._price_history[-1]
+
+        # COI = (start_price - cost) - (end_price - cost) = start_price - end_price
+        start_margin = np.mean(start_prices - costs)
+        end_margin = np.mean(end_prices - costs)
+
+        coi = max(0, start_margin - end_margin)
+        self._coi_history.append(coi)
+        return coi
+
+    def get_cumulative_erosion(self, costs: np.ndarray) -> float:
+        """Compute total COI erosion from first observation to now."""
+        if len(self._price_history) < 2:
+            return 0.0
+
+        initial = np.mean(self._price_history[0] - costs)
+        current = np.mean(self._price_history[-1] - costs)
+        return max(0, initial - current)
+
+    def get_erosion_trend(self) -> float:
+        """Get average COI per window (erosion rate)."""
+        if not self._coi_history:
+            return 0.0
+        return float(np.mean(self._coi_history))
+
+    def reset(self):
+        """Reset tracker for new episode."""
+        self._price_history.clear()
+        self._transaction_history.clear()
+        self._coi_history.clear()
+
+
+def compute_multi_session_coi(
+    sessions: List["Session"],
+    costs: np.ndarray,
+    alpha: float,
+    initial_prices: np.ndarray,
+) -> Dict[str, float]:
+    """Compute COI accounting for multi-session agent behavior.
+
+    This is the key fix for the fundamental error:
+    - Agents use different sessions to gather information
+    - Each session reveals price information
+    - Coordinated agents find the minimum across their session pool
+
+    The COI is computed as:
+    1. What platform intended to charge: initial_prices - costs
+    2. What agents actually paid: min(prices seen across sessions) - costs
+    3. Leak = (1) - (2)
+
+    Args:
+        sessions: All sessions in the episode
+        costs: Product costs
+        alpha: Contamination level (fraction of agent sessions)
+        initial_prices: Prices at episode start (E[p])
+
+    Returns:
+        Dictionary with COI metrics
+    """
+    n = len(costs)
+
+    # Separate agent and human sessions by ground truth label
+    agent_sessions = [s for s in sessions if s.actor == "A"]
+    human_sessions = [s for s in sessions if s.actor == "H"]
+
+    # Track prices seen by agents per product (for min finding)
+    agent_prices_seen: Dict[int, List[float]] = {i: [] for i in range(n)}
+    human_prices_paid: Dict[int, List[float]] = {i: [] for i in range(n)}
+
+    for sess in agent_sessions:
+        for e in sess.events:
+            if 0 <= e.product_idx < n:
+                agent_prices_seen[e.product_idx].append(e.price_seen)
+
+    for sess in human_sessions:
+        for e in sess.events:
+            if 0 <= e.product_idx < n and e.action == "purchase":
+                human_prices_paid[e.product_idx].append(e.price_seen)
+
+    # Compute COI components
+    policy_coi = float(np.mean(initial_prices - costs))  # E[p] - c
+
+    # Agent COI: they find the minimum price via exploration
+    agent_coi_by_product = np.zeros(n)
+    for i in range(n):
+        if agent_prices_seen[i]:
+            min_price = min(agent_prices_seen[i])
+            agent_coi_by_product[i] = max(0, min_price - costs[i])
+        else:
+            agent_coi_by_product[i] = initial_prices[i] - costs[i]
+
+    agent_coi = float(np.mean(agent_coi_by_product))
+
+    # Human COI: they pay whatever price is offered
+    human_coi_by_product = np.zeros(n)
+    for i in range(n):
+        if human_prices_paid[i]:
+            avg_price = np.mean(human_prices_paid[i])
+            human_coi_by_product[i] = max(0, avg_price - costs[i])
+        else:
+            human_coi_by_product[i] = initial_prices[i] - costs[i]
+
+    human_coi = float(np.mean(human_coi_by_product))
+
+    # Total leak: weighted by contamination
+    # Agents erode COI, humans pay full price
+    realized_coi = (1 - alpha) * human_coi + alpha * agent_coi
+    leak = policy_coi - realized_coi
+
+    # Order statistic effect: more agents = more erosion
+    n_agents = len(agent_sessions)
+    price_std = float(np.std(initial_prices))
+    order_erosion = order_statistic_erosion(n_agents, price_std, policy_coi)
+
+    return {
+        'policy_coi': policy_coi,
+        'agent_coi': agent_coi,
+        'human_coi': human_coi,
+        'realized_coi': realized_coi,
+        'leak': leak,
+        'order_stat_erosion': order_erosion,
+        'n_agent_sessions': n_agents,
+        'n_human_sessions': len(human_sessions),
+        'survival_ratio': realized_coi / (policy_coi + EPS) if policy_coi > EPS else 1.0,
+    }

lab/case/thesis/separability.py

@@ -0,0 +1,104 @@
+"""Behavioral separability for thesis human/agent classification.
+
+Implements KL-divergence based separability scoring (Eq 20-21):
+- Δ_H = D_KL(T̂' || T̄_H): divergence from human reference kernel
+- Δ_A = D_KL(T̂' || T̄_A): divergence from agent reference kernel
+- α̂(τ') = σ(β(Δ_H - Δ_A)): per-session contamination estimate
+"""
+from __future__ import annotations
+from typing import Dict, List, TYPE_CHECKING
+import numpy as np
+
+if TYPE_CHECKING:
+    from .simplified import Session
+
+
+# Reference transition kernels T̄_H, T̄_A estimated from real data (Eq 19)
+TRANS_H = {
+    "start": {"view": 0.85, "end": 0.15},
+    "view": {"detail": 0.4, "add_to_cart": 0.3, "view": 0.2, "end": 0.1},
+    "detail": {"add_to_cart": 0.5, "view": 0.3, "end": 0.2},
+    "add_to_cart": {"purchase": 0.6, "view": 0.25, "end": 0.15},
+    "purchase": {"end": 1.0},
+    "checkout": {"purchase": 0.8, "end": 0.2},
+    "hover": {"view": 0.5, "detail": 0.3, "end": 0.2},
+}
+
+TRANS_A = {
+    "start": {"view": 0.95, "end": 0.05},
+    "view": {"detail": 0.6, "view": 0.25, "add_to_cart": 0.1, "end": 0.05},
+    "detail": {"view": 0.5, "add_to_cart": 0.15, "detail": 0.3, "end": 0.05},
+    "add_to_cart": {"view": 0.4, "purchase": 0.2, "end": 0.4},
+    "purchase": {"end": 1.0},
+    "checkout": {"purchase": 0.3, "end": 0.7},
+    "hover": {"view": 0.6, "detail": 0.35, "end": 0.05},
+}
+
+
+def kl_div(p: Dict[str, float], q: Dict[str, float], eps: float = 1e-10) -> float:
+    """Compute KL(p || q) with smoothing."""
+    if not p or not q:
+        return 0.0
+    all_keys = set(p.keys()) | set(q.keys())
+    total = 0.0
+    for k in all_keys:
+        pk = p.get(k, eps)
+        qk = q.get(k, eps)
+        if pk > eps:
+            total += pk * np.log(pk / max(qk, eps))
+    return max(0.0, total)
+
+
+def build_kernel(events: List) -> Dict[str, Dict[str, float]]:
+    """Build empirical transition kernel from event sequence."""
+    trans: Dict[str, Dict[str, int]] = {}
+    prev = "start"
+    for e in events:
+        curr = getattr(e, 'action', None) or e.get('action', 'end') if isinstance(e, dict) else 'end'
+        trans.setdefault(prev, {})
+        trans[prev][curr] = trans[prev].get(curr, 0) + 1
+        prev = curr
+    # add terminal transition
+    trans.setdefault(prev, {})
+    trans[prev]["end"] = trans[prev].get("end", 0) + 1
+
+    # normalize to probabilities
+    kernel = {}
+    for s, dests in trans.items():
+        total = sum(dests.values())
+        kernel[s] = {d: c / total for d, c in dests.items()} if total > 0 else {"end": 1.0}
+    return kernel
+
+
+def compute_divergence(kernel: Dict[str, Dict[str, float]], ref_h: Dict = None, ref_a: Dict = None) -> tuple[float, float]:
+    """Compute Δ_H, Δ_A divergence from reference kernels (Eq 20-21)."""
+    ref_h = ref_h or TRANS_H
+    ref_a = ref_a or TRANS_A
+    delta_h = sum(kl_div(kernel.get(s, {}), ref_h.get(s, {})) for s in kernel) / max(len(kernel), 1)
+    delta_a = sum(kl_div(kernel.get(s, {}), ref_a.get(s, {})) for s in kernel) / max(len(kernel), 1)
+    return delta_h, delta_a
+
+
+def estimate_alpha(session: "Session", beta: float = 2.0) -> float:
+    """Estimate per-session contamination α̂(τ') = σ(β(Δ_H - Δ_A)).
+
+    High Δ_H (far from human) and low Δ_A (close to agent) -> high α̂ (likely agent).
+    """
+    if not session.events:
+        return 0.5
+    kernel = build_kernel(session.events)
+    delta_h, delta_a = compute_divergence(kernel)
+
+    if delta_h + delta_a < 1e-6:
+        return 0.5
+
+    # sigmoid: high when trajectory is more divergent from human than agent
+    return 1.0 / (1.0 + np.exp(-beta * (delta_h - delta_a)))
+
+
+def batch_estimate_alpha(sessions: List["Session"]) -> tuple[float, List[float]]:
+    """Estimate aggregate and per-session contamination."""
+    if not sessions:
+        return 0.0, []
+    alphas = [estimate_alpha(s) for s in sessions]
+    return float(np.mean(alphas)), alphas

lab/case/thesis/simplified.py

@@ -8,6 +8,14 @@ Objects:
 - Demand proxy q_hat via weighted action aggregation
 - COI leakage penalty for agent reconnaissance
 - Limbo: alternating price/demand history for trajectory analysis
+
+COI Correction (Jan 2026):
+The fundamental COI formulation is:
+    COI = E[p_start] - p_transaction
+
+This measures price erosion over time, not instantaneous margin × alpha.
+Agents use multiple sessions to gather information and find minimum prices.
+The price path from episode start to transaction captures information leakage.
 """
 from __future__ import annotations
 from dataclasses import dataclass, field

lab/case/thesis/simplified_env.py

@@ -6,6 +6,14 @@ Supports multiple reward modes and contamination scenarios.
 Action: price multipliers [0.5, 1.5] applied to reference prices
 Observation: [prices, demand_agg, alpha_est, margins, position_proxy]
 Reward: configurable objective (revenue, profit, robust, coi-aware)
+
+COI Correction (Jan 2026):
+The fundamental COI formulation is now:
+    COI = E[p_start] - p_transaction
+
+This measures price erosion over time, not instantaneous margin × alpha.
+Agents using different sessions gather information and drive prices down.
+The COITracker now tracks prices over windows to capture this effect.
 """
 from __future__ import annotations
 from dataclasses import dataclass
@@ -20,7 +28,7 @@ except ImportError:
     HAS_GYM = False
 
 from .simplified import System, Session, Event, Limbo, put_prices_to_market, compute_demand, estimate_alpha
-from .coi import COIWindow, compute_coi_window, coi_erosion
+from .coi import COIWindow, compute_coi_window, coi_erosion, COITracker, compute_multi_session_coi
 
 
 @dataclass
@@ -73,6 +81,12 @@ class PricingEnv(gym.Env if HAS_GYM else object):
         self._episode_rewards: list[float] = []
         self._demand_agg = np.zeros(self.n)
 
+        # COI tracking: store initial prices for E[p] calculation
+        self._initial_prices: np.ndarray | None = None
+        self._coi_tracker = COITracker(window_size=10)
+        self._last_coi_metrics: Dict[str, float] = {}
+        self._last_window_coi: float = 0.0
+
         self.action_space = spaces.Box(low=0.5, high=1.5, shape=(self.n,), dtype=np.float32)
         obs_dim = self.n + self.n + 1 + 1 + self.n + 1  # prices + demand + alpha_hat + alpha + margins + t
         self.observation_space = spaces.Box(low=-np.inf, high=np.inf, shape=(obs_dim,), dtype=np.float32)
@@ -109,8 +123,29 @@ class PricingEnv(gym.Env if HAS_GYM else object):
         if self._last_prices is not None:
             vol_penalty = cfg.lambda_vol * float(np.mean(np.abs(prices - self._last_prices) / (sys.refs + 1e-6)))
 
+        # Track prices for windowed COI calculation
+        self._coi_tracker.add_step(prices)
+
+        # CORRECTED COI CALCULATION:
+        # COI = E[p_start] - p_transaction (price erosion over time)
+        # Use initial prices as E[p] and compute multi-session COI
+        coi_metrics = compute_multi_session_coi(
+            sessions=sys._last_sessions,
+            costs=sys.costs,
+            alpha=self._alpha,
+            initial_prices=self._initial_prices,
+        )
+        leak = float(coi_metrics['leak'])
+
+        # Also compute window-based COI for trend analysis
+        window_coi = self._coi_tracker.compute_window_coi(sys.costs)
+
+        # Store both for info dict
+        self._last_coi_metrics = coi_metrics
+        self._last_window_coi = window_coi
+
+        # For backward compatibility, also compute the old-style COI
         coi = compute_coi_window(sys._last_sessions, sys.costs, demand_mapping=demand)
-        leak = float(coi.leak)
 
         reward_fns = {
             "revenue": lambda: revenue,
@@ -127,6 +162,11 @@ class PricingEnv(gym.Env if HAS_GYM else object):
         self._t, self._alpha = 0, self.cfg.alpha_true
         self._last_prices, self._last_demand = None, None
         self._episode_rewards, self._demand_agg = [], np.zeros(self.n)
+
+        # COI tracking: store initial prices as E[p] for COI = E[p] - p calculation
+        self._initial_prices = self._sys.refs.copy()
+        self._coi_tracker.reset()
+
         return self._build_obs(), {"alpha_true": self._alpha, "alpha_est": self._sys.alpha,
                                    "costs": self._sys.costs.copy(), "refs": self._sys.refs.copy()}
 
@@ -150,6 +190,9 @@ class PricingEnv(gym.Env if HAS_GYM else object):
         n_agents = int(self._alpha * self.cfg.sessions_per_step)
         coi = compute_coi_window(self._sys._last_sessions, self._sys.costs, demand_mapping=demand)
 
+        # Corrected COI metrics (price erosion over time)
+        coi_m = self._last_coi_metrics
+
         info = {
             "alpha_true": self._alpha, "alpha_est": self._sys.alpha,
             "alpha_error": abs(self._alpha - self._sys.alpha),
@@ -157,9 +200,19 @@ class PricingEnv(gym.Env if HAS_GYM else object):
             "n_purchases": int(np.sum(purchases)),
             "avg_margin": float(np.mean((prices - self._sys.costs) / self._sys.costs)),
             "n_sessions": len(demand), "n_agents": n_agents, "price_std": float(np.std(prices)),
+            # Legacy COI metrics (for backward compatibility)
             "coi_erosion": coi_erosion(coi.policy, coi.agent),
             "coi_policy": float(coi.policy), "coi_agent": float(coi.agent),
             "coi_leakage": float(coi.leak), "coi_survival": float(coi.survival_ratio),
+            # CORRECTED COI metrics: E[p] - p (price erosion)
+            "coi_policy_corrected": float(coi_m.get('policy_coi', 0)),
+            "coi_agent_corrected": float(coi_m.get('agent_coi', 0)),
+            "coi_human_corrected": float(coi_m.get('human_coi', 0)),
+            "coi_realized": float(coi_m.get('realized_coi', 0)),
+            "coi_leak_corrected": float(coi_m.get('leak', 0)),
+            "coi_order_stat_erosion": float(coi_m.get('order_stat_erosion', 0)),
+            "coi_survival_corrected": float(coi_m.get('survival_ratio', 1.0)),
+            "coi_window": float(self._last_window_coi),
             "cumulative_reward": sum(self._episode_rewards), "step": self._t,
         }
         return self._build_obs(), reward, self._t >= self.cfg.max_steps, False, info