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)
