"""Minimal implementation of thesis pricing system. Implements the core loop: prices -> sessions -> demand -> prices with behavioral separability and robust pricing objective. Objects: - Session trajectories tau_s from mixture of H/A behavioral profiles - 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 from typing import Dict, List, Tuple import numpy as np from .coi import COIWindow, compute_coi_window from .separability import TRANS_H, TRANS_A, kl_div, build_kernel, compute_divergence, estimate_alpha ACTION_WEIGHTS = {"add_to_cart": 0.8, "checkout": 0.9, "purchase": 1.0, "view": 0.15, "detail": 0.25, "hover": 0.3, "start": 0.05, "end": 0.0} @dataclass class Event: action: str product_idx: int price_seen: float ts: float @dataclass class Session: sid: str events: List[Event] actor: str # H or A (ground truth label) theta: Dict[str, float] = field(default_factory=dict) def compute_demand(session: Session) -> float: """Compute demand proxy q_hat = sum_k omega(a_k) for session.""" return sum(ACTION_WEIGHTS.get(e.action, 0.1) for e in session.events) def sample_trajectory(rng: np.random.Generator, trans: Dict, prices: np.ndarray, costs: np.ndarray, theta: Dict[str, float], is_agent: bool, session_noise: float = 0.02, surge: float = 0.08, max_mult: float = 1.8) -> Tuple[List[Event], int]: """Sample session trajectory from behavioral kernel.""" pidx = int(rng.integers(0, len(prices))) cost, base = float(costs[pidx]), float(prices[pidx]) * (1.0 + rng.normal(0.0, session_noise)) base = float(np.clip(base, cost * 1.01, float(prices[pidx]) * 2.0)) price, signal, state, t = base, 0.0, "start", 0.0 events = [] while state != "end" and len(events) < 30: probs = trans.get(state, {"end": 1.0}) nxt = rng.choice(list(probs.keys()), p=list(probs.values())) if nxt == "purchase": # purchase conversion check rel = max((price - cost) / (cost + 1e-6), 0.0) p_buy = float(np.clip(theta.get("base_conv", 0.2) * np.exp(-theta.get("price_sens", 2.0) * rel), 0.0, 1.0)) if rng.random() > p_buy: nxt = "end" state = nxt if state not in {"start", "end"}: events.append(Event(action=state, product_idx=pidx, price_seen=float(price), ts=t)) signal += float(ACTION_WEIGHTS.get(state, 0.1)) price = float(np.clip(base * (1.0 + surge * signal), cost * 1.01, base * max_mult)) t += max(0.2, rng.gamma(1.5, 0.8) if is_agent else rng.gamma(2.0, 1.2)) return events, pidx def put_prices_to_market(prices: np.ndarray, costs: np.ndarray, alpha: float = 0.2, n_sessions: int = 50, seed: int | None = None) -> Tuple[List[Session], Dict[str, float]]: """Generate sessions from mixture model. Returns sessions and demand mapping sid -> q_hat.""" rng = np.random.default_rng(seed) sessions, demand = [], {} for i in range(n_sessions): sid = f"s{i:04d}" is_agent = rng.random() < alpha trans = TRANS_A if is_agent else TRANS_H theta = {"price_sens": rng.uniform(0.05, 0.2), "base_conv": 0.01} if is_agent else \ {"price_sens": rng.uniform(1.5, 4.0), "base_conv": rng.uniform(0.2, 0.5)} events, _ = sample_trajectory(rng, trans, prices, costs=costs, theta=theta, is_agent=is_agent) session = Session(sid=sid, events=events, actor="A" if is_agent else "H", theta=theta) sessions.append(session) demand[sid] = compute_demand(session) return sessions, demand @dataclass class LimboUpdate: utype: str # "prices" or "demand" data: np.ndarray | Dict[str, float] t: int class Limbo: """Historical trajectory of alternating price/demand observations.""" def __init__(self): self.history: List[LimboUpdate] = [] self._t = 0 def add_update(self, utype: str, data: np.ndarray | Dict[str, float]) -> Dict: self.history.append(LimboUpdate(utype=utype, data=data, t=self._t)) self._t += 1 return {"action": "observe_demand" if utype == "prices" else "set_prices"} def get_prices_history(self) -> List[np.ndarray]: return [u.data for u in self.history if u.utype == "prices"] def get_demand_history(self) -> List[Dict[str, float]]: return [u.data for u in self.history if u.utype == "demand"] class System: """Main pricing system implementing robust Stackelberg objective. Manages the alternating loop: set prices p_t -> observe demand Q_hat(p_t) -> estimate contamination alpha from behavioral signals -> compute next prices. """ def __init__(self, n_products: int = 10, costs: np.ndarray | None = None, lambda_coi: float = 0.5, seed: int | None = 42): self.n = n_products self.rng = np.random.default_rng(seed) self.costs = costs if costs is not None else self.rng.uniform(10, 50, n_products) self.refs = self.costs * (1 + self.rng.uniform(0.2, 0.5, n_products)) self.lambda_coi = lambda_coi self.limbo = Limbo() self._alpha_est = 0.2 self._sessions: List[Session] = [] self._last_sessions: List[Session] = [] self._last_coi: COIWindow | None = None @property def alpha(self) -> float: return self._alpha_est def _estimate_alpha_from_sessions(self) -> float: if not self._sessions: return self._alpha_est return float(np.mean([estimate_alpha(s) for s in self._sessions[-50:]])) def _revenue_under_demand(self, prices: np.ndarray, demand: Dict[str, float]) -> float: agg = np.zeros(self.n) for sid, q in demand.items(): sess = next((s for s in self._sessions if s.sid == sid), None) if sess and sess.events: agg[sess.events[0].product_idx] += q return float(np.dot(prices, agg)) def _compute_coi_window(self, demand: Dict[str, float]) -> COIWindow: if not self._last_sessions: zeros = np.zeros(self.n, dtype=float) return COIWindow(policy=0.0, agent=0.0, leak=0.0, survival_ratio=0.0, policy_by_product=zeros, agent_by_product=zeros, demand_weights=zeros) return compute_coi_window(self._last_sessions, self.costs, demand_mapping=demand) def _objective(self, prices: np.ndarray, demand: Dict[str, float]) -> float: """Robust objective: R(p,d) - lambda * COI_leak.""" profit = self._revenue_under_demand(prices, demand) - float(np.sum(self.costs)) self._last_coi = self._compute_coi_window(demand) return profit - self.lambda_coi * self._last_coi.leak def compute_prices(self, demand: Dict[str, float] | None = None) -> np.ndarray: """Compute next prices via heuristic margin adjustment based on alpha estimate.""" self._alpha_est = self._estimate_alpha_from_sessions() margin_scale = 1.0 - 0.5 * self._alpha_est # defensive pricing under high contamination margins = (self.refs - self.costs) * margin_scale noise = self.rng.normal(0, 0.02, self.n) * self.costs prices = np.clip(self.costs + margins + noise, self.costs * 1.02, self.refs * 1.3) self.limbo.add_update("prices", prices) return prices def observe_demand(self, prices: np.ndarray, alpha_true: float = 0.2, n_sessions: int = 50) -> Dict[str, float]: sessions, demand_map = put_prices_to_market(prices, costs=self.costs, alpha=alpha_true, n_sessions=n_sessions, seed=int(self.rng.integers(0, 10000))) self._last_sessions = sessions self._sessions.extend(sessions) self.limbo.add_update("demand", demand_map) return demand_map def step(self, alpha_true: float = 0.2, n_sessions: int = 50) -> Tuple[np.ndarray, Dict[str, float], float, COIWindow]: demand_hist = self.limbo.get_demand_history() prices = self.compute_prices(demand_hist[-1] if demand_hist else None) demand = self.observe_demand(prices, alpha_true, n_sessions) reward = self._objective(prices, demand) return prices, demand, reward, self._last_coi or self._compute_coi_window(demand) def run(self, n_steps: int = 100, alpha_true: float = 0.2) -> Dict: traj = {"prices": [], "demand": [], "rewards": [], "alpha_est": [], "alpha_true": alpha_true, "coi_policy": [], "coi_agent": [], "coi_leak": [], "coi_survival": []} for _ in range(n_steps): p, d, r, coi = self.step(alpha_true) traj["prices"].append(p); traj["demand"].append(d); traj["rewards"].append(r) traj["alpha_est"].append(self._alpha_est) traj["coi_policy"].append(coi.policy); traj["coi_agent"].append(coi.agent) traj["coi_leak"].append(coi.leak); traj["coi_survival"].append(coi.survival_ratio) return traj if __name__ == "__main__": sys = System(n_products=5, seed=42) traj = sys.run(n_steps=20, alpha_true=0.25) print(f"avg reward: {np.mean(traj['rewards']):.2f}, final alpha_hat: {traj['alpha_est'][-1]:.3f}, " f"COI_policy: {np.mean(traj['coi_policy']):.3f}, COI_agent: {np.mean(traj['coi_agent']):.3f}, leak: {np.mean(traj['coi_leak']):.3f}") prices = np.array([20.0, 35.0, 50.0, 25.0, 40.0]) costs = np.array([15.0, 28.0, 40.0, 18.0, 30.0]) sessions, demand = put_prices_to_market(prices, costs=costs, alpha=0.3, n_sessions=20, seed=123) print(f'sessions: {len(sessions)}, agents: {sum(1 for s in sessions if s.actor=="A")}') for n in [1, 5, 10, 50, 100]: # theoretical: erosion = 1 - 2/(N+1) for uniform order statistic print(f'N={n:3d} agents -> COI erosion: {1.0 - 2.0/(n+1):.3f}') events = [Event('view', 0, 20.0, 0.1), Event('detail', 0, 20.0, 0.5), Event('cart', 0, 20.0, 1.0), Event('purchase', 0, 20.0, 2.0)] print(f'human-like session alpha_hat: {estimate_alpha(Session(sid="test", events=events, actor="H")):.3f}') events_a = [Event('view', 0, 20.0, 0.1), Event('detail', 0, 20.0, 0.2), Event('view', 0, 20.0, 0.3), Event('detail', 0, 20.0, 0.4)] print(f'agent-like session alpha_hat: {estimate_alpha(Session(sid="test2", events=events_a, actor="A")):.3f}')