2nd/10_Wiki/Topics/Economics & Algorithms/Dynamic Pricing.md

---
id: wiki-2026-0508-dynamic-pricing
title: Dynamic Pricing
category: 10_Wiki/Topics
status: verified
canonical_id: self
aliases: [동적 가격 책정, 변동 가격제, Surge Pricing]
duplicate_of: none
source_trust_level: A
confidence_score: 0.9
verification_status: applied
tags: [economics, pricing, monetization, ml]
raw_sources: []
last_reinforced: 2026-05-10
github_commit: pending
tech_stack:
  language: Python
  framework: scikit-learn / XGBoost
---

# Dynamic Pricing

## 매 한 줄
> **"매 가격은 매 순간 다르다"**. 매 수요·재고·시간·세그먼트 signal 의 기반에서 매 price 가 매 real-time 의 조정. 매 Uber surge, 매 airline yield management, 매 2026 게임 IAP A/B price 의 mainstream.

## 매 핵심

### 매 입력 signal
- **수요 (Demand)**: 매 search volume, 매 conversion rate, 매 cart-add rate.
- **공급 (Supply / Inventory)**: 매 남은 stock, 매 server capacity.
- **시간 (Time)**: 매 hour-of-day, 매 day-of-week, 매 holiday.
- **사용자 segment**: 매 LTV tier, 매 churn risk, 매 region 의 PPP.
- **경쟁사 price**: 매 web scraping 의 competitor catalog.

### 매 알고리즘 family
- **Rule-based**: 매 if (inventory < 20%) then price *= 1.3.
- **Elasticity model**: 매 demand curve 의 fit → 매 revenue-maximizing point 의 추출.
- **Bandit / RL**: 매 contextual bandit 의 사용 — 매 explore vs exploit.
- **Deep learning**: 매 transformer 의 시퀀스 → 매 next-period price prediction.

### 매 응용
1. Airline / hotel yield management (매 origin domain).
2. Ride-sharing surge (Uber, Lyft).
3. E-commerce flash sale + personalized coupon.
4. Game IAP regional pricing + LTV tier offer.

## 💻 패턴

### Elasticity 추정 (log-log regression)
```python
import numpy as np
import statsmodels.api as sm

# price, qty observed across past promotions
log_p = np.log(prices)
log_q = np.log(quantities)
X = sm.add_constant(log_p)
model = sm.OLS(log_q, X).fit()
elasticity = model.params[1]  # 매 typical -1.2 ~ -2.5
print(f"Price elasticity: {elasticity:.2f}")
```

### Revenue-maximizing price (constant elasticity)
```python
def optimal_price(cost, elasticity):
    """매 monopoly markup formula: P* = c * e/(e+1) for e<-1"""
    if elasticity >= -1:
        raise ValueError("Inelastic demand — revenue unbounded")
    return cost * elasticity / (elasticity + 1)

print(optimal_price(cost=2.0, elasticity=-1.5))  # → 6.0
```

### Contextual bandit (LinUCB)
```python
import numpy as np

class LinUCB:
    def __init__(self, n_arms, n_features, alpha=1.0):
        self.alpha = alpha
        self.A = [np.eye(n_features) for _ in range(n_arms)]
        self.b = [np.zeros(n_features) for _ in range(n_arms)]

    def select(self, context):
        ucb = []
        for a in range(len(self.A)):
            A_inv = np.linalg.inv(self.A[a])
            theta = A_inv @ self.b[a]
            mu = context @ theta
            sigma = self.alpha * np.sqrt(context @ A_inv @ context)
            ucb.append(mu + sigma)
        return int(np.argmax(ucb))

    def update(self, arm, context, reward):
        self.A[arm] += np.outer(context, context)
        self.b[arm] += reward * context
```

### XGBoost demand forecaster
```python
import xgboost as xgb
import pandas as pd

features = ["price", "hour", "dow", "is_holiday", "competitor_price",
            "inventory", "user_ltv_tier", "region_ppp"]
dtrain = xgb.DMatrix(df[features], label=df["units_sold"])
params = {"objective": "reg:squarederror", "max_depth": 6, "eta": 0.1}
model = xgb.train(params, dtrain, num_boost_round=300)

def expected_revenue(price, ctx):
    ctx2 = {**ctx, "price": price}
    qty = model.predict(xgb.DMatrix(pd.DataFrame([ctx2])))[0]
    return price * qty
```

### Personalized price (LTV tier)
```python
def personalized_price(base_price, user):
    tier = user["ltv_tier"]  # "whale", "dolphin", "minnow"
    region_factor = REGION_PPP[user["country"]]  # 매 0.4 ~ 1.2
    tier_factor = {"whale": 1.0, "dolphin": 0.85, "minnow": 0.6}[tier]
    return round(base_price * region_factor * tier_factor, 2)
```

### Surge guardrails
```python
def safe_surge(base, raw_multiplier):
    # 매 PR backlash 의 prevent
    capped = min(raw_multiplier, 3.0)
    floored = max(capped, 0.7)
    return base * floored
```

### A/B price test (Bayesian)
```python
import numpy as np
from scipy.stats import beta

def bayesian_ab(buyers_a, visitors_a, buyers_b, visitors_b, n_sim=100_000):
    a = beta(1 + buyers_a, 1 + visitors_a - buyers_a).rvs(n_sim)
    b = beta(1 + buyers_b, 1 + visitors_b - buyers_b).rvs(n_sim)
    return float(np.mean(b > a))  # 매 P(B > A)
```

## 매 결정 기준
| 상황 | Approach |
|---|---|
| 매 stable demand, 매 cost-plus | Rule-based + manual ladder |
| 매 elastic, 매 abundant data | Elasticity model + grid search |
| 매 cold start, 매 many SKUs | Contextual bandit |
| 매 high-stakes (regulated) | Constrained optimization + audit log |

**기본값**: 매 elasticity model 의 시작, 매 enough data 의 수집 후 contextual bandit 의 graduate.

## 🔗 Graph
- 부모: [[게임 수익화 모델]]
- 변형: [[Surge Pricing]]
- 응용: [[IAP_In_App_Purchase]] · [[Live-ops]]

## 🤖 LLM 활용
**언제**: 매 elasticity 추정 의 EDA, 매 price ladder design, 매 A/B test 의 statistical analysis.
**언제 X**: 매 production pricing decision 의 single LLM call — 매 hallucination risk 의 too high.

## ❌ 안티패턴
- **Race-to-bottom**: 매 competitor 의 blind matching → margin collapse.
- **Surge backlash**: 매 cap 없는 multiplier → user trust 의 손상 (매 Uber NYE 8x 의 사례).
- **Personalization 의 leak**: 매 same item 의 different price 의 user-visible → fairness backlash.
- **Cold-start naïveté**: 매 new SKU 에 매 zero data 의 RL 의 직접 deploy → wild swing.

## 🧪 검증 / 중복
- Verified (Phillips 2005 *Pricing and Revenue Optimization*; Uber Engineering blog 2023).
- 신뢰도 A.

## 🕓 Changelog
| 날짜 | 변경 |
|---|---|
| 2026-05-08 | Phase 1 |
| 2026-05-10 | Manual cleanup — full content with elasticity, bandit, A/B patterns |