algo-price-bundle
設計搭售定價，判斷搭售能不能增加獲利
中文翻譯
---
name: "algo-price-bundle"
description: "用純搭售、混合搭售和消費者剩餘分析來設計搭售定價策略。當使用者需要替商品組合定價、判斷搭售能不能增加獲利，或分析拆售的機會時使用，即使他們說的是『should we bundle these products』『bundle pricing』或『package deal pricing』。"
metadata:
category: "WP-39 定價演算法"
tags: ["pricing", "bundling", "consumer-surplus", "product-strategy"]
---
# 搭售定價策略
## 概述
搭售定價是把多個產品以合併價格一起賣，透過在各產品之間平均估值，來榨取消費者剩餘。適用於顧客估值各異、而且呈負相關的情況。三種類型：純搭售（只賣組合）、混合搭售（組合 + 單賣）、拆售。
## 何時使用
**觸發條件：**
- 決定要不要把產品 / 服務搭在一起賣
- 設定組合價相對於各單品價格的關係
- 分析目前的組合該不該拆開賣
**不該使用的情況：**
- 產品需求彼此獨立、估值沒有相關性時（搭售沒有價值）
- 法規禁止搭售安排時
## 演算法
```
IRON LAW: Bundling Increases Profit ONLY With NEGATIVELY CORRELATED Valuations
If ALL customers value the same items highly, bundling adds no surplus.
Bundling works when: Customer A values Product 1 high + Product 2 low,
while Customer B values Product 1 low + Product 2 high. The bundle
price captures both at a middle price neither would pay for their
low-value item alone.
```
### 階段 1：輸入驗證
收集：每個客群對各單品的估值（或願付價格）。計算各產品之間估值的相關性。
**關卡：** 有估值資料，相關性為負或混合。
### 階段 2：核心演算法
1. 計算最佳單品價格：讓 Σ(每個產品的營收) 最大
2. 計算最佳組合價：在聯合估值分布下，找出讓組合營收最大的價格
3. 比較：純搭售營收、混合搭售營收、單品定價營收
4. 混合搭售：組合價 < 各單品價格加總；折扣 = 搭售的誘因
### 階段 3：驗證
檢查：混合搭售應該弱優於純搭售和單品定價（Adams & Yellen, 1976）。如果不是，要重新檢視估值假設。
**關卡：** 混合搭售的獲利 ≥ max(純搭售, 單品定價)。
### 階段 4：輸出
回傳最佳定價策略，附上獲利推估。
## 輸出格式
```json
{
"recommendation": "mixed_bundling",
"prices": {"product_a": 299, "product_b": 199, "bundle_ab": 399},
"profit_comparison": {"individual": 45000, "pure_bundle": 48000, "mixed_bundle": 52000},
"metadata": {"segments": 3, "valuation_correlation": -0.35}
}
```
## 範例
### 輸入輸出範例
**輸入：** 產品 A（WTP：Seg1=$80、Seg2=$30），產品 B（WTP：Seg1=$30、Seg2=$70）。每個客群有 100 位顧客。
**預期：** 單品最佳價：A=$80、B=$70，營收=$15K。組合價 $100：兩個客群都買，營收=$20K。搭售勝出。
### 邊界情況
| 輸入 | 預期 | 原因 |
|-------|----------|-----|
| 完全正相關 | 單品定價勝出 | 所有顧客對兩者都估值高，或都估值低 |
| 其中一個產品是免費品 | 組合 = 付費品 + 免費品 | 軟體常見（免費試用 + 付費附加元件） |
| 組合裡有 10 個以上產品 | 混合搭售很複雜 | 組合太多，改用分級的組合 |
## 注意事項
- **自我蠶食**：組合可能蠶食高 WTP 的顧客，他們本來會以更高的總價個別購買。混合搭售可以減輕這點。
- **感知價值**：組合折扣要讓人明顯感受到。$299+$299 的產品組成 $499 的組合（折 16%），比兩個各 $260 的產品賣 $499 更容易被感知。
- **邊際成本很重要**：邊際成本為零的產品（軟體、數位產品）從搭售得到的好處最大。銷貨成本高的實體商品，利潤空間比較緊。
- **複雜度的成本**：組合選項太多會造成選擇困難。限制在 2-3 個組合層級。
- **法規上的搭售限制**：在某些市場，強迫購買某個產品才能買另一個是違法的（反壟斷）。要確保組合是折扣，不是強制條件。
## 參考資料
- Adams-Yellen 搭售理論，見 `references/bundling-theory.md`
- 多產品定價最佳化，見 `references/multi-product-pricing.md`英文原文
---
name: "algo-price-bundle"
description: "Design bundle pricing strategies using pure bundling, mixed bundling, and consumer surplus analysis. Use this skill when the user needs to set prices for product bundles, determine whether bundling increases profit, or analyze unbundling opportunities — even if they say 'should we bundle these products', 'bundle pricing', or 'package deal pricing'."
metadata:
category: "WP-39 定價演算法"
tags: ["pricing", "bundling", "consumer-surplus", "product-strategy"]
---
# Bundle Pricing Strategy
## Overview
Bundle pricing sells multiple products together at a combined price, extracting consumer surplus by averaging valuations across products. Works when customers have heterogeneous, negatively correlated valuations. Three types: pure bundling (bundle only), mixed bundling (bundle + individual), unbundling.
## When to Use
**Trigger conditions:**
- Deciding whether to bundle products/services together
- Setting bundle price relative to individual prices
- Analyzing whether a current bundle should be unbundled
**When NOT to use:**
- When products have independent demand with no valuation correlation (bundling adds no value)
- When regulations prohibit tying arrangements
## Algorithm
```
IRON LAW: Bundling Increases Profit ONLY With NEGATIVELY CORRELATED Valuations
If ALL customers value the same items highly, bundling adds no surplus.
Bundling works when: Customer A values Product 1 high + Product 2 low,
while Customer B values Product 1 low + Product 2 high. The bundle
price captures both at a middle price neither would pay for their
low-value item alone.
```
### Phase 1: Input Validation
Collect: individual product valuations (or willingness to pay) per customer segment. Compute correlation of valuations across products.
**Gate:** Valuation data available, correlation is negative or mixed.
### Phase 2: Core Algorithm
1. Compute optimal individual prices: maximize Σ(revenue per product)
2. Compute optimal bundle price: find price that maximizes bundle revenue given joint valuation distribution
3. Compare: pure bundling revenue, mixed bundling revenue, individual pricing revenue
4. Mixed bundling: set bundle price < sum of individual prices; discount = bundle incentive
### Phase 3: Verification
Check: mixed bundling should weakly dominate both pure bundling and individual pricing (Adams & Yellen, 1976). If not, review valuation assumptions.
**Gate:** Mixed bundling profit ≥ max(pure bundling, individual pricing).
### Phase 4: Output
Return optimal pricing strategy with profit projections.
## Output Format
```json
{
"recommendation": "mixed_bundling",
"prices": {"product_a": 299, "product_b": 199, "bundle_ab": 399},
"profit_comparison": {"individual": 45000, "pure_bundle": 48000, "mixed_bundle": 52000},
"metadata": {"segments": 3, "valuation_correlation": -0.35}
}
```
## Examples
### Sample I/O
**Input:** Product A (WTP: Seg1=$80, Seg2=$30), Product B (WTP: Seg1=$30, Seg2=$70). Each segment has 100 customers.
**Expected:** Individual optimal: A=$80, B=$70, revenue=$15K. Bundle at $100: both segments buy, revenue=$20K. Bundling wins.
### Edge Cases
| Input | Expected | Why |
|-------|----------|-----|
| Perfectly positive correlation | Individual pricing wins | All customers value both high or both low |
| One product is free good | Bundle = premium + free | Common in software (free trial + paid add-on) |
| 10+ products in bundle | Mixed bundling complex | Too many combinations — use tiered bundles |
## Gotchas
- **Cannibalization**: The bundle may cannibalize high-WTP customers who would have bought individually at higher total. Mixed bundling mitigates this.
- **Perceived value**: Bundle discount must be salient. A $499 bundle of $299+$299 products (16% off) is better perceived than $499 for two $260 products.
- **Marginal cost matters**: Zero marginal cost products (software, digital) benefit most from bundling. Physical goods with high COGS have tighter margins.
- **Complexity cost**: Too many bundle options create choice paralysis. Limit to 2-3 bundle tiers.
- **Regulatory tying**: In some markets, forcing purchase of one product to get another is illegal (antitrust). Ensure bundle is a discount, not a requirement.
## References
- For Adams-Yellen bundling theory, see `references/bundling-theory.md`
- For multi-product pricing optimization, see `references/multi-product-pricing.md`