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Chinese

Bundle Pricing Strategy

捆绑定价策略（Bundle Pricing Strategy）

Overview

概述

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.

Bundle pricing是指将多种产品组合在一起以统一价格销售，通过平均不同产品的估值来获取Consumer Surplus。当客户对产品的估值存在异质性且呈负相关时，该策略最为有效。主要分为三种类型：pure bundling（仅捆绑销售）、mixed bundling（捆绑+单独销售）、unbundling（拆分销售）。

When to Use

适用场景

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

触发条件：

决定是否将产品/服务捆绑销售
设定套餐价格相对于单品价格的定价
分析现有套餐是否应该拆分销售

不适用场景：

产品需求独立，估值无相关性（捆绑销售无法增加价值）
法规禁止搭售安排

Algorithm

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.

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

阶段1：输入验证

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.

收集：各客户群体对单个产品的估值（或支付意愿）。计算不同产品估值之间的相关性。 准入条件： 具备估值数据，且相关性为负或混合相关。

Phase 2: Core Algorithm

阶段2：核心算法

Compute optimal individual prices: maximize Σ(revenue per product)
Compute optimal bundle price: find price that maximizes bundle revenue given joint valuation distribution
Compare: pure bundling revenue, mixed bundling revenue, individual pricing revenue
Mixed bundling: set bundle price < sum of individual prices; discount = bundle incentive

计算最优单品价格：最大化各产品收入总和
计算最优套餐价格：根据联合估值分布找到能最大化套餐收入的价格
对比：pure bundling收入、mixed bundling收入、单品定价收入
Mixed bundling：设定套餐价格＜单品价格总和；折扣即为捆绑激励

Phase 3: Verification

阶段3：验证

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).

验证：mixed bundling的收益应弱优于pure bundling和单品定价（Adams & Yellen, 1976）。若不符合，需重新审视估值假设。 准入条件： mixed bundling利润≥max(pure bundling利润, 单品定价利润)。

Phase 4: Output

阶段4：输出

Return optimal pricing strategy with profit projections.

返回最优定价策略及利润预测。

Output Format

输出格式

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}
}

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

示例

Sample I/O

输入输出示例

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.

输入： 产品A（支付意愿：群体1=$80，群体2=$30），产品B（支付意愿：群体1=$30，群体2=$70）。每个群体各有100名客户。 预期结果： 最优单品定价：A=$80，B=$70，收入=$15000。套餐定价$100：两个群体都会购买，收入=$20000。捆绑销售更优。

Edge Cases

边缘案例

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

输入	预期结果	原因
完全正相关估值	单品定价更优	所有客户对两款产品的估值均同时偏高或偏低
一款产品为免费品	套餐=付费产品+免费产品	软件行业常见（免费试用+付费增值服务）
套餐包含10+款产品	Mixed bundling操作复杂	组合过多——建议使用分层套餐

Gotchas

注意事项

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.

客户分流（Cannibalization）：套餐可能会分流原本会以更高总价购买单品的高支付意愿客户。Mixed bundling可缓解这一问题。
感知价值：套餐折扣需清晰可见。例如，原价$299+$299的产品组合成$499的套餐（优惠16%），比两款原价$260的产品组合成$499的套餐更能让客户感知到优惠。
边际成本：边际成本为零的产品（软件、数字产品）从捆绑销售中获益最多。高COGS的实体产品利润空间更有限。
复杂度成本：过多套餐选项会导致选择困难症。建议限制为2-3个套餐层级。
监管搭售限制：部分市场中，强制购买一款产品才能获得另一款产品属于违法行为（反垄断）。需确保套餐是折扣优惠，而非强制要求。

References

参考资料

For Adams-Yellen bundling theory, see
```
references/bundling-theory.md
```
For multi-product pricing optimization, see
```
references/multi-product-pricing.md
```

关于Adams-Yellen捆绑理论，详见
```
references/bundling-theory.md
```
关于多产品定价优化，详见
```
references/multi-product-pricing.md
```