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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

  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
  1. 计算最优单品价格：最大化各产品收入总和
  2. 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
  3. 对比：pure bundling收入、mixed bundling收入、单品定价收入
  4. 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

InputExpectedWhy
Perfectly positive correlationIndividual pricing winsAll customers value both high or both low
One product is free goodBundle = premium + freeCommon in software (free trial + paid add-on)
10+ products in bundleMixed bundling complexToo 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