---

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

{
  "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