\"algo-price-bundle\"

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