Auction Winner's-Curse Haircut

Table of Contents

• [Example](#example)
• [Workflow](#workflow)
• [Common Patterns](#common-patterns)
• [Guardrails](#guardrails)
• [Quick Reference](#quick-reference)

Example

Scenario: Bidder has estimated a target's value at rawvaluation = $30. Six informed bidders are competing. Estimates across bidders are moderately dispersed (signaldispersion = 40 out of 100). The target is a well-known commodity (everyone models it similarly).

Inputs:

• raw_valuation: 30
• valuetype: commonvalue
• ninformedbidders: 6
• signal_dispersion: 40

Haircut computation:

haircut_pct = min(35, 10 + log(6) x 5 + 40 x 0.2)
            = min(35, 10 + 1.792 x 5 + 8)
            = min(35, 10 + 8.96 + 8)
            = min(35, 26.96)
            = 26.96  (clamped below 35 ceiling)

Output:

• adjusted_valuation = 30 x (1 - 0.2696) = $21.91
• haircut_pct = 26.96
• classification_rationale: "Common-value target with 6 informed bidders and moderate signal dispersion. Winning is material evidence of over-estimation; Kagel-Levin experimental range (15-30%) applies."
• applied: true

Contrast -- private-value case: Same rawvaluation = $30, but valuetype = private_value (target matters uniquely to this bidder). Haircut = 0. Adjusted = $30. Applied = false. Rationale: "No informational-asymmetry discount; winning is not adverse because other bidders do not value the target similarly."

Workflow

Copy this checklist and track progress:

Winner's-Curse Haircut Progress:
- [ ] Step 1: Classify value_type (common / private / mixed)
- [ ] Step 2: Validate inputs (range checks, N >= 1)
- [ ] Step 3: Short-circuit for private-value
- [ ] Step 4: Compute haircut_pct via formula
- [ ] Step 5: Apply haircut to raw_valuation
- [ ] Step 6: Emit structured output with rationale

Step 1: Classify value_type

Classification is a judgment call and MUST be explicit. The caller should pass it; this skill validates the choice against the decision tree in [resources/template.md](resources/template.md#value-type-decision-tree).

• common_value -- target's value is similar for all bidders because information is shared and the underlying quantity is the same (examples: named closer on waivers, headline prospect call-up, publicly traded stock in a tender, liquid commodity)
• private_value -- target's value is meaningfully higher (or lower) for this bidder than for others, due to fit, complementarity, or idiosyncratic preference (examples: handcuff to a reliever you already own, platoon fit for your lineup, a house next door to an existing property)
• mixed -- target has a shared core value plus a private-value increment (examples: late-season FAAB claim on a hot hitter where everyone agrees on the base projection but the bidder's specific category need is extra)

Step 2: Validate inputs

• raw_valuation is a finite non-negative number
• value_type is one of the three allowed strings
• ninformedbidders is an integer >= 1 (clamp at upper bound if exotic, e.g. 50)
• signal_dispersion is in [0, 100]

Step 3: Short-circuit for private-value

If valuetype == "privatevalue", skip the formula entirely:

• haircut_pct = 0
• adjustedvaluation = rawvaluation
• applied = false

See [resources/methodology.md](resources/methodology.md#why-private-value-gets-zero-haircut) for the Bayesian reason this short-circuit is correct.

Step 4: Compute haircut percentage

For common_value targets:

haircut_pct = min(35, 10 + log(N) x 5 + signal_dispersion x 0.2)

The min(35, ...) ceiling hard-caps the haircut at 35% even at extreme N and dispersion. This reflects that empirical Kagel-Levin estimates rarely exceed 30%; 35% is the outer envelope.

For mixed targets, interpolate:

mix_common_weight  = 0.6  (default; caller may override)
mix_private_weight = 1 - mix_common_weight
haircut_pct = mix_common_weight x (common_value_haircut) + mix_private_weight x 0

See [resources/methodology.md](resources/methodology.md#haircut-formula-derivation) for formula intuition (log-N captures the adverse-selection severity growing with more competitors; linear dispersion term captures the variance of bidder estimates).

Step 5: Apply haircut

adjusted_valuation = raw_valuation x (1 - haircut_pct / 100)

Step 6: Emit structured output

Return:

{
  "adjusted_valuation": <number>,
  "haircut_pct": <number in [0, 35]>,
  "classification_rationale": "<one-sentence justification>",
  "applied": <bool>
}

Validate using [resources/evaluators/rubricauctionwinnerscursehaircut.json](resources/evaluators/rubricauctionwinnerscursehaircut.json). Minimum standard: average score >= 3.5.

Common Patterns

Pattern 1: Headline Common-Value Target, Many Bidders

• Example: Top-100 prospect call-up in fantasy FAAB (N=6-8); prediction-market contract on a high-salience event; M&A target covered by many investment banks
• Typical inputs: N in [5, 10], signal_dispersion in [30, 60]
• Typical haircut: 22-32%
• Why: Strong adverse-selection; winning almost surely means you were highest of many similar estimates
• Watch for: Do not double-count with first-price shading -- the two are independent corrections (see auction-first-price-shading for shading)

Pattern 2: Private-Value Complement (Handcuff)

• Example: Backup reliever to your own closer; land adjacent to land you already own; puzzle piece that fits only your collection
• Typical inputs: N = 1-2, valuetype = privatevalue
• Typical haircut: 0% (short-circuited)
• Why: No adverse selection -- winning is not evidence you over-estimated, because others genuinely value the target less
• Watch for: Make sure the private-value claim is real. If three other bidders also have a complementary use, it is closer to common-value

Pattern 3: Mixed Late-Season Streaming Claim

• Example: Hot hitter whose projection everyone agrees on, but fits a specific category need you have; ad-auction keyword with a common CPC baseline but a bidder-specific conversion uplift
• Typical inputs: N in [3, 5], signaldispersion in [20, 40], valuetype = mixed with mixcommonweight around 0.5-0.7
• Typical haircut: 10-18%
• Why: Partial adverse selection, partial private value
• Watch for: Explicitly estimate and record the common/private split; do not default to mixed when a clear binary classification applies

Pattern 4: Thin-Field Common Value (Low N)

• Example: Niche common-value target in a small auction pool (N = 2)
• Typical inputs: N = 2, dispersion anywhere
• Typical haircut: 14-18%
• Why: Even with only 2 bidders, common-value winner's curse operates -- winning means you exceeded the other informed estimate. Still smaller than large-N cases because adverse-selection severity grows with log(N)
• Watch for: Do not set haircut to 0 just because N is low; private-value requires a separate claim about value heterogeneity

Guardrails

1. Classification must be explicit. Never infer value_type silently from other inputs. The caller passes it; the skill validates. A missing or ambiguous classification is an error, not a default.

1. Private-value short-circuit is absolute. If the caller asserts private-value, haircut is zero even when N is large. This is correct: if others genuinely value the target less, then their bids do not carry adverse information about your own estimate.

1. Never stack this haircut with another winner's-curse correction. Downstream systems that already apply Bayesian bid shading (e.g., auction-first-price-shading's N-bidder shade) are correcting a different phenomenon (strategic shading for expected surplus). Apply both; do not apply either twice.

1. Cap at 35%. The empirical Kagel-Levin range is 15-30%. The 35% ceiling provides headroom for very large N plus high dispersion but prevents the formula from producing absurd discounts (e.g., 80%).

1. N >= 1. N = 1 means the bidder is alone; log(1) = 0 so the formula yields haircutpct = 10 + signaldispersion x 0.2. For a true monopsony (no competing informed bidder), the caller should pass private_value instead -- there is no adverse-selection mechanism without competitors.

1. Signal dispersion is a proxy, not a measurement. In practice it is rarely directly observable. Estimate from: historical bid-spread in comparable auctions, disagreement among public projection systems, or degree of public information asymmetry. Document the basis.

1. Mixed value requires an explicit weight. Do not silently default to 0.6. Callers should state the common/private split and its justification. If they cannot, classify as commonvalue (conservative) or privatevalue (aggressive), not mixed.

1. Domain-neutral contract. This skill does not know about FAAB, fantasy baseball, or any specific auction environment. Callers translate their domain inputs into the generic four-field contract; the skill returns a generic output which the caller then interprets.

Quick Reference

Core formula:

if value_type == "private_value":
    haircut_pct = 0
    applied = false

elif value_type == "common_value":
    haircut_pct = min(35, 10 + log(N) x 5 + signal_dispersion x 0.2)
    applied = true

elif value_type == "mixed":
    common_haircut = min(35, 10 + log(N) x 5 + signal_dispersion x 0.2)
    haircut_pct = mix_common_weight x common_haircut   # default 0.6
    applied = true

adjusted_valuation = raw_valuation x (1 - haircut_pct / 100)

Haircut lookup (common_value, approximate):

Input contract:

Output contract:

Key resources:

• [resources/template.md](resources/template.md): Classification decision tree (common vs private vs mixed), worked examples (closer = common; handcuff = private; late-season hot hitter = mixed), input/output templates
• [resources/methodology.md](resources/methodology.md): Kagel & Levin experimental evidence, formal Bayesian posterior derivation, log-N and dispersion intuition, value-type classification heuristics with fantasy-FAAB examples, why private-value gets zero haircut
• [resources/evaluators/rubricauctionwinnerscursehaircut.json](resources/evaluators/rubricauctionwinnerscursehaircut.json): 8-criterion quality rubric