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Apply auction theory to compare the four canonical auction formats and assess revenue equivalence.
Passed 20 of 22 test cases with the skill, and 18 of 22 without it.
and 3 more in the full report
3 fixed17 passed either way1 still failing1 broke
Tokens, turns and time describe resource use, not a dollar price.
One of 3 test cases the skill fixed. Same model, same prompt, with and without the skill.
We are designing an auction for regional 5G spectrum licenses among 4 competing telecom companies. Assume bidder valuations are privately held and distributed uniformly between $10M and $50M, but participating executives exhibit risk aversion. Please generate a full auction analysis report. Organize the response with a Value Model section (specifying value type, distribution, bidder count, and risk attitude), a Format Comparison Markdown table comparing English ascending, Dutch descending, first-price sealed, and second-price sealed formats on equilibrium strategies and expected revenues, a Revenue Equivalence Assessment examining whether RET holds along with format rankings and failure sources, an Optimal Reserve Price section showing r* and its derivation, and a final Recommendation section detailing format choice and reserve strategy.
| Checked | Without skill | With skill |
|---|---|---|
| Recommends a first-price sealed-bid auction over a second-price auction due to bidder risk aversion. | Missed | Passed |
| States that the Revenue Equivalence Theorem does not hold due to bidder risk aversion. | Passed | Passed |
| Formats the response using the top-level section header '## Auction Analysis:'. | Missed | Passed |
The instructions your model reads when the skill loads.
Auction theory analyzes strategic bidding behavior across different selling mechanisms. The four canonical formats — English (ascending), Dutch (descending), first-price sealed-bid, and second-price sealed-bid (Vickrey) — generate identical expected revenue under standard assumptions. The Revenue Equivalence Theorem (RET) is the central benchmark; deviations from its assumptions drive all practical auction design decisions.
IRON LAW: Revenue equivalence holds ONLY with risk-neutral bidders,
independent private values (IPV), and symmetric bidders — violate ANY
assumption and auction format matters.
Step 1 — Identify the Value Model Classify the setting: independent private values (IPV), common values, or affiliated values. IPV means each bidder knows their own value with certainty; common values mean the object has one true value unknown to all; affiliated values generalize both.
Step 2 — Derive Equilibrium Bidding Strategies For each auction format, solve for the Bayesian Nash equilibrium. In second-price / English auctions under IPV, bidding true value is dominant. In first-price / Dutch auctions, bidders shade below true value: b(v) = E[Y1 | Y1 < v] where Y1 is the highest competing value.
test cases passed, vs 18 / 22 without
More skills from the same source and nearby in the registry, with their headline benchmark lift.