| paper | d4-journals-jet-2009-0038 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named results assert equilibrium existence or nonexistence and factor-price comparative statics, but none claims an algorithm, a complexity bound, or computational hardness. The proposed nonatomic auction would also change the finite-player allocation and equilibrium object, so it cannot supply the missing computational anchor.
fails bit a — no named computational result to mirror
No computational result is covered; Theorems 1 and 2 concern factor-price comparative statics, while Theorems 3 and 4 concern finite-player equilibrium existence and its necessity.
This paper contains no named computational result: none of its theorems or corollaries classifies a problem as tractable, hard, or parameterized. So I cannot give a continuous problem anchored to a qualifying result.
The nearest candidate is Theorem 3, proved here: if bidders’ valuations are increasing at ties and satisfy the own effect property, the English auction has an efficient ex post equilibrium. That is an equilibrium existence theorem, not an algorithmic result. Theorem 4 is also about equilibrium existence, giving a conditional necessity result. Theorems 1 and 2 establish comparative statics for factor prices. None supplies the complexity anchor this exercise requires.
A continuum of auction bidders is imaginable, with types given by bidder characteristics and mass representing population shares. But the paper’s \(\mu\) is a probability distribution over signal profiles for a finite set of bidders; it models uncertainty, not a continuous population. With one indivisible object, the continuum version also needs a new account of who wins and how the auction works. That would be a substantial new model, not a convincing mirror of the paper’s named results.
The negative case starts at the paper’s main weakness as a mirror candidate: it proves no computational result. Theorem 3 gives conditions for an efficient ex post equilibrium; Theorem 4 gives a conditional necessity result. Theorems 1 and 2 give comparative statics for factor prices. None defines an algorithmic problem or studies its complexity. The distribution \(\mu\) in the auction section is uncertainty over signals of a finite set of named bidders, not a distribution of population mass over types.
The strongest rescue of Theorem 3 would put many bidders into a few classes with shared valuation structure and ask whether an efficient equilibrium can be computed. That creates a basic modeling problem: with one indivisible object, a bidder in a continuum has zero mass, while the theorem’s efficiency criterion selects a highest-valued individual. One can give the population positive per-capita supply or make the prize divisible, but then the allocation, payoffs, and auction become a different game. The paper’s conditions and exit strategies are built around finite sets of bidders, winners, and auction histories. Even if that new game were worthwhile, the paper supplies no computational question or input representation for it. Adding those would start a separate algorithmic project.
The trade theorems offer no stronger anchor. Duplicating sectors or factor owners does not enter their zero-profit equations, so multiplicity has no natural role in the comparative statics. Replacing sectors with a distribution of cost functions could produce a continuous comparative-statics model, but that changes the sector space and still supplies no complexity problem. Theorem 4 remains an equilibrium-existence result, with \(\mu\) over finite-bidder signal profiles.
A computational study of a carefully specified nonatomic auction might be sensible in its own right. The weakness in the negative case is that one cannot rule out that future model; the paper gives little reason to treat it as a continuous mirror of these results.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.