| paper | d4-journals-jet-2016-0043 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Propositions 2 and 3 characterize finite-\(N\) equilibrium bidding schedules, but give no algorithm, complexity result, or computational formulation used by the paper. Computing a mass-indexed price path would be new research; making strategic bidders nonatomic would also require a different equilibrium concept.
fails bit a — no named computational result to mirror
No computational result is anchored: Propositions 2 and 3 characterize finite-auction equilibria, and Proposition 9 gives a finite-auction security strategy.
This paper has no named computational result of the kind required for an anchor. Its numbered propositions characterize equilibrium bidding strategies and payoffs—for example, Proposition 2 gives the risk-neutral equilibrium bid functions, and Proposition 9 identifies a security strategy. Neither asserts a complexity result or presents a computational formulation that the paper solves.
So I can’t honestly give a continuous problem *per anchor* or claim a continuous mirror of a computational result in this paper. The paper does study an auction with \(N\) bidders, but proposing an atomless-bidder version would be a new analytic model, not a mirror grounded in an eligible result here.
The absence of a complexity theorem is accurate, but it does not rule out a worthwhile mirror. Proposition 2 gives the paper’s central object: the equilibrium dropout schedule. A computational question about finding that schedule for a continuous population is a direct extension of the result, even though the paper itself does not analyze running time.
A natural case is a large partnership or member owned organization with many stakeholders drawn from a small set of valuation and risk types. Represent those types by masses \(\mu_t\), and ask for an exact or \(\varepsilon\)-accurate equilibrium price path \(p(q)\), where \(q=k/N\) is the fraction of bidders who have dropped out, along with the aggregate compensation flow by type. The asset remains indivisible; the mass model describes who exits and how compensation accumulates, while the eventual winner is an individual from the highest surviving type. This anchors directly to Propositions 2 and 3, and asks for algorithms whose complexity depends on the number of types, input precision, and population size.
The indivisible winner does create a real limit issue: an individual’s compensation increment and the security payoff \(x/N\) shrink as \(N\) grows. That makes Proposition 9 a poor anchor. But the cumulative price path and total compensation need not vanish, since the increments sum to \(p_{N-1}\). Proposition 2’s price schedule is therefore a better target than the per-person guarantee. The paper’s distribution \(F\) describes uncertainty over a finite sample of bidders; it does not already give the deterministic, mass-indexed equilibrium computation for a society with type proportions \(\mu\). The proposed question is not airtight—the equilibrium computation is outside the paper’s original scope—but the missing complexity analysis is a reason to ask it, not by itself a reason to rule it out.
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.