| paper | d4-conf-ijcai-2015-0675 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Theorem 5.9 concerns eventual equilibrium, and the paper’s other numbered results likewise give analytic properties rather than computational guarantees. Section 4 assumes simplex maximization is polynomial-time but does not establish that claim or give a solver formulation used to compute an answer, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed population interpretation concerns the equilibrium results, especially Theorem 5.9; it leaves no computational result covered by a mirror.
I can’t make a qualifying case anchored in this paper: it has no named result asserting that a computational problem is in P, NP-hard, FPT, or otherwise characterized by complexity.
The closest result is Theorem 5.9, proved here. It says that if \(v\) is continuously differentiable, homogeneous of degree \(k\ge1\), and has a unique maximum \(x^\ast\) over \(\Delta_n\), then for every fixed \(q\), \(x^\ast\) is an eventual consensus point at each time \(t\le q\). That is an equilibrium result, not a computational one, so it cannot serve as the required anchor.
One could imagine a population mirror with types representing agents who share productivity and other parameters, and mass representing their fraction of the population. But the resulting question would extend an analytic equilibrium claim; it would not mirror a computational result from this paper. I therefore have no honest, prover-ready continuous complexity question to offer per the requested standard.
The case against a mirror rests on a gap in the paper, not on whether its results survive a limit: it states no complexity result for a computational problem. Theorem 5.9 is the closest candidate. A continuous population version could ask whether a socially optimal allocation is an eventual equilibrium in a society of types, but that remains an equilibrium question. It would extend the paper’s analysis, not chart the complexity of a problem it studied.
The stronger computational candidate is finding an optimal contract by maximizing \(v\) over the allocation simplex. But Section 4 treats that as a primitive: it says the task is straightforward *assuming* this maximization is polynomial-time. The paper gives no input encoding or complexity classification for \(v\). With an arbitrary \(v\), the computational problem is unspecified; with one of the production-function families in Section 6, it becomes a separate optimization question about that family. Either could motivate new work, but neither is a computational result to mirror here.
A type distribution can be imposed on the agents, but it does not fix that gap. In an atomless version, one agent’s proposal has no effect on the aggregate, so the paper’s individual deviation incentives lose their force. Treating each type as a bloc restores influence by changing who the strategic players are. These are possible new models, but their analysis would still be about equilibrium unless a computational problem and its input representation were added.
So the supplied case for a mirror has no surviving computational anchor: Theorem 5.9 is analytical, and the proposed population interpretation does not make it computational. The limit of this negative case is that it cannot establish that no authors-recognized computational extension would be worthwhile. It supports the narrower conclusion that this paper supplies no such mirror as written.
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.