| paper | d4-conf-ijcai-2019-1011 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | no |
Theorems 1–4 give equilibrium contribution bounds and outcome properties, but do not state a computational claim or an algorithm for selecting an equilibrium. The closest mass model also makes individual contributions non-pivotal at funding thresholds; preserving pivotality would require changing the strategic players or the mechanism.
fails bit a — no named computational result to mirror
None: Theorems 1–4 analyze equilibria for PPRN, PPSN, PPRx, and PPSx; no continuous computational result is proposed.
This paper contains no named computational complexity result to anchor a continuous mirror. Theorem 1 characterizes Nash equilibria for PPRN; Theorem 2 characterizes subgame perfect equilibria for PPSN; and Theorems 3 and 4 do the same for PPRx and PPSx. They state equilibrium properties and conditions for existence, not that a computational problem is in P, NP-hard, or otherwise classified.
The closest possible mirror would use masses of agents by valuation and belief type, with contribution mass as the decision variable, and ask whether an equilibrium with the paper’s provision or rejection outcome exists. But that would mirror the paper’s equilibrium analysis, not a named computational result of the kind required here. Calling one of these theorems a tractability anchor would overstate what it proves.
The strongest case against a mirror is that the paper gives no computational problem to continuize. Theorems 1–4 characterize equilibria and give conditions for their existence; they do not ask how hard it is to find an equilibrium, or classify an algorithmic task. So the proponent is right that an equilibrium-computation question would be a new framing, not a mirror of a named computational result.
The most charitable version would group agents by complete type—valuation, belief, and any relevant arrival or mechanism parameters—and ask whether the mechanism has an equilibrium with provision or rejection. For PPRN and PPRx, the stated conditions reduce to aggregate quantities such as sums of valuations and contributions. PPSN and PPSx add evaluations of the cost function and its inverse, but the theorems still supply the equilibrium form directly. A continuous input might make those calculations integrals instead of sums; that alone does not uncover a computational problem the paper leaves open. Optimizing budgets or thresholds, or computing equilibria under a new distribution of types, could be worthwhile research, but it would add a problem the paper does not study.
There is also a real limit to the best population mirror. In an atomless society, one agent has zero mass and cannot change whether a funding threshold is reached. That removes the individual pivotality the mechanisms’ equilibrium arguments rely on. Treating a whole type group as a strategic contributor could preserve pivotality, but then the group acts as a bloc; replacing RBTS’s indexed peer selection with random matching would likewise change the mechanism. These are possible new models, not objections to high multiplicity in general: a large population with repeated valuation and belief types is perfectly plausible. They do, however, make it harder to claim that the paper’s equilibrium theorems already contain a useful continuous computational mirror.
So the negative case is strong against a *mirror of this paper’s results*, though it cannot establish that no worthwhile computational project could grow from the mechanisms. That stronger project would need to be specified and justified on its own.
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.