| paper | d4-conf-ijcai-2009-0248 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | yes |
The paper computes a payment scheme from an LP, but the LP formulation and experimental timings are not a numbered result. Propositions 1 and 2 establish equilibrium properties; neither asserts that a computational problem can be solved or states a computational guarantee, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed extension concerns the minimum-payment mechanism and its truthfulness constraints; the paper's propositions do not provide a numbered computational result, and its running-time evidence is experimental.
This paper has no named computational result of the kind required for an anchor. Proposition 1, proved here, says honest reporting is a Nash equilibrium in every strategic game induced by a type-belief update. Proposition 2, also proved here, says acquiring the first signal makes honest reporting the unique Nash equilibrium in every such game. Neither states a complexity result about a computational problem.
Section 3.2 formulates minimum-payment design as an LP, and Section 6 reports running times, but neither is a numbered result establishing tractability or another complexity classification. I therefore can’t give a valid anchor or a continuous problem per anchor without stretching the paper’s claims.
The proponent is right that the paper has no theorem classifying a problem as polynomial-time or NP-hard. But that does not mean it has no computational problem to mirror: Section 3.2 explicitly formulates minimum-budget payment design as an LP, and Section 6.1 evaluates the computation. Proposition 2 gives that design problem a concrete target: make honest reporting the unique equilibrium using an initial acquired signal. The continuous question can be anchored there without pretending Proposition 2 is a complexity theorem.
Consider a large platform with many customers reporting on a service in each of several discrete time periods. Keep the paper’s finite-state Markov process and discrete time. Let each complete customer type \(u\) specify its signal technology, reporting cost \(C_u\), and lying incentives \(\Delta_u\); let \(\mu_{t,u}\) be that type’s share of the reporting population in period \(t\). The computational problem is to find the minimum expected payment per customer, and a reference-report assignment across cohorts, subject to truthful reporting being the unique equilibrium and participation constraints holding for every type and signal. The seed can remain the center’s single acquired signal; subsequent cohorts draw reference reports from earlier truthful cohorts.
That is a population mirror: the society is the mass distribution over complete customer types. It does not treat signal probabilities as population shares, and it does not continuize time. It also fits the application: customers are numerous, anonymous for the mechanism’s purposes, and groupable by the characteristics the payment constraints use. The paper’s LP is the homogeneous special case. The broader version asks how the optimization scales with the number of Markov states, signal types, customer-type support \(\tau\), periods, and input bit length, and whether large discrete cohorts admit efficient preprocessing or approximation.
So the proponent rules out a literal mirror of a stated complexity classification, which the paper does not provide. They do not rule out a worthwhile computational mirror of its named equilibrium result and explicit payment-optimization problem.
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.