| paper | d4-journals-mss-2009-0031 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 3 is an axiomatic rationalizability characterization, and Theorems 1 and 2 likewise give extension and rationalizability criteria; none claims an algorithmic guarantee or computational hardness. Since bit (a) fails, the proposed session-mixture or testing directions would be follow-on problems rather than mirrors of a computational result in this paper.
fails bit a — no named computational result to mirror
The cited results characterize independent ordering extensions, individual choice rationalizability, and collective Nash rationalizability. The paper supplies no computational result to mirror.
The paper contains no named computational-complexity result of the kind your anchor rule requires. Its closest result is Theorem 3, proved here: under individual decisiveness and the stated domain condition, a collective choice correspondence is Nash-rationalizable exactly when it is noncooperative and satisfies joint congruence. That is an exact axiomatic characterization, not a claim that a computational problem is in P, hard, FPT, or otherwise classified. Theorem 2 gives a similar characterization for individual choice over lotteries; Theorem 1 concerns independent ordering extensions.
A possible population setting would be a large experimental panel running repeated copies of small games, with types defined by role, preferences, and available menus, and mass representing the share of trials of each type. But the paper’s result concerns the rationalizability of choices within a finite-player game. Treating repeated sessions as a continuous society adds a population layer; the paper does not study the resulting computational problem. Its continuous objects are lotteries and mixed strategies, which are outcome or strategy-space continuity, not continuization of the population.
So I can point to a plausible extension, but I cannot honestly give the requested anchor-linked continuous problem: doing so would present a new question as if it were a computational result of this paper.
The case against starts with the paper’s actual contribution: it gives axiomatic characterizations, not computational results. Theorem 3 characterizes Nash rationalizability through noncooperation and joint congruence; Theorems 1 and 2 characterize ordering extensions and individual choice. The paper does not analyze the complexity of deciding any of these properties, or give an algorithm with a stated running time. The proponent’s anchor is therefore an important theorem, but not a computational result to mirror.
The closest stronger candidate is to study the computation needed to test Nash rationalizability from finite observations. The paper describes such a test, but its theorem supplies a criterion, not a complexity analysis. Turning it into a continuous-population problem—for example, a distribution of experimental sessions with different preference profiles—would ask whether aggregate observations are a mixture of individually rationalizable behaviors. That is a potentially coherent new problem, but averaging sessions changes the object: the theorem applies to each joint choice correspondence, and does not characterize mixtures of them. Replicating identical games instead just repeats the same finite-player test. A single game with a continuum of players would change the strategic setting and the meaning of unilateral deviation.
So no proposed anchor survives as a continuous mirror of a computational result in this paper. The broader claim that no useful follow-on could ever be built from its ideas is harder to defend: computational testing of rationalizability or population mixtures might be worthwhile in its own right. But that would be a new computational programme built around the paper’s axioms, not a continuization of a computational contribution the paper makes.
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.