| paper | d4-journals-mss-2017-0037 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1 and Theorem 2 prove equilibrium implementation by a specified bargaining game, but assert no computation, complexity bound, or hardness result. A cohort continuizes negotiations rather than the agents in one, while a shareholder model would need new aggregation and allocation rules.
fails bit a — no named computational result to mirror
Theorem 1 and Theorem 2 establish implementation of the balanced and weighted market allocations; neither supplies a computational result to mirror.
This paper has no named computational result to anchor a continuization case to. Its Theorem 1, proved in the paper, says that every subgame perfect equilibrium of the alternating pricing game yields the balanced market allocation, and that this allocation occurs in such an equilibrium. Theorem 2 extends the implementation result to a weighted bias target. Neither theorem classifies the complexity of a problem or gives an algorithm whose tractability could be tested in a continuous population.
The strongest tempting scenario is a large cohort of otherwise identical two-person partnerships being dissolved. But that makes the *number of negotiations* large; each negotiation still has the paper’s two agents and one indivisible object. Treating the cohort’s distribution of partnership types as the society would continuize a population of instances, not the population inside the paper’s problem. It could motivate a separate batch-computation question, but it would not be an honest mirror of a named computational result here.
So there is no qualifying anchor, and no per-anchor continuous problem to hand to a prover. The paper’s contribution is to mechanism design and equilibrium implementation, not computational social choice complexity.
The attached case does not actually propose a continuous mirror: it treats Theorem 1 as a tempting but non-computational anchor, then rejects the cohort-of-partnerships scenario. Those are the strongest candidates here, and neither yields a mirror of the paper’s problem.
Theorem 1 says that the alternating pricing game implements the balanced market allocation in subgame perfect equilibrium; Theorem 2 extends that implementation result. Neither gives a complexity classification or an algorithmic problem over a population. The paper has two agents with arbitrary utility functions, and it does not specify a finite encoding for those functions. One could impose an encoding and ask how to compute the equilibrium transfer, but that would be a new computational problem built around the theorem, not a computational result in the paper whose population can be continuized.
The best rescue is a partnership with many shareholders on each side. If each side acts as one party, its shareholders’ preferences must first be aggregated into a collective utility. The mechanism then still has two players; the distribution describes the parties behind them, rather than a population participating in the allocation. If the shareholders instead act as individual agents, the model needs new rules for ownership, transfers, and fairness, and the paper’s two-agent implementation result no longer anchors it.
A large cohort of dissolving partnerships has the same issue in another form. Its mass is over negotiations, not over participants within a negotiation. Applying the paper’s result to each partnership and aggregating the outcomes would be a batch-analysis question, not a continuous-population mirror of the result.
This is a strong negative case, though not a proof that no worthwhile extension can ever be made. A model of shareholder populations might be valuable in its own right. Its weakness as a mirror is that it needs a new collective-preference model and a new computational question before the paper’s results become relevant.
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.