| paper | d4-journals-geb-2003-0033 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named propositions characterize equilibrium outcomes and bound the number of partnerships; none makes a computational claim. The proposed continuum-of-producers question remains an analytic extension, and preserving individual effort incentives and sequential roles does not carry over cleanly to a nonatomic population.
fails bit a — no named computational result to mirror
No results receive a computational mirror; Propositions 1 and 4 are discussed as equilibrium claims, while the paper’s other results likewise concern equilibrium structures and industry efficiency.
The most favorable continuous-population setting is a very large market of interchangeable producers: each type is a complete description of a producer’s technology, effort cost, and profit-sharing terms; mass is the share of producers of that type. In the paper’s symmetric case, there is just one type, so \(\tau=1\) while the number of producers is large. A continuous version would describe partnership sizes as masses, with effort and Cournot output determining each partnership’s per-capita payoff.
But this is only a neighboring *analytic* question, not a ChoCo computational mirror. The paper has no named result asserting a complexity classification or algorithmic bound. Proposition 1 says that, when \(1<a/c<n/(n-1)\), the unique subgame-perfect equilibrium partition is all singletons. Proposition 4 bounds the number \(r\) of partnerships in any non-singleton equilibrium structure by \(r\le(-1+\sqrt{1+4n})/2\). Both are equilibrium claims proved by analysis; neither classifies the complexity of a computational problem. So there is no qualifying anchor here, and I would not nominate a continuous problem per anchor or predict an A/B/C outcome.
The adjacent continuous question would be whether a continuum of producers has analogous equilibrium partnership structures. It is plausible as a mean-field game-theory question, but the paper’s sequential proposer process and individual effort incentives do not carry over automatically: in a nonatomic model, one producer’s effort has no effect on aggregate output. Preserving those features may require changing the model. That leaves a modest case for a continuous *economic* analogue, but no honest case that this paper supplies an anchor for the programme’s complexity landscape.
There is no computational result in this paper to anchor a ChoCo mirror. Propositions 1–4 and Corollary 1 characterize equilibrium partnership structures and give a bound; the table illustrates outcomes for \(n=18\). None states an algorithm or a complexity result for a computational problem. The proposed question—whether a continuum of producers has analogous equilibrium structures—is therefore an economic equilibrium question, not a continuous computational-social-choice question.
The stronger computational reframe would be to ask for an algorithm that finds an equilibrium mass partition from rational demand, cost, and type data. But preserving the paper’s sequential formation game makes the producers’ positions in the move order part of their complete type: the paper’s outcomes depend on who proposes when, and it says the concentration effect relies on sequentiality. Encoding those positions gives each producer a distinct role, so the population no longer has the high-multiplicity structure the mirror needs. Erasing the roles gives a different game; the paper itself says the effect disappears in a one-shot formation game.
There is a further limit to the natural one-type continuum proposed by the other analyst. Within a large partnership, each member receives only a \(1/k\) share of gross profit when the partnership has \(k\) members, while bearing their own effort cost. With fixed \(a\) and \(c\), the private return to effort falls as \(k\) grows; in a nonatomic partnership, an individual’s effort has no effect on aggregate output, so positive-cost effort collapses to zero. Rescaling technology or costs might preserve incentives, but that would define a new model and still leave the sequential-role problem.
A broader project on computing equilibria in continuum partnership games could be worthwhile. The paper supplies no computational anchor for it, though, and the best continuous question raised here remains analytic rather than a mirror of the complexity programme.
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.