| paper | d4-journals-geb-2002-0015 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper’s named results establish a representation, comparative statics, and bargaining equilibria, but none makes a computational claim. A continuous population version would require a new collective bargaining model, so no stated anchor yields a recognizable computational mirror.
fails bit a — no named computational result to mirror
The cited representation and comparative-statics results, along with the strategic bargaining results, concern individual preferences and two-agent outcomes; none supplies a computational result over a population.
I can’t make an honest case with a qualifying anchor: this paper has no named computational result asserting tractability, hardness, or a parameterized complexity classification.
The closest results are analytical. For example, Theorem 2 (proved here) says that when both agents are risk-averse, the Nash bargaining solution gives each utility \(1/2\), regardless of changes in risk aversion. Corollary 1 (proved here) says that when both are risk-lovers, a player’s Nash-solution utility increases as the opponent becomes more risk-loving. These are comparative-statics claims, not complexity results. Theorem 1 is a representation theorem attributed to Yaari, also not a computational result.
The paper’s continuum is over lotteries and outcomes; its society remains two bargaining agents. A population model grouping many bargainers by risk-preference type would introduce a new collective bargaining problem, with no named result here to anchor it. Under the programme’s scope, that is not a continuous mirror of this paper’s results. So there is no prover-ready mirror question I can defend from the required anchors.
The negative case is unusually strong here: the paper contains no named result about computational complexity. Theorem 1 is an axiomatic representation theorem. Theorem 2 and Corollary 1 establish comparative statics for a two-person Nash bargaining problem. The strategic results likewise concern equilibrium existence and outcomes. None specifies a computational problem, an input encoding, or an algorithmic or hardness claim for a continuous population to mirror.
The best population version of Theorem 2 would have many independent bargaining pairs, with risk-preference types drawn from distributions. Each pair would still have two bargainers; with finite supports, one could evaluate the at most \(\tau_1\tau_2\) type-pair cases and aggregate their outcomes. The theorem supplies no population-level decision problem beyond that aggregation. Treating a whole mass as one bargaining party would require defining its collective preferences and bargaining objective. Those choices could be interesting, but the resulting theorem would concern a new model rather than a continuous mirror of Theorem 2.
Corollary 1 has the same problem: it compares one opponent becoming more risk-loving. A distribution over risk types supplies no single opponent or specified aggregate comparison. Pairing agents independently again yields pairwise applications of the result; making the pairing or coalition formation consequential adds a new mechanism. Theorem 1 offers no better anchor: its continuity is over lotteries, while its preference relation belongs to an individual. Making that preference theorem computational would continuize the outcome or representation, not the population.
One can imagine building a computational bargaining problem around a continuum of people, but this paper does not identify the collective choice, constraints, or algorithmic question that would make it the paper’s mirror. The case is strongest for that paper-centered judgment; it cannot rule out every worthwhile model someone might build from its ideas.
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.