| paper | d4-journals-jet-2006-0056 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper's propositions characterize equilibrium outcomes and existence; they do not assert an algorithm, a complexity result, or a computable formulation. The mass-contracting proposal is a plausible research direction, but computing its equilibrium would be a new task rather than a continuous analogue of a computational result in this paper.
fails bit a — no named computational result to mirror
No result is computationally mirrored; the proposed mass-contracting extension draws on Proposition 6's principal–agent application, while the paper's other results and applications remain untouched.
The strongest positive angle is the principal–agent application: a large population of similar agents contracts with one principal, and externalities affect agents left outside a contract. A type could record an agent’s contract payoff and outside-option response; \(\mu_t\) would be the fraction of agents of type \(t\). The principal’s decision would be how much mass of each type to contract with and what transfers to offer; agents choose whether to trade permanently or remain in negotiations. A possible computational question is to find a Markov-perfect equilibrium’s contracting path and transfers, and determine whether an efficient full-mass contract forms as the discount factor approaches one. That is a plausible population-based extension of Section 5.2.
But the paper contains no named computational result of the kind your anchor rule requires. Proposition 6, proved here, says that in the principal–agent model an efficient Markov-perfect equilibrium forms the grand coalition in one step with positive externalities, and in two steps with negative externalities. Proposition 8, also proved here, says that in the three-firm market-entry model, equilibria lead to an inefficient two-firm coalition and positive-probability exit as players become perfectly patient. These are equilibrium characterizations, not results about an algorithm or a problem’s computational complexity. Proposition 1 proves equilibrium existence; Propositions 2–5 establish equilibrium existence or efficiency properties. None asserts that a computational problem is in P, NP-hard, or otherwise classifies its complexity.
So the mass-contracting question is a research direction, not a qualifying mirror anchored in this paper. Its weakest point is that the paper analyzes a finite-player bargaining game and does not specify how proposals, acceptance, or equilibrium are represented for a continuum of agents. Under the requested standard, there are no anchors and therefore no continuous problems I can honestly present as the paper’s anchored computational mirrors.
The decisive problem is that this paper poses no computational problem. Proposition 6 characterizes efficient equilibrium paths in a principal–agent model; Proposition 8 characterizes inefficient outcomes in a three-firm market-entry model; Proposition 1 establishes equilibrium existence. None gives an algorithm, a complexity classification, or even a finite input and output for a computational task. The proposal to “find a Markov-perfect equilibrium’s contracting path and transfers” supplies a new task in place of a result to mirror.
The principal–agent setting is the strongest proposed anchor, and a high-multiplicity version is sensible: many interchangeable agents can be represented by masses, and type can capture their payoffs and outside options. But making that a computational problem requires choices the paper does not make. Its model allows continuous actions and arbitrary payoff functions \(F\) and \(\beta\), without specifying how those functions are encoded, how an equilibrium is represented, or which equilibrium to compute when there are several. A finite-type version with computable payoffs and a specified equilibrium-selection task could be worth studying, but its algorithmic questions would come from those additions, not from Proposition 6.
Proposition 8 does not provide a firmer anchor. Its result concerns three firms whose merger synergies and market capacity shape their strategic choices. A continuum of firms would require new rules for how a mass of entrants competes for a market that supports one firm, and how a coalition’s merger changes payoffs. That may yield a model, but it would not make Proposition 8 a computational result.
So the negative case is strongest on the narrower claim: this manuscript offers no qualifying computational anchor for a continuous mirror. It is weaker as a claim that no worthwhile continuous extension exists anywhere. The principal–agent application plainly admits a plausible mass-based model; the gap is that turning it into a computational project requires specifying a new, encoded problem rather than continuizing a computational result in this paper.
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.