| paper | d4-conf-atal-2014-0112 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The two propositions are numbered, but they characterize when eliminability holds without stating an algorithm, complexity bound, hardness result, or formulation used to compute it. Neither is a valid computational anchor under the required test, so no continuous analogue of a computational result of this paper remains to grade.
fails bit a — no named computational result to mirror
The proposed anchors are Propositions 10 and 12; the paper's other stated results concern logical characterizations and equilibrium properties, not named computational results.
I can’t make a compliant anchor-based case for this paper: it contains no numbered computational result that establishes a complexity classification, gives an algorithm, or presents a formulation that the paper then computes with. Its numbered results are game-theoretic characterizations, not computational claims.
The closest candidates are Proposition 10 and Proposition 12, both stated in this paper. Proposition 10 says that a present equilibrium in a Boolean game with global costs is eliminable by side-payments exactly when there are a coalition \(C\), a member \(i\) with positive cost at the equilibrium, and a unilateral alternative for \(i\) that preserves every coalition member’s already-satisfied goal, while either satisfying a previously unsatisfied coalition member’s goal or reducing the coalition’s total cost. Proposition 12 says that with local costs, a present equilibrium is eliminable by side-payments exactly when there are distinct players \(i,j\) and an alternative for \(i\) that leaves \(i\)’s goal status unchanged while changing \(j\)’s from unsatisfied to satisfied. These are crisp witnesses for eliminability, but neither says the underlying decision problem is in P, hard, or otherwise computationally classified.
A possible population setting would be a large fleet of similar robots, with types recording goals, controlled variables, and costs. But the paper’s Boolean games give each player unique control of variables, and goals can depend on other players’ choices. Turning that into a continuous population would require specifying how aggregate actions determine Boolean goal satisfaction; a nonatomic model can also erase the effect of a single player’s deviation. That could motivate a new model, but it is not a continuous problem anchored by a computational result in this paper.
So there is no lead anchor, and I would not claim that this paper supplies a named result for a continuous mirror. The positive opening is that Propositions 10 and 12 offer structural criteria that might inspire one; the gap is that the paper does not make or compute the complexity claim the programme needs.
The strongest objection is that Propositions 10 and 12 characterize when a *named player’s unilateral deviation* can be supported by a coalition. They do not formulate an algorithmic problem or give a complexity result. One can turn their predicates into finite-input decision problems, but that would be a problem we define, not a computational result this paper studies. The paper’s Boolean-game model gives each variable to exactly one player, which makes that distinction consequential. [The paper’s model and Proposition 12](https://www.ifaamas.org/Proceedings/aamas2014/aamas/p845.pdf)
Proposition 10 is the better anchor. Its cost-sum condition looks amenable to type-level aggregation, and global costs could be integrated over a population. But the condition still depends on one particular player changing their assignment while everyone else’s assignment stays fixed. With a fixed vocabulary \(\Phi\), there can be at most \(|\Phi|\) players with nonempty control; extra identical agents are dummies. To give many agents their own choices, we must expand the variables and add symmetry or aggregate-goal rules. In an anonymous continuum, one agent then has zero mass, so their switch cannot change the population state. Making a positive mass switch would be a coalition deviation, a different strategic move. Preserving an individual’s pivotal effect instead requires identity-linked dependencies or finite atomic players, which defeats the intended population abstraction.
Proposition 12 makes that problem sharper. Its witness is a pair \(i,j\): changing \(i\)’s choice leaves \(i\)’s goal status unchanged and flips \(j\)’s goal from false to true. In an anonymous nonatomic model, an individual change cannot flip another agent’s aggregate-dependent goal. Keeping that effect requires named cross-agent dependencies, whose type descriptions grow with the population, or an influential atom. Replicating \(j\) as a mass of beneficiaries does not rescue the result: under the paper’s local-cost criterion, one newly satisfied beneficiary suffices, and the paper places no budget cap on what a goal-satisfied player may pay. A mass-based funding threshold would have to be added to make the amount of population matter.
The best repaired proposal would ask whether a positive-mass bloc can coordinate an action change and fund it from per-capita budgets. That could be a coherent continuous game, perhaps reducible to an optimization problem over type masses. But it changes the unilateral deviation and payment structure that make these propositions work; the paper provides no computational result whose continuous counterpart that would be. Mean-field games with binary actions already provide neighboring analytic models, including work on threshold strategies and equilibrium uniqueness, but they do not answer this computational blocking question. [Huang and Ma, *Mean Field Stochastic Games with Binary Action Spaces and Monotone Costs*](https://arxiv.org/abs/1701.06661)
So I would reject both propositions as support for a ChoCo mirror of this paper. The honest limit of that case is that one could invent a worthwhile continuous coalition-blocking problem inspired by them. What is missing is a reason to treat it as a continuization of the paper’s contribution rather than a new mean-field game with newly chosen rules.
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.