| paper | d4-conf-wine-2021-0009 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The numbered theorems establish equilibrium and stability properties, but none states an algorithmic, complexity, or hardness result. The proposed continuum equilibrium question is a possible new research direction, yet it has no computational result from this paper to anchor it.
fails bit a — no named computational result to mirror
A possible extension would ask whether the equilibrium claims in Theorems 1–3 persist in a replicated-module limit; it would leave the elimination-order result, experiments, and other claims without a computational mirror anchored in this paper.
I cannot honestly name a result in this paper that meets the requested computational anchor rule. The paper classifies no computational problem as tractable, hard, FPT, or otherwise. Its named results concern equilibrium properties. For example, Theorem 3, proved here, says that if every player has at least three good friends, full propagation is a Nash equilibrium and is connected coalition-proof on the good-friendship subgraph. Theorem 1 gives a related coalition-proof equilibrium result for trees; Theorem 2 concerns survival under iterative elimination of dominated strategies. These are substantial results, but none analyzes the complexity of a computational problem.
The strongest possible positive lead, if the scope is broadened, is a typed-mass full-propagation equilibrium test. Imagine a large broadcast or relay network made of many repeated local network roles. A type records everything relevant to an agent’s incentives: stake, minimum retained charge, position in the local network, and the roles of its contacts. Its mass \(\mu_t\) is its fraction of the population. Each agent chooses how much reward to retain and how much to pass to each contact; utility comes from the uniform winner lottery and any reward attributed to referrals. Because an individual’s lottery payoff vanishes as population size grows, the continuum model would use the finite payoff multiplied by population size, which preserves best-response comparisons. It would also need a typed local-network description: \(\mu\) alone does not record who can refer whom.
The prover’s question would be: given rational type masses, the local-network template, the reward and minimum charge, and the full-propagation profile, is that profile a Nash equilibrium and connected coalition-proof under the limiting payoff? A solution is “yes,” or a type, feasible alternative forwarding action, and profitable deviation (or a connected deviating coalition). Theorem 3 suggests a tractable subcase when the three-good-friends condition carries over to the role network. That is a research conjecture, though; the theorem does not establish a complexity result for this continuum problem.
This is a plausible population scenario—many relays sharing a small number of network roles—and the underlying forwarding and lottery incentives remain recognizable. But it is not an anchored positive case under ChoCo’s stated gate. The proposed problem asks about equilibrium computation, the paper proves equilibrium properties without analyzing that computation, and replacing its individual network with masses and a role template may change the strategic effects. So the honest verdict is: no qualifying computational anchor. The equilibrium results are useful motivation for a new mirror question, not evidence that this paper already supplies one.
The strongest case against a ChoCo mirror is that the paper has no named computational result to mirror. Theorem 1 concerns connected coalition-proof equilibrium on trees, Theorem 2 concerns survival under iterative elimination of dominated strategies, and Theorem 3 extends an equilibrium claim to certain networks. None studies the complexity or algorithms for a computational problem. That is a decisive failure of the programme’s anchor requirement; it is not a claim about what a continuous version would answer.
The best rescue is the proposed mass model of repeated relay roles. It exposes the main modeling difficulty: in this game, a player’s payoff depends on who can reach whom, which path claims a player, and how many aware descendants lie below each referral. In the paper’s notation, \(n_{ij}\) and \(|N^*|\) depend on that network structure. A distribution over individual roles does not determine those quantities. A faithful type would need to encode the relevant relationships and overlaps, which can make the support grow with the network. A graphon or distribution over whole relay modules could retain them, but then the new object and its finite input representation are doing essential work that the paper’s theorems do not supply.
There is a plausible special case: many copies of a fixed, bounded relay module, with payoffs rescaled to preserve incentive comparisons as the lottery grows. That could support a continuous equilibrium question. But it would be a new game-theoretic limit model, not a computational result established or analyzed here. Turning it into a complexity question would require choosing how modules, strategies, and connected coalitions are represented; the paper gives no such computational formulation. Thus the typed-mass proposal motivates a separate research direction, but it does not rescue an anchor for this paper under ChoCo’s stated gate.
I would not defend the stronger universal claim that no worthwhile continuous mirror is possible in any scenario: repeated network modules make that too strong. The case against is strongest and decisive for the narrower programme judgment: none of the paper’s named results is a computational anchor, and the most plausible continuization leads first to a new equilibrium model whose computational target must be supplied separately.
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.