| paper | d4-conf-ecai-2014-0208 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1 gives a constructive equilibrium characterization by backward induction, so it has computational character despite making no complexity claim. But each player's agenda slot affects their strategic role and is unique, leaving no positive-mass complete type to aggregate. Grouping players into blocs could define a related game, but it changes the proposal and rejection mechanism rather than preserving the paper's problem.
fails bit b-none — no population with multiplicity to relax
The opponent's strongest point is that agenda position is part of a complete strategic type, and each position is unique; the proponent notes the agenda problem but does not address how this prevents repeated full types.
fatal: True
No result is covered by a surviving mirror; Theorem 1, Propositions 1–4, and the power and welfare analyses remain specific to the finite agenda game.
A plausible high-multiplicity setting is a large population of member organizations forming consortia, where many organizations share one of a few complete rankings over admissible coalition structures. A type would be one such ranking, and \(\mu_t\) the fraction of organizations with type \(t\). That gives the paper’s coalition-formation story a possible continuous population.
The paper’s closest numbered result is Theorem 1, proved here. It characterizes subgame-perfect equilibrium: in the last round, the mover proposes the all-singleton structure. In each earlier round, mover \(\rho_t\) proposes a structure minimizing their expected rank, subject to every later mover \(\rho_i\) receiving an expected rank no worse than their continuation equilibrium rank. A later mover accepts exactly when the offer meets that condition. This is a constructive equilibrium characterization by backward induction; it does not classify the complexity of computing an equilibrium. Propositions 1–4 concern agreement timing and power relationships. The simulation findings are not numbered complexity results.
So there are no eligible computational anchors here under the requested standard, and consequently no honest per-anchor continuous problem to hand to a prover. A type-mass version of the bargaining game could be a worthwhile follow-on. It would need to specify how partitions of a continuum are represented and how a sequential agenda and its “first rejecting mover” work with infinitely many agents. The weakest point in the positive case is that those choices would define a new computational problem; the paper’s named results do not anchor it.
The only named candidate the proponent identifies is Theorem 1, and it does not provide the kind of anchor ChoCo is looking for. It characterizes an equilibrium by backward induction. The paper makes no complexity claim about computing that equilibrium, or about any other computational problem. Propositions 1–4 and the simulations report agreement, power, and welfare properties; they do not fill that gap.
A direct continuous mirror of Theorem 1 runs into a structural problem. The paper’s agents rank partitions of the particular set \(N\), and their agenda position determines when they propose, which offers they can reject, and what continuation outcome they face. As the population grows, the set of partitions changes, so an unrestricted ranking over \(\Pi(N)\) is not a fixed preference type that can simply be assigned positive mass. Compact preferences over coalition compositions could fix that, but they add structure the paper does not supply.
Agenda position is a further obstacle. Agents with identical rankings but different positions do different things in this game; to preserve the mechanism, position must be part of their type. Since each position is unique, grouping those agents by preference loses information the equilibrium depends on. Encoding position as a continuous coordinate leaves the protocol without its finite sequence of turns: after a rejection it needs a next proposer, and its terminal round is defined by the last agent. Treating an entire preference class as one bloc would give the bloc a collective proposal and rejection role absent from the paper. That could define a new bargaining game, but it would not be a continuous version of the theorem’s game.
Power and welfare are the strongest alternative candidates. A continuum could report average welfare across preference types, but the paper’s power index is specific to agenda positions and averages over all combinations of complete rankings of \(\Pi(N)\). A distribution over a few stable types does not preserve that averaging procedure as \(N\) grows. Normalizing welfare by population size would not resolve the agenda and preference-domain problems.
A more structured model of large organizations, with preferences over coalition compositions and an agenda of bloc moves, might be worth studying on its own. The negative case is therefore strong against a direct, computationally anchored ChoCo mirror of this paper. It is weaker as a universal claim that no worthwhile related continuous bargaining model can be built: that depends on whether the authors would recognize the bloc protocol as their problem, and the paper alone cannot settle that judgment.
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.