At a Glance
An agent’s reported information directly predicts its earnings in agent-to-agent markets to within 0.0457 nats; yet populations don’t respond smoothly to incentives — they jump between wealth attractors.
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What They Found
Reported belief quality (measured from elicited posteriors) maps to market earnings almost exactly: relative information gaps explain relative growth gaps to millinat precision. Coalition value behaves as theory predicts when signals are independent, but synergistic signals (an XOR pair) produce a large superadditive gain. This aligns with Emergence-Aware Monitoring Pattern. Populations consistently concentrate wealth on particular agents and flip between discrete attractors rather than shifting smoothly as incentives change. Practitioners can apply Tool Use Pattern to reason about how tools shape information flows.
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By the Numbers
1Measured growth gap matched measured information gap within 0.0457 nats (inside the pre-registered 0.05 nats band) across four perception structures.
2In live 40-round parimutuel markets the cleanest-information agent captured ≥99.9% of the wealth pool in every seed; complete ordering by information held in 4 of 5 seeds.
3A designed XOR signal produced a coalition supermodular gain of 0.621 nats (≥ ln(2)/2 ≈ 0.347 nats); joint growth was capped by the world entropy ≈ 2.079 nats.
What This Means
Engineers building systems where multiple model instances trade, bid, or negotiate should care because reported beliefs predict economic outcomes and can be measured reproducibly. Technical leaders and researchers studying Agent-to-Agent Protocol can use these measurable links to design monitoring, incentives, and tests that detect whether agents truly hold valuable information.
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Learn MoreYes, But...
Findings come from experiments with a single frontier model (Claude Opus 4.8) and synthetic 3-bit worlds, so performance in richer real-world environments may differ. Sampling noise and absorbing all-in wealth dynamics broke symmetry among identical clones, so equal information does not guarantee equal final wealth under default sampling. The experiment was pre-registered and reproducible but modestly budgeted, meaning some broader mean-field regimes were out of scope. Inter-Agent Miscommunication
Methodology & More
Runs used a fully pre-registered protocol: agents (model instances) observed noisy signals about a simple 3-bit world, reported posteriors, and bet in a parimutuel pool where payoffs are zero-sum. Claimed information was measured as the expected divergence of reported posteriors from the prior; economic outcome was expected log growth of wealth. Four perception structures were tested (disjoint, overlapping, cloned, noisy) plus a designed XOR pair to create synergistic information. All model calls and analysis were cached so every number is reproducible from the committed repository. Human-in-the-Loop Pattern Key findings confirm an information–wealth coupling at frontier model scale: relative reported information explains relative growth to within 0.0457 nats, coalition value shows the expected diminishing returns under independence and strong synergy for the XOR pair, and joint growth never exceeded the entropy ceiling. However, population dynamics do not follow a smooth, linear-response picture: across dozens of runs populations collapsed into concentrated wealth states and switched between attractors in a seed-dependent, step-like way. Practical implications are twofold: information elicitation provides a reliable signal for agent valuation and monitoring, but steering or regulating many-agent systems may require interventions that flip attractors rather than small nudges.
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Credibility Assessment:
Single author, no listed affiliation, arXiv preprint, zero citations and no author reputation signals — insufficient identifiable credibility.