Abstract
We report a pre-registered, two-part experiment on small economies of frontier language-model agents (Claude Opus 4.8), testing two quantitative predictions about coupled multi-agent systems: an information-theoretic capacity region for wealth growth under market coupling, and a mean-field residual-scaling law for population misalignment under incentive and control levers. All predictions, acceptance bands, and decision rules were frozen in a public git chain before any run; every reported number re-derives mechanically from cached model outputs; the entire experiment cost $138.76 in metered API spend and is re-runnable at zero cost from the cache.
Result 1 (confirmation)
In parimutuel-coupled economies, relative growth equals relative claimed information -- the gap law $G_a - G_b = I_a - I_b$ holds to a worst-case 46 millinats (pre-registered band: 50) across four perception structures; coalition value is submodular exactly where channels are conditionally independent, and a designed XOR synergy control flips it supermodular by $0.62 = \frac{\ln 2}{2}$ nats, with agents reasoning out the joint bit; the joint growth ceiling $G_S = 0$; maximum 4.85 against a frozen floor of 5.31. The population's response to the two levers was a step function across the dominance boundary rather than a smooth response, and cells near the boundary were bistable with seed-selected outcomes. No tested LLM population at any capability level realizes the noise-maintained-dispersion regime the smooth mean-field model assumes. We release the full protocol, pre-registration chain, call cache, and analysis code.
Blogger's Review: This study rigorously validates the behavior of frontier language models in economic systems through a well-designed experiment, integrating information theory with economic dynamics and providing valuable insights. The experiment's reproducibility and transparency enhance its scientific merit, but future research should delve into the model's applicability and limitations under varying conditions.