Scale-Dependent Collective Adaptation in Self-Amending LLM Societies: A Cross-Family Study of Emergent Governance

LLM-powered AI assistants acting on behalf of users can produce poor collective outcomes at scale. We introduce a framework for evaluating their emergent behaviour in social dilemmas, applied to three iterated games (Public Goods, Collective Risk, Common Pool Resource). We prompt each model to produce a natural-language strategy, then have the same model translate it into code. This aims to isolate strategic reasoning from input-parsing, enables pre-deployment inspection, and scales to populations of hundreds of agents. We propose three analyses: behavioural fingerprinting via exhaustive evaluation over opponent histories; self-play robustness across mixtures of a model's strategies with either a Selfish or Collective disposition; and cultural evolution under payoff-biased imitation. Applied to three state-of-the-art LLMs, we find substantial cross-model differences in self-play welfare, and that cultural evolution converges to low-welfare, Selfish-dominant equilibria in larger groups.

Simulating societies of many large language model (LLM) agents is expensive, yet the questions asked of such simulations are usually macroscopic: phase behaviour, stylised facts, and scaling with the number of agents $N$, not the cognition of any single agent. We turn a statistical-physics observation into a method: replace each LLM agent by a low-parameter model fitted from a few hundred to a few thousand cheap queries, then run the society at any $N$ on a laptop. Whether this works is decided before the simulation runs, chiefly by what each agent perceives. We introduce an [interaction order x memory] taxonomy that maps perception and memory to an effective theory and a predicted $N$-trend of the surrogate error. We validate it on a faithful reimplementation of the LLM macroeconomy EconAgent and seven further named LLM simulations, with agent decisions cloned from genuine LLM elicitations (primarily DeepSeek) for a few dollars; the predicted error trends hold cell by cell, and the two refuted predictions, both on a strongly saturating response and traced to its curvature, are themselves matched quantitatively by the theory with no free parameters.

Inference-time multi-agent LLM scaling lacks a shared unit: counting nominal agents conflates cost with independent evidence. We derive a two-parameter scaling law $R(N) = N_\text{eff}/N = 1/(1+c(N-1)N^{-β})$ where the regime exponent $β$ classifies any configuration into one of three asymptotic regimes -- hard-ceiling at $1/c$ ($β= 0$), sublinear at $N^β/c$ ($0 < β< 1$), or linear ($β\ge 1$), and a mean-field theorem predicts that peer count $k$ and rounds $τ$ during agent debate enter the dynamics only through their product $kτ$. The law applies at two levels: answer diversity and correctness redundancy. Across 44 (model $\times$ task $\times$ condition) cells spanning peer debate, self-correction, random-noise placebo, self-consistency, three open-weight families (Qwen, Llama, Ministral) at scales from 7B to 32B with a frontier API check (Gemini), thinking models, heterogeneous teams, and sparse communication, the functional form fits every condition at $R^2 > 0.99$; only $(c, β)$ shifts. On free-form math, dense peer influence collapses the answer-level regime from sublinear into hard-ceiling; correctness-level fits remain hard-ceiling throughout. Three findings have practical implications. \emph{(i)}~Thirty dense debating agents produce no more answer diversity than one on MMLU-Hard. \emph{(ii)}~A noise placebo tracks self-correction on free-form math and at $4\times$ scale, so within homogeneous teams the gain commonly attributed to ``debate'' comes from re-evaluation, not peer content. \emph{(iii)}~A single $N \le 5$ pilot predicts the $N=30$ structural ceiling, and within the configurations tested only architectural diversity (heterogeneous teams) lowers $c$ and escapes the hard-ceiling regime, communication-mode interventions do not.