Poor Man's Agentic Modeling: Simulating Large LLM-Agent Societies on a Laptop

Igor Itkin

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Poor Man's Agentic Modeling: Simulating Large LLM-Agent Societies on a Laptop

Igor Itkin

arXiv:2608.11215v1Jul 19, 2026cs.AIcond-mat.stat-mechcs.CLcs.LGcs.MAphysics.soc-ph

TL;DR

LLM-agent societies are costly to simulate even though researchers mainly study their macroscopic behaviour and scaling with N. This paper replaces agents with fitted low-parameter surrogates organized by perception and memory, finding that the taxonomy predicts when surrogate error vanishes, saturates, or depends on interaction structure.

Problem
LLM-agent societies are expensive to simulate, limiting systematic study of macroscopic behaviour and scaling with the number of agents N.
Method
The paper fits low-parameter surrogates from genuine LLM decisions and uses an interaction-order × memory taxonomy to predict surrogate-error trends before simulation.
Results
Across eight named LLM simulations, the surrogate reproduced macroscopic signatures while blind tests evaluated the taxonomy’s pre-registered cell assignments.
Takeaways & Limitations
Surrogate success is determined chiefly by agents’ perception and memory design, which can identify the relevant error regime before running the simulation.
Takeaways & Limitations
The strongest test—running target models to reproduce their published macroscopic numbers—remains open, and the commutation decomposition is an organising heuristic rather than a theorem.

Abstract

from arXiv · show

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.

1 Introduction

The paper proposes replacing costly LLM agents with cheap, query-fitted surrogates for macroscopic studies, with validity determined chiefly by agent perception. It introduces a perception-based criterion and validates it through EconAgent, preregistered taxonomy tests, and analysis of LLM-driven decisions.

Motivation: Cheap surrogates fitted from a small number of queries can replace expensive agents for macroscopic studies at arbitrary N on a laptop.The motivation is that macroscopic behaviour in large interacting systems is governed by a few collective variables, while most microscopic detail is irrelevant.
Criterion: Agent perception determines the effective regime: population-wide aggregate responses are mean-field, with scalar-surrogate error vanishing as N−1/2.The paper presents this as a criterion for deciding when the surrogate approach applies.
Validation: The criterion is validated on a faithful, code-authoritative reimplementation of EconAgent, where surrogates reproduce the target’s macroscopic signatures.The validation also reveals what those signatures do and do not measure.
Validation: The taxonomy is falsified directly using preregistered cell assignments tested blind on held-out contact graphs and a real LLM’s measured response function.This is the second of three validation approaches described in the introduction.
Findings: EconAgent’s Okun’s-law reproduction is an accounting identity satisfied by a behaviour-free policy, whereas its Phillips curve is behavioural and carried by one labour-cyclicality coefficient.The coefficient is estimated from cloned decisions, and its macroscopic value is recovered as an out-of-sample prediction.

2 Related work

Prior work establishes macroscopic phenomena, supplies candidate few-parameter dynamics and closure machinery, or keeps LLMs in the loop without analyzing scaling. This paper joins these strands by fitting per-agent low-parameter surrogates to genuine LLM decisions and studying macroscopic observables as N varies.

LLM-agent societies: Expensive LLM societies reproduce human-like macroscopic phenomena and define observables, but lack paired low-parameter models with analyzed scaling.Examples include Generative Agents, EconAgent, OASIS, and AgentSociety.
Sociophysics and coarse-graining: Sociophysics offers few-parameter rules, but leaves open which rule a given LLM agent realizes.Referenced candidates include voter and Ising models, bounded-confidence dynamics, kinetic opinion equations, and active-matter flocking dynamics.
Sociophysics and coarse-graining: Coarse-graining, equation learning, mean-field games, heterogeneous-agent macroeconomics, and closure theory provide reductions and machinery, but not finite-N closure or LLM-specific targets.The cited frameworks also motivate cautions about moments, small-N exponents, and the N →∞ limit.
Novelty: MF-LLM couples a population mean field to per-agent LLM decisions, whereas this paper replaces agents and studies macroscopic observables as N varies.The passage identifies MF-LLM as the closest prior work and states that it neither analyzes scaling nor replaces the agent.
Novelty: The paper’s contribution is a low-parameter surrogate per agent, fitted from genuine LLM decisions on named simulation prompts to reproduce its macroscopic observable.This is presented as the join no prior work makes.

3 The perception-ordered taxonomy

The taxonomy orders surrogate error by what agents perceive and whether they retain memory, predicting which effective closure is needed and how error scales with population size N. Its theory distinguishes sampling-noise decay from persistent errors caused by heterogeneous perception, nonlinear response curvature, interaction structure, or memory.

Core framework: The commutation defect ∥PΦt − ˆΦtP∥ measures the gap between the LLM society’s macroscopic dynamics and its low-parameter surrogate.Exact reproduction requires coarse-graining to commute with the dynamics: PΦt = ˆΦtP.
Predicted N-trends: Global, identical perception yields mean-field error that vanishes as N^-1/2, whereas private or neighbourhood perception can make error plateau or grow with N.Averaging is valid when the population mean is sufficient; otherwise it discards the heterogeneous structure driving decisions.
Taxonomy axes: Interaction order classifies how many other agents inform each decision, while memory determines whether past states must be tracked.Global feeds use scalar mean fields; community feeds require block or graphon mean fields; local interactions require pair approximations, with memory kernels for long memory.
Curvature and heterogeneous perception: Curved responses create a Jensen bias that stalls community-error decay at |m1|, breaking the B^-1/2 law, while symmetric responses retain B^-1/2 decay.For private feeds, B = N, so the same mechanism produces a finite population-size knee when curvature is present.
Global-feed exactness: Identical global perception makes curvature irrelevant: the mean-field defect is only the O(N^-1/2) fluctuation of mean noise and vanishes as N →∞.This contrasts with heterogeneous misperception, which reinstates an O(1) Jensen floor.

4 Methods

The method classifies an LLM society by perception and memory to predict surrogate-error scaling before fitting, then clones agent decisions with a low-parameter model and tests macroscopic observables out of sample. It screens observables for behavioural content, scales the surrogate society to large N, and validates the predicted error trend.

Algorithm 1: Algorithm 1 classifies the simulation’s perception cell, predicts the surrogate-error trend before fitting, clones a low-parameter agent from genuine decisions, and validates macroscopic behaviour at large N.The procedure screens the observable, reads the fitted response’s error floor and knee, and sweeps N geometrically beyond the target size.
Formal problem: The surrogate is fitted by behavioural cloning on teacher decisions, while the macroscopic observable remains an out-of-sample test rather than a fitting target.The formal objective minimises finite-size surrogate error between microscopic dynamics and coarse-grained surrogate dynamics.
Observable screening: Before validation, the method rejects any observable reproduced by a behaviour-free policy because it is an accounting identity rather than behavioural evidence.This discriminator is fixed in advance and applied uniformly.
Behavioural cloning: For EconAgent, the student uses twelve parameters: two logistic heads for work and consumption, each based on six features from teacher-generated state-action decisions.The NumPy reimplementation preserves an identical environment so the surrogate can replace the LLM agents directly.
Method validation: The reusable classification and perception-floor modules are first checked on the Minority Game and network epidemic models, whose scaling is known exactly.These checks precede their use on LLM targets.

5 Results

The results show that perception structure predicts surrogate-error scaling and that cheap surrogates can reproduce meaningful macroscopic behaviour, while model and prompt choices remain consequential. Across response heads and LLMs, most predictions hold quantitatively, with failures explained by curvature or finite perception resolution.

EconAgent: Okun’s published −0.918 correlation is behaviourally uninformative, whereas the Phillips correlation of −0.619 tests a genuine procyclical labour mechanism.A Bernoulli(0.5) work policy already yields Okun −0.998 because GDP is an affine function of working agents; the Phillips relation instead emerges out of sample from price-keyed labour.
LLM reproduction: Reasoning changes the cloned Phillips correlation sharply, producing −0.73 and −0.66 with reasoning versus −0.43 and +0.04 without it across plain and amplified wording.Under reasoning, DeepSeek-chat reaches −0.665 ± 0.12, about |∆| ≈0.05 from −0.619, but sibling models reach −0.78 and −0.84.
Interaction-order scaling: All three graph-dynamics predictions held: mean-field error shrank with N, community error reached an O(1) floor, and local error tracked degree structure.At large N, the three errors ordered exactly as predicted by interaction order.
Response-head tests: On the near-linear consumption head, global and private errors fell as N−1/2, community error stayed at an O(1) floor, and block-aware closure repaired it.The saturating work head was the exception: private-feed error remained at 0.018, while curvature predicted the Jensen floor and compressed the B = 5 to 80 ratio to about 2.0 versus ideal 4.0 and measured 1.93.
Cross-model validation: Twelve of thirteen models satisfied the coarse-graining predictions; only gpt-4o-mini failed the factor-of-two block-aware criterion by N = 3200.Its block error nevertheless fell monotonically relative to scalar error, while every other model met the criterion.
Perception thresholds: Perception thresholds depend on weak-majority resolution: Opus-4.8 and GLM-5.2 have Nc = ∞, DeepSeek has Nc = ∞ with βeff ≈1.9, while GPT-4o, Llama, and GPT-4-Turbo have finite Nc.Strong majorities are read perfectly with P = 1; finite Nc occurs when βeff(N) decays through 1, making it a perception threshold rather than a thermodynamic critical point.

6 Discussion

The discussion identifies perception and memory design as the decisive, pre-simulation determinants of whether low-parameter surrogates reproduce LLM-society observables. It also frames surrogate parameters as measurements of the mechanisms generating macroscopic laws, not merely cost-saving approximations.

Organising claim: Perception and memory design determine whether a low-parameter surrogate reproduces an LLM society’s macroscopic observable, before simulation begins.The paper presents this as its single organising claim.
Interaction structure: A global aggregate feed yields mean-field behaviour with scalar-surrogate error vanishing as N^-1/2.Community or graph-structured feeds instead produce O(1) or growing error and require block, graphon, or pair-plus-memory closures.
Additional axes: Fluctuating shared drivers and curved per-agent responses are additional practical axes beyond interaction order and memory.These factors are identified as affecting the surrogate’s effective behaviour alongside the main taxonomy.
Surrogates as instruments: Estimated surrogate parameters act as measurements of macroscopic mechanisms, including labour cyclicality, reasoning steps, societal saturation, decaying memory, and perception resolution.Examples span EconAgent, Williams’ epidemic, AgentSociety’s polarisation, and De Marzo consensus.

7 Limitations

The named-target reproductions establish mechanism-and-scaling matches, but the strongest validation—running each target’s exact models to reproduce its published macroscopic number—remains open. The EconAgent result is a code-calibrated reimplementation validated against its released non-LLM baseline.

Validation scope: The strongest test—running a target’s exact models to match its published macroscopic number—remains open.The named-target reproductions instead match mechanisms and scaling, while two reproduce a target’s published functional form on a new model.
Validation scope: EconAgent is a code-calibrated reimplementation validated against the released non-LLM baseline.
Memory limitation: The measured memory kernel shows conviction braking below the memoryless assimilation rate and a real, decaying, truncatable past-interaction tail.

8 Conclusion

The paper argues that macroscopic LLM-agent societies can be simulated cheaply when perception determines an effective theory and the surrogate-error trend with N. Surrogate fitting acts as a measurement of which microscopic properties control macroscopic observables.

Core contribution: Perception-ordered taxonomy maps simulation design to an effective theory and predicts how surrogate error changes with N.The taxonomy was tested with blind, pre-registered predictions on both axes at the LLM layer.
Core contribution: Two refuted predictions were quantitatively explained by response curvature, with the classification shown to be automatable.The conclusion identifies curvature as the source of both refutations rather than treating them as unexplained failures.
Interpretation: Surrogate fitting exposes the microscopic property on which a macroscopic observable depends.The paper characterizes the surrogate’s fit as a measurement rather than merely a computational replacement.
Reproducibility: A few dollars of DeepSeek elicitation supported the study, while cached decision traces make seeded results deterministic and LLM experiments cost-free to rerun.Runners, perception and scaling primitives, pre-registrations, outcomes, and figure scripts are included.

Appendices · A Proof of Proposition 1 (community floor) · B Proof of Proposition 2 (the knee N∗)

The appendices derive the community-floor error by aggregating independent community deviations and show that private feeds produce an N-dependent folded-normal error with a knee at N∗. The proofs use Gaussian behavior for affine responses and leading-order central-limit and second-order approximations for smooth nonlinear responses.

A Proof of Proposition 1 (community floor): Community deviations are defined as Db = A(g∗ + δb) − A(g∗), with independent Gaussian perturbations δb ∼ N(0, σ2).This sets up the aggregate-response deviation for each community under the proof of the community floor.
A Proof of Proposition 1 (community floor): The scalar surrogate predicts A(g∗), so the aggregate prediction error is determined by the realised population aggregate’s deviation from that value.The proof compares the population aggregate under a B-community feed with the scalar surrogate prediction.
A Proof of Proposition 1 (community floor): For affine A, the community deviation Db is Gaussian with mean m1 and variance v1.The Gaussian characterization supplies the parameters used in the aggregate-error calculation.
A Proof of Proposition 1 (community floor): For B communities, the average deviation is exactly N(m1, v1/B) for affine A and holds to leading order for smooth nonlinear A.The nonlinear extension follows from the central limit theorem in B and a second-order expansion in σ.
B Proof of Proposition 2 (the knee N∗): With a private feed, each of the N agents receives an independent draw, so B = N and the error is E|N(m1, v1/N)|.The proof reduces private-feed error to the folded-normal mean with variance decreasing as 1/N.
B Proof of Proposition 2 (the knee N∗): The private-feed folded-normal mean has two regimes separated by the knee N∗ = v1/m2 1.This identifies the crossover scale in the N-dependent error behavior.

C Proof of Proposition 3 (exact commutation at the mean-field cell)

At the mean-field cell, averaging commutes exactly with the update because all agents perceive the same global state, while finite-population noise contributes only O(N^-1/2) fluctuations. Heterogeneous perception, memory, or neighbourhood averaging breaks this sufficiency through bias or added dependence terms.

Exact commutation: Identical perception lets f(g_t) leave the population average, yielding the exact mean update E[g_t+1 | g_t] = a g_t + f(g_t).The averaging step is valid because every agent perceives the same g_t.
Exact commutation: The noise average has mean 0 and variance σ^2/N, producing an O(N^-1/2) fluctuation without involving response curvature.Thus curvature does not affect the mean-field commutation result.
Departures from commutation: With symmetric mean-zero perception errors of variance τ^2, the mean update acquires an O(1) Jensen bias that does not average away.This is the Jensen term identified in Proposition 1.
Departures from commutation: History-dependent decisions add a memory term, while neighbourhood averaging makes the mean an insufficient statistic and adds an interaction-order term.Both effects alter the mean update beyond the exact mean-field cell.

D Proof of Proposition 4 (consensus threshold and its crossing) · E External validation suite

The proof establishes a consensus threshold at βc = 1, with the ordered branch determined by β rather than population size N. The external validation suite then broadens taxonomy checks across additional LLM simulations and supporting analyses.

D Proof of Proposition 4 (consensus threshold and its crossing): At βc = 1, the disordered fixed point m = 0 loses stability in a supercritical pitchfork.The derivative of tanh(βm) at m = 0 equals β, and m = 0 is stable for β < 1.
D Proof of Proposition 4 (consensus threshold and its crossing): The nonzero self-consistent root obeys 1 = β −1.
D Proof of Proposition 4 (consensus threshold and its crossing): The ordered branch exists according to β alone and is independent of N.
D Proof of Proposition 4 (consensus threshold and its crossing): A finite critical group size arises only when the measured slope βeff(N) decays through 1.βeff(N) measures how an agent reads a weak majority in a list of N opinions; the crossing reflects perception rather than the thermodynamic limit.
E External validation suite: The external suite validates taxonomy cells using further named LLM simulations spanning the remaining perception cells.These validations complement the load-bearing experiments in EconAgent, the two blind tests, De Marzo, and the measured memory kernel.
E External validation suite: The appendix also reports cross-domain comparison against automatic differentiation, a distillation scaling law, an automated cell classifier, and two negative results.Each is presented as a self-contained confirmation of the taxonomy rather than a separate study.

E.1 Named targets across the perception cells … E.8 Smallville: the field’s most-cited numbers

Across eight named LLM simulations, the perception–memory cell predicts when low-parameter surrogates reproduce macroscopic behavior and how error scales with population size. The case studies also identify failures caused by interaction structure, missing market coupling, or an insufficient closure.

E.1 Named targets across the perception cells: AgentTorch’s global behavior supports archetype broadcasting, whereas local contagion requires network structure; OASIS’s feed choice switches between mean-field convergence and an O(1) polarisation floor.AgentSociety is the hardest local, long-memory case: scalar mean field cannot represent between-block polarisation, and error grows under densification.
E.2 A cross-domain check: closure versus autodiff: A degree-aware heterogeneous closure recovers transmission within 13%, fatality within 6%, and mortality RMSE 22 in 0.34 seconds, versus 48 for well-mixed dynamics.The closure uses thirteen degree blocks and calibrates two parameters with a derivative-free simplex, rather than differentiable million-agent machinery.
E.3 A distillation scaling law: EconAgent’s macro-observable error reaches tolerance after a couple thousand decisions, plateaus at four features, and is approximately separable, with 90% rank-one log-error.The measured error depends jointly on elicitation budget B, surrogate capacity p, and population N.
E.4 The classification is automatable: An LLM classifier matched hand-assigned cells in all eight tested simulations, including Generative Agents, without receiving taxonomy terms, enabling a pre-flight surrogate check.The authors note that published systems may have appeared in the classifier’s training data.
E.5 Williams et al.: a generative epidemic in the mean-field cell: From 462 real DeepSeek decisions, the Williams et al. surrogate reproduces the published logistic sign structure, flattened epidemic curve, and transition from one wave to several.The stay-home response is saturating: symptoms and prevalence increase staying home, while prevalence squared has a negative coefficient.
E.6 LLMTraveler: filling the empty cell: LLMTraveler’s fitted rule P(switch) = σ(β ∆−γ), with β = +0.40 and γ ≈0, reaches the Dynamic User Equilibrium at +4.7%, within the published ±10% band.The 16-traveler, two-route simulation retains persistent switching around equilibrium.
E.7 TwinMarket: the stylised facts need the market, not just the agent: TwinMarket returns remain near-Gaussian with excess kurtosis ≈0 at moderate coupling, but the same weak trader becomes supercritical as coupling rises, with excess kurtosis past 7.The limiting ingredient is un-elicited price-impact coupling rather than trader capacity.
E.8 Smallville: the field’s most-cited numbers: In Smallville’s 25-agent cascade, word-of-mouth reaches 13 of 25 and 5 attend, while a well-mixed control reaches all 25, showing diffusion depends on local interaction structure.The surrogate fits transmission and attendance logits from real DeepSeek decisions on a 25-node acquaintance graph.