Poor Man's Agentic Modeling: A Systematic Review and Scaling Toolkit for Low-Parameter Surrogates of LLM-Agent Societies

Simulations in which every agent is a large language model (LLM) are powerful but costly, and the questions asked of them are almost always macroscopic — phase behaviour, stylised facts, scaling with the number of agents N — not the cognition of any single agent. This survey organises the literature behind a cheaper alternative: replace each LLM agent with a low-parameter surrogate whose few parameters are fit from small experiments, and study how the macroscopic observable scales as N grows. Through a four-wave adversarial multi-agent literature search yielding 115 existence-verified sources, it assembles the tools needed for this programme: eleven ways to replace an LLM agent (from one-parameter sociophysics rules to policies read directly off model internals), and a statistical-physics scaling toolkit (finite-size scaling, data collapse, universality, causal emergence). The organising result is that the mean-field-ness of an LLM society is the product of two coarse-graining choices — interaction order (what an agent perceives) and memory length — which together predict, cell by cell, whether 'more agents make the cheap model better' holds or breaks. No prior work joins a low-parameter surrogate to a named LLM simulation's macro observable with a finite-size-scaling analysis; that triple-join is the open contribution. This is the companion review to the main paper 'Poor Man's Agentic Modeling: Simulating Large LLM-Agent Societies Without a GPU Cluster', where the taxonomy and scaling toolkit are validated empirically.