The Yerkes-Dodson Curve for AI Agents: Emergent Cooperation Under Environmental Pressure in Multi-Agent LLM Simulations

Designing environments that maximize the rate of emergent behavior development in AI agents remains an open problem. We present the first systematic study of stress-performance relationships in large language model (LLM) multi-agent systems, drawing an explicit parallel to the Yerkes-Dodson law from cognitive psychology. Using a grid-world survival arena, we conduct 22 experiments across four phases, varying environmental pressure through resource scarcity (upkeep cost) and reproductive competition (sexual selection). Our key finding is that cooperative behavior follows an inverted-U curve: trade interactions peak at 29 under medium pressure (upkeep=5), while both low and extreme pressure produce 8--12 trades. Under extreme pressure, behavioral repertoire collapses to movement-only within 5--12 turns. We further show that sexual selection -- a softer pressure mechanism where all agents survive but not all reproduce -- eliminates inter-agent aggression entirely and produces communicative behavior absent under survival pressure. These results suggest that environmental pressure calibration is a viable curriculum design strategy for LLM agent development, analogous to the inverted-U relationship between arousal and performance in biological systems.