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

Ivan Pasichnyk

TL;DR

It is shown 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, suggesting that environmental pressure calibration is a viable curriculum design strategy for LLM agent development.

Abstract

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.

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

TL;DR

It is shown 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, suggesting that environmental pressure calibration is a viable curriculum design strategy for LLM agent development.

Abstract

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.
Paper Structure (35 sections, 2 figures, 4 tables)

This paper contains 35 sections, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. LLM agents in game-theoretic settings.
  4. Survival instinct in LLM agents.
  5. Multi-agent environments and emergent behavior.
  6. Curriculum learning and open-ended evolution.
  7. Yerkes-Dodson law.
  8. Sexual selection theory.
  9. Method: Survival Arena
  10. Environment
  11. Agent architecture
  12. Action space
  13. Pressure axis 1: Upkeep (survival cost)
  14. Pressure axis 2: Sexual selection (V7)
  15. LLM as agent policy
  16. ...and 20 more sections

Figures (2)

  • Figure 1: The Yerkes-Dodson curve for LLM agent cooperation. Left axis: successful trades (blue circles). Right axis: game duration in turns (red squares). The green shaded region marks the "edge of viability" where cooperation peaks. At upkeep = 7, the game collapses to 20 turns as agents die rapidly, eliminating opportunities for social interaction. Note: upkeep = 2 has two replicates (11 and 12 trades); the figure shows one representative point.
  • Figure 2: Multi-metric analysis of P2b experiments. Top-left: Trades show inverted-U (peak at upkeep = 5). Top-right: Attacks decrease monotonically with pressure as agents die before fighting. Bottom-left: Average agents alive per turn decreases with pressure. Bottom-right: Shannon entropy increases monotonically---a misleading artifact of small-sample bias (see Section \ref{['sec:entropy']}).