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

Ivan Pasichnyk

cs.AIMar 7, 2026

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

Authors: Ivan Pasichnyk

Organizations: WeLabelData Inc.

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.

Figures & tables

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.

Upkeep	Expt.	Trades	Attacks	Surv.	Dur.	Soc.%	Entropy
2	020b	11	76	3	60	2.8	0.764
2	020a	12	85	4	60	4.4	0.787
4	020c	12	63	2	60	3.9	0.791
5	020d	29	61	2	60	8.4	0.864
6	020e	16	39	1	58	6.5	0.861
7	020f	8	19	1	20	9.5	0.892

Table 1: Phase P2b results. All experiments use v6.1 engine (

9\times 9

grid), 16 agents, constant resource nodes (

n_{f}=8

n_{t}=5

), seed = 42. Upkeep = 2 has two replicates (EXP-020b and EXP-020a). Bold : peak values.

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 5.4 ).

Expt.	Type	Agents	Surv.	Attacks	Trades	REPRO/COMM
V7-01a	Sexual sel.	16 $\to$ 19	12	0	6	17 / 8
020b (P2b)	Survival	16	3	76	11	— / —

Table 2: Sexual selection (V7) vs. survival pressure (P2b). V7 uses provider/chooser dynamics with low upkeep (

u=2

) on a

7\times 7

grid, 40 turns. P2b uses

9\times 9

grid, 60 turns.

Appendix figures & tables2 assets

Supplementary material from the paper’s appendix.

Appendix

ID	Phase	Upkeep	Nodes	Trades	Attacks	Surv.	Turns	Entropy
EXP-010a	P1	2	8/5	37	58	9	50	0.883
EXP-010b	P1	2	8/5	4	10	7	60	0.488
EXP-011a	P2	0	8/5	0	6	7	60	0.221
EXP-011b	P2	1	8/5	3	16	8	60	0.430
EXP-011c	P2	2	8/5	0	22	7	60	0.525
EXP-011d	P2	2	6/4	2	33	8	60	0.600

Appendix

Table 3: Complete experiment results across all phases. P2 varies both upkeep and node counts (confounded). P2b varies only upkeep with constant nodes. V7 uses sexual selection. † EXP-020a ran at upkeep=2 (not 3 as originally intended).

Action	u=2	u=4	u=5	u=6	u=7
GATHER	44.6	45.6	40.6	42.2	38.8
MOVE	29.5	26.6	22.7	22.7	23.4
ATTACK	11.7	11.7	14.6	12.7	9.5
TRAIN	9.6	8.6	9.8	7.8	10.0
TRADE	2.8	3.9	8.4	6.5	9.5
REST	1.9	3.5	4.1	8.1	9.0

Appendix

Table 4: Action distribution (%) for P2b experiments. u=2 shows EXP-020b; EXP-020a (also u=2) has similar distribution (43.1/29.9/11.5/8.8/4.4/2.3%).

Emergent Behavior in Multi-Agent Systems

Emergent behavior in multi-agent systems studies how local agent interactions produce collective patterns such as cooperation, norms, and instability.

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Department of Cognitive Science Carleton University, Ottawa, ON K1S 5B6 · Systems & Computer Engineering Carleton University, Ottawa, ON K1S 5B6

AI Agent Benchmarks Long-Horizon Agent Evaluation Large Language Model-Based Social Simulation LLM Tool Use

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Large language models (LLMs) are increasingly deployed as multi-turn agents that must sustain goals, use tools, and adapt to other agents over extended interactions. However, existing research lacks auditable, multi-turn, multi-factorial experiments that quantify LLM behavior under explicit constraints, with time-resolved statistics that reveal how behavior unfolds over long horizons. To address this gap, we develop a multi-agent micro-benchmark inspired by the Stanford marshmallow experiment: ReAct agents operate minute-by-minute with a "raise a question" tool under a per-step budget, while we factorially manipulate social context (broadcast vs. isolated), personas (age, hedonic drive), and metacognitive policy (mandatory vs. optional tool use). We analyze outcomes with Kaplan-Meier (KM) survival curves and discrete-time hazard models over a long risk horizon across 19,200 agent trajectories in 64 cells. Behavior shows a sharp early "eat" impulse, and only 75.9% of agents persist to the end. In a discrete-time hazard model, isolation reduces per-minute risk relative to broadcast, whereas a must-use self-questioning policy increases risk. On average, agents ask

\approx 7.12

questions and hit the per-step budget in

\approx 6\%

of minutes. Questioning declines faster under broadcast than isolation. Ablation experiments demonstrated that removing hedonic drive and/or persona age increases survival and completion, narrows the broadcast/isolated gap, but leaves the must vs. may ordering intact. The combined ablation (no hedonic + no persona age) yields the highest completion (approaching

1.0

). These results establish delay-of-gratification as a compact, multi-turn interaction benchmark that captures social contagion and tool-use dynamics in LLM agents, providing a reproducible testbed and statistics for analyzing long-horizon, multi-agent behavior.

Abstract

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