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Social Behavior Among Autonomous AI: How Large Language Models Interact in Dynamic Networks
Narges Fardnia, Fatemeh Seyedin, Matthias Becker, Mahmoudreza Babaei, Adrian Weller
TL;DR
The paper asks how AI systems cooperate with one another in adaptive networks, a question that matters as people increasingly rely on AI. It tests four LLMs in public goods games across model, network, and prompt conditions, finding cooperation patterns associated with model, topology, and prompt design.
Problem
How different AI systems interact with one another in adaptive networks remains an important question as people increasingly rely on AI systems.
Source: §1 · pp. 1–2Method
The study tests Mistral, Llama3, Gemma3, and Phi3 in public goods games under single- and mixed-model conditions, varying network topology and prompts.
Source: §1 · p. 2, §3 · pp. 3–4Results
Mistral and Llama3 were highly cooperative while Phi3 tended toward defection, Erdős-Rényi networks fostered cooperation, and society-benefit prompts had a cooperation rate of 0.93.
Source: §4.1 · p. 5, §4.2 · p. 5, §5 · p. 6Takeaways & Limitations
Abstract
from arXiv · showhide
Cooperation is a cornerstone of human societies, enabling collective progress in dynamic and uncertain environments. With the advent of AI systems acting autonomously, it becomes crucial to understand not only human-AI cooperation but also AI-AI interactions in adaptive networks. In this work, we examine the interactions of AI using Large Language Models -- Mistral, Llama3, Gemma3, and Phi3 -- in a public goods game within dynamic network structures. Our experiments were conducted under single-model and mixed-model conditions across Watts-Strogatz (WS), Barabasi-Albert (BA), and Erdos-Renyi (ER) networks. We analyzed the impact of model architecture, network topology, and prompt design on cooperative behavior. Results show that Mistral and Llama3 offer high cooperation rates, while Phi3 shows defective tendencies. Additionally, the random structure of Erdos-Renyi networks dramatically improves cooperation. Prompt design also plays a key role; a society-benefits prompt leads to a higher cooperation level. These findings offer a preliminary framework for LLM-based simulations in adaptive social networks.
1. Introduction
The introduction motivates studying AI cooperation as AI systems take on social roles, then asks how LLMs cooperate with one another. The study compares models, network structures, and prompts, reporting differences across all three.
1. Introduction
- Cooperation can benefit groups, but in a one-turn prisoner’s dilemma self-interest can make defection the rational choice.The introduction contrasts this dilemma with humans’ initial tendency to cooperate and their potential to defect when trust erodes.Source: §1 · p. 1
- AI–AI interaction needs study as people increasingly rely on AI, alongside questions about whether humans trust or cooperate with machines.The introduction notes that people may trust machines less, yet can collaborate with them under suitable conditions.Source: §1 · pp. 1–2
- The study tests Mistral, Llama3, Gemma3, and Phi3 in public goods games across dynamic networks, comparing model, topology, and prompt effects.The experiments include single-model and mixed-model conditions across Watts-Strogatz, Barabási-Albert, and Erdős-Rényi networks.Source: §1 · p. 2
- Mistral and Llama3 were highly cooperative, while Phi3 tended toward self-interest; Erdős-Rényi networks and society-benefit prompts were associated with higher cooperation.The authors present these findings as a preliminary framework for studying LLM cooperation in adaptive social networks.Source: §1 · p. 2
2. Related Work
Prior work links network structure to cooperation and studies AI in human networks, but advanced LLMs remain underexplored in dynamic-network social dilemmas. This work combines LLM agents with a flexible simulation environment to investigate that gap.
2. Related Work
- Network topology can shape path lengths, trust, information flow, and the balance between cooperation and free-riding.The cited background describes Watts-Strogatz networks as balancing local clustering with global connectivity through modest rewiring.Source: §2 · p. 2
- Research on hybrid human-AI networks reports that strategically placed bots can enhance coordination, creativity, and cooperation through network properties such as clustering and modularity.The cited work often embeds simple AI bots within human social networks.Source: §2 · p. 2
- AI’s social impact depends not only on algorithmic capability but also on its position and connectivity within a network.The passage connects this point to work on human-machine collaboration and hybrid networks.Source: §2 · p. 2
- Dynamic-network applications of LLMs remain underexplored, especially for cooperation; simulation platforms such as Empirica have mainly used rule-based bots.Prior PGG approaches have emphasized reinforcement learning in static or simple networks, while evolving-network studies highlight rewiring and heterogeneous connectivity.Source: §2 · p. 2
- The study combines Empirica and Ollama to investigate how network topology and advanced AI reasoning interact in cooperative dynamics.The authors frame this integration as addressing gaps concerning collective intelligence and social welfare.Source: §2 · p. 2
3. Methodology
The methodology places eight LLM agents in a repeated public goods game with changing network ties. It varies model composition, initial topology, and prompts while holding payoff and rewiring rules constant across conditions.
3. Methodology
- Eight agents start with $1.00 and play 16 rounds, choosing to cooperate or defect before reshaping their network ties.Results are averaged across multiple runs of each experiment.Source: §3 · p. 3
- Cooperation costs an agent $0.05 per neighbor and gives each neighbor $0.10; agents must defect if their budget cannot cover the cost.Defection leaves the agent’s budget unchanged, and LLM decisions use budget, neighbors, and neighbors’ prior actions.Source: §3 · p. 3
- After actions, agents may keep or remove a neighbor or form a tie with a non-neighbor, using the same rewiring mechanism across conditions.The process randomly selects a current neighbor or a random non-neighbor for possible removal or connection.Source: §3 · pp. 3–4
- Experiments vary initial topology and LLM strategies across Watts-Strogatz, Barabási-Albert, and Erdős-Rényi networks, keeping payoff structure and rewiring rules constant.The study uses 16 rounds and reports averages across multiple runs.Source: §3 · pp. 3–4
- The study compares an all-same-model baseline with a mixed crew assigning two agents to each of four LLMs.The mixed-model condition examines how model differences relate to behavior and coordination.Source: §3 · p. 4
- Agents receive general, self-benefit, or society-benefit prompts after being given a shared explanation of the public goods game.The prompts respectively emphasize neutral action, maximizing individual wealth, or maximizing total society wealth.Source: §3 · p. 4
4. Results
Across mixed- and single-model public-goods experiments in WS, BA, and ER networks, cooperation varied by model and topology. ER had the highest cooperation for all models except Llama3, and society-benefit prompts had the highest cooperation rate.
4.1. Cooperation Rate
- Mixed-model Mistral cooperation was 0.94–1.00 while Phi3 was lowest at 0.28–0.37; single-model Mistral was complete and Llama3 reached 0.86 on ER.Source: §4.1 · p. 5, Table 1 · p. 5, Table 2 · p. 5
4.2. Network Dynamics and Prompt Impacts
- Society-benefit prompts led cooperation rate (0.93) and mean score (3.59), versus self-benefit (0.89; 3.40) and general prompts (0.65; 2.86).Source: §4.2 · p. 5
- In mixed-model runs, ER degree rose from 2.5 to 5 and clustering from 0.57 to 0.80; BA degree rose from 3.5 to 5.75, while WS degree changed from 6.25 to 6.5.WS clustering increased from 0.88 to 0.94; Figure 3 tracks degree and clustering across rounds and network structures.Source: §4.2 · p. 5, Figure 3 · p. 6
- In single-model runs, Mistral and Llama3 tended to increase mean degree and clustering, while low-cooperation Gemma3 showed declines in both.The authors suggest cooperation fosters stronger, more cohesive ties, while defective behavior leads to fragmentation and reduced connectivity.Source: §4.2 · p. 5, Figure 4 · p. 6, Figure 5 · p. 6
5. Discussion and Conclusion
Cooperation varied with network topology, model, and prompt design: ER networks fostered cooperation, and the society-benefit prompt achieved the highest cooperation rate. The findings suggest lightweight LLMs can model adaptive social behavior, while future work could explore more robust models, human-AI interactions, and richer prompts.
5. Discussion and Conclusion
- ER networks foster cooperation, Mistral and Llama3 are reliable collaborators, Phi3 tends to defect, and Gemma3 is context-dependent.The findings identify network topology and model as factors shaping cooperation.Source: §5 · p. 6
- The society-benefit prompt achieved the highest cooperation rate, aligning with collective goals.Source: §5 · pp. 6–7
- The findings suggest lightweight LLMs can model adaptive social behaviors and interactions in intelligent systems.Source: §5 · p. 7
- Future studies could explore more robust LLMs, human-AI interactions, and richer prompts to enhance cooperative AI systems.Source: §5 · p. 7
Declaration on Generative AI
The authors used GPT-4 and Grammarly for grammar and spelling checks, then reviewed and edited the content and retained full responsibility for the publication.
Declaration on Generative AI
- The authors used GPT-4 and Grammarly for grammar and spelling checks, then reviewed and edited the content and retained full responsibility for the publication.Source: Declaration on Generative AI · p. 7