The Role of Social Learning and Collective Norm Formation in Fostering Cooperation in LLM Multi-Agent Systems

Abstract: A growing body of multi-agent studies with LLMs explores how norms and cooperation emerge in mixed-motive scenarios, where pursuing individual gain can undermine the collective good. While prior work has explored these dynamics in both richly contextualized simulations and simplified game-theoretic environments, most LLM systems featuring common-pool resource (CPR) games provide agents with explicit reward functions directly tied to their actions. In contrast, human cooperation often emerges without full visibility into payoffs and population, relying instead on heuristics, communication, and punishment. We introduce a CPR simulation framework that removes explicit reward signals and embeds cultural-evolutionary mechanisms: social learning (adopting strategies and beliefs from successful peers) and norm-based punishment, grounded in Ostrom's principles of resource governance. Agents also individually learn from the consequences of harvesting, monitoring, and punishing via environmental feedback, enabling norms to emerge endogenously. We establish the validity of our simulation by reproducing key findings from existing studies on human behavior. Building on this, we examine norm evolution across a $2\times2$ grid of environmental and social initialisations (resource-rich vs. resource-scarce; altruistic vs. selfish) and benchmark how agentic societies comprised of different LLMs perform under these conditions. Our results reveal systematic model differences in sustaining cooperation and norm formation, positioning the framework as a rigorous testbed for studying emergent norms in mixed-motive LLM societies. Such analysis can inform the design of AI systems deployed in social and organizational contexts, where alignment with cooperative norms is critical for stability, fairness, and effective governance of AI-mediated environments.

• The paper introduces a simulation framework that demonstrates how social learning and group norm formation sustain cooperation without direct reward signals.
• It employs agent-based modeling to validate that punishment, imitation, and explicit norm voting critically influence resource sustainability and agent survival.
• Findings reveal that model-specific biases and coordination mechanisms drive adaptive behaviors, with larger LLMs outperforming smaller ones in challenging environments.

Social Learning and Norm Formation for Cooperation in LLM Multi-Agent Systems

Introduction and Motivation

This paper presents a simulation framework for studying the emergence of cooperation and collective norms in multi-agent systems composed of LLM agents. The framework is grounded in Ostrom's institutional design principles and cultural evolutionary theory, focusing on common-pool resource (CPR) dilemmas where individual incentives to over-exploit a shared resource conflict with the collective interest in sustainability. Unlike prior work that provides agents with explicit reward signals, this framework removes direct reward observability, requiring agents to infer payoffs and adapt through social learning, punishment, and group norm formation. The approach aims to more closely mirror human social dynamics, where cooperation emerges from local heuristics, communication, and indirect feedback.

Figure 1: Framework overview. Agents choose effort and consumption, may punish at personal cost, imitate higher-payoff peers, and set group harvest thresholds via propose-to-vote. Payoff-biased social learning is the main evolutionary driver; the voting step scales efficiently with two API calls per agent per round.

Framework Design and Mechanisms

The simulation environment models a renewable resource shared by $N$ agents, each with latent strategies and beliefs. Agents make decisions in four modules per round:

• Harvest and Consumption: Agents select effort levels, harvest resources, and consume a fixed amount.
• Individual Punishment: Agents may monitor and punish peers who violate group norms, incurring personal costs.
• Social Learning: Agents observe peer outcomes and may adopt strategies from higher-payoff individuals via payoff-biased imitation.
• Group Decision: Agents propose and vote on collective harvest caps, updating the group norm by a median-voter rule.

For LLM agents, all adaptation occurs through in-context learning and prompt-based decision-making, with no direct parameter copying. The framework operationalizes cultural evolution via a variation-selection-retention loop, with selection driven by social learning and explicit norm voting, and retention via norm broadcasting.

Validation with Agent-Based Modeling

The framework is validated against established findings in human CPR studies using agent-based modeling (ABM):

• Punishment sustains cooperation: Disabling punishment leads to rapid collapse of cooperation and resource depletion.

  Figure 2: Cooperation fades once punishment is disabled at $t=15$. Enabling punishment sustains cooperation longer, but removal leads to rapid decline.

• Survival time varies with punishment strength and growth rate: Stronger punishment generally improves survival under moderate growth rates, but the effect is non-linear.

  Figure 3: Survival time across punishment strength and growth rate. Stronger punishment improves survival when growth rates are moderate, but the relationship is not strictly linear.

• Altruistic vs. selfish populations: Altruistic groups outperform in harsh environments, while selfish groups do better in rich environments. Mixed populations excel in rich settings due to efficient norm selection.

  Figure 4: Altruistic groups do better in harsh environments; selfish groups do better in rich environments. Mixed populations perform best in rich environments.

LLM-Agent Simulations and Comparative Analysis

The framework is extended to LLM agents, with each action implemented via dedicated prompts. Populations are initialized with altruistic or selfish norms, and their ability to sustain cooperation is evaluated across different LLM models and environmental conditions.

Harsh Environment ($r=0.2$)

• Larger models (claude-sonnet-4, deepseek-r1, gpt-4o) with altruistic initializations survive longer, mirroring ABM results.
• Smaller models collapse early regardless of initialization, indicating limited adaptability.

  Figure 5: Survival time comparison across LLMs in the harsh environment. Larger models with altruistic populations perform better; smaller models collapse earlier.

Rich Environment ($r=0.6$)

• Deepseek-r1 adapts and explores, often reaching the simulation cap.
• gpt-4o and claude-sonnet-4 plateau at lower survival times, exhibiting conservative/altruistic biases.
• Smaller models survive longer when initialized selfish, while altruistic initializations sometimes underharvest and starve.

  Figure 6: Survival time comparison across LLM models in the rich environment. Deepseek-r1 survives longer; smaller models perform better when initialized selfish.

Norm Structure and Model Clustering

Analysis of final norm vectors reveals clustering by model family, with provider-specific pretraining and preference-tuning pipelines imprinting consistent behaviors. Initialization effects are secondary to model effects.

Figure 7: Norm structure at the end of each run. Models exhibit clear family clustering; initialization effects are secondary.

Efficiency Dynamics

Efficiency traces show a common tendency to overexploit resources early, leading to collapse, especially for selfish populations and in harsh environments. In rich environments, claude-sonnet-4 and gpt-4o maintain lower efficiency after stabilization, indicating reluctance to explore greedy strategies.

Figure 8: Efficiency transition across LLM models. Early overexploitation leads to collapse; conservative models maintain lower efficiency in rich environments.

Ablation Studies: Alignment Mechanisms

Ablation experiments isolate the effects of implicit (social learning) and explicit (group norm voting) alignment:

• Neither channel: Rapid collapse, confirming the necessity of coordination mechanisms.
• Only group decision: Explicit alignment alone can sustain cooperation, sometimes outperforming the full system in selfish populations.
• Only social learning: Imitation without a shared norm amplifies stochastic fluctuations and hastens collapse.
• Model interaction: Explicit alignment suffices for "thinking" models (deepseek-r1), while non-thinking models (gpt-4o) require both channels for stability.

Figure 9: Survival time comparison of deepseek-r1 and gpt-4o in ablation conditions. Explicit alignment is critical for stability, especially in non-thinking models.

Figure 10: Survival time comparison of qwen3-32b in ablation conditions (All, OSL, OGD, Neither).

Implications and Future Directions

The framework provides a rigorous testbed for probing the emergence of cooperative norms in LLM societies under mixed-motive conditions. Key findings include:

• Systematic differences in cooperative tendencies across LLM models, with larger models better able to adapt and sustain cooperation.
• Coordination mechanisms (social learning and explicit norm sharing) are essential for stability; their absence leads to rapid collapse.
• Model-specific inductive biases shape exploration, norm formation, and group outcomes, with provider clustering evident in norm structure.

Practically, these results inform the design of AI systems for social and organizational contexts, emphasizing the importance of model selection, transparency, and safeguard mechanisms to ensure alignment with cooperative norms. Theoretically, the work advances understanding of cultural evolution and governance in artificial societies, highlighting the interplay between individual adaptation, social learning, and institutional arrangements.

Future research should extend the framework to more complex socio-ecological systems, multi-level governance, and richer communication mechanisms. Investigating the co-evolution of institutional structures and agent norms, as well as robustness across diverse prompting and model families, will further clarify the generality of observed behaviors.

Conclusion

This paper introduces a CPR simulation framework for LLM multi-agent systems, enabling endogenous norm evolution and cooperation without explicit reward signals. Through ABM and LLM simulations, the framework is validated and shown to elicit diverse cooperative behaviors, with systematic differences across models. Coordination mechanisms are essential for sustaining cooperation, and model-specific biases significantly influence emergent norms. The framework serves as a theoretically grounded and empirically robust platform for advancing research on governance, cooperation, and norm formation in agentic societies.