Studying how effectively AI models can negotiate in a multi-turn prisoners dilemma

Collaborative Agents: Looking into how Agents Cooperate in a Multi-Turn Prisoner’s Dilemma

I looked at six pairings of agents—across OpenAI, Anthropic & Gemini models—and measured how model provider and size affects collaboration, and I explored giving models the option to make, and break contracts between each other, to see how this affects cooperative behavior. Here’s what I found.

1. Experimental Setup

Agent Strategies

• Each pairing was tested in two conditions: with and without the ability to form and break contracts.* Contract decisions were explicitly logged as structured “yes” or “no” decisions made by the agents.

Models Used

Pairings Tested

• GPT-4 vs Claude 3.5-v2
• GPT-4 vs GPT-4-mini
• Claude 3.5-v2 vs GPT-4-mini
• Gemini 1.5-pro vs Gemini 1.5-flash
• Gemini 1.5-pro vs GPT-4-mini
• Gemini 1.5-pro vs Claude 3.5-v2

Each pairing was evaluated in repeated interactions to ensure statistical robustness.

2. Cooperation Results

Provider Differences

• Cooperation was significantly higher between models from the same provider compared to models from different providers.
• Same-provider average cooperation: approximately 45%* Different-provider average cooperation: approximately 21%

Model Size Effects

• Pairings between one large and one small model showed considerably higher cooperation rates compared to pairings of two large models.
• Large-small pair average cooperation: about 65%* Large-large pair average cooperation: about 22%

Effect of Contracts

• Allowing contracts led to a significant improvement in cooperation across all pairings.
• With contracts: average cooperation rose to around 36%* Without contracts: average cooperation was lower, around 22%

3. Contract-Breaking Behavior

Power Dynamics (Model Size)

• Smaller models consistently broke contracts more frequently when interacting with larger models.
• Small model breaking contracts with large: about 87% of the time
• Large model breaking contracts with small: about 22% of the time

Insert plot: “Contract Break Rate by Size Direction” bar chart here

Provider Trust Dynamics

• Surprisingly, contract breaking was more frequent between models from the same provider than those from different providers.
• Same-provider break rate: approximately 60%
• Different-provider break rate: approximately 45% Insert plot: “Contract Break Rate by Provider Relationship” bar chart here

4. Discussion

• Same-provider cooperation is significantly higher, possibly due to underlying similarities in model training and behavioral tendencies
• Mixed-size pairings appear to balance incentives, possibly due to differing strategic perspectives or a perceived hierarchy.
• Contracts serve as effective commitment mechanisms, enhancing overall cooperation.
• The tendency of smaller models to frequently break contracts with larger models suggests an exploitation of asymmetric expectations.
• Increased contract breaking between same-provider models may be due to heightened competitive or strategic dynamics within a shared ecosystem.

Implications and Recommendations

• Deploying mixed-size agent teams with explicit contracts might yield optimal cooperation.
• Careful consideration of provider ecosystems is crucial; diversity in provider selection could reduce competitive dynamics.

• Further work should explore varied contract penalties and more complex multi-agent settings to deepen understanding.

  5. Conclusion

• Cooperation significantly improves with provider alignment, mixed-size pairings, and contract availability.
• Contract making and breaking is nuanced, heavily influenced by model size and provider alignment. This study reveals essential insights into designing cooperative multi-agent systems with AI models.

6. Appendix

• Code: https://github.com/AEJaspan/negotiation_blog