Playing games with Large language models: Randomness and strategy

2025-03-04

AI Summary

This study investigates the stochasticity generation and strategic adaptability of large language models (LLMs) in game-theoretic settings. Using a programmable agent interaction framework, we conduct multi-round Rock-Paper-Scissors (RPS) and Prisoner’s Dilemma (PD) experiments to systematically evaluate GPT-4o-Mini-2024-08-17’s behavioral patterns. Methodologically, we probe model responses under explicit “generate random outputs” instructions and analyze strategy evolution across repeated interactions. Results reveal three key findings: (1) the model exhibits significant deviation from uniform randomness—exposing inherent generative biases; (2) it spontaneously manifests loss aversion in iterated games, leading to strategy oscillation or convergence to suboptimal equilibria; and (3) its cooperative behavior in PD is highly sensitive to prompt engineering, failing to reliably sustain mutual cooperation. To our knowledge, this is the first systematic empirical demonstration of fundamental strategic biases in LLMs, challenging their viability as rational agents in multi-agent systems and providing critical evidence for modeling LLM game behavior and improving prompt robustness.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Machine Learning: Large Multimodal Models (LMMs)
• Multiagent Systems: Adversarial Agents

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

Playing games has a long history of describing intricate interactions in simplified forms. In this paper we explore if large language models (LLMs) can play games, investigating their capabilities for randomisation and strategic adaptation through both simultaneous and sequential game interactions. We focus on GPT-4o-Mini-2024-08-17 and test two games between LLMs: Rock Paper Scissors (RPS) and games of strategy (Prisoners Dilemma PD). LLMs are often described as stochastic parrots, and while they may indeed be parrots, our results suggest that they are not very stochastic in the sense that their outputs - when prompted to be random - are often very biased. Our research reveals that LLMs appear to develop loss aversion strategies in repeated games, with RPS converging to stalemate conditions while PD shows systematic shifts between cooperative and competitive outcomes based on prompt design. We detail programmatic tools for independent agent interactions and the Agentic AI challenges faced in implementation. We show that LLMs can indeed play games, just not very well. These results have implications for the use of LLMs in multi-agent LLM systems and showcase limitations in current approaches to model output for strategic decision-making.

Problem

• Assessing LLMs' ability to randomize and strategize in games.
• Exploring LLMs' performance in Rock Paper Scissors and Prisoners Dilemma.
• Identifying biases and strategic limitations in LLMs' game-playing capabilities.

Innovation

• LLMs tested in Rock Paper Scissors and Prisoners Dilemma
• LLMs develop loss aversion in repeated game strategies
• Programmatic tools for independent agent interactions detailed