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Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis
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Systematically evaluates GPT-3, GPT-3.5 and GPT-4 as rational game-theory players across dictator game, Rock-Paper-Scissors and a ring-network game, probing desire building, belief refinement and optimal action selection.
Problem
Whether LLMs can act as rational players in game theory (building desires from preferences, refining beliefs about opponents, and taking optimal actions), whose capability boundaries are unclear despite growing use of LLMs as substitutes for humans in game experiments.
Approach
Operationalizes rationality as three testable characteristics (desire, belief, optimal action) and maps each to a classic game (dictator game, Rock-Paper-Scissors, ring-network game), comparing LLM behavior against expected rational and human behavior under prompt-based setups.
Key results
- In the dictator game, GPT-4 matched preference-consistent choices in nearly all settings, but GPT-3 accuracy under the Competitive-Interest preference was below half and GPT-3.5 made errors on Altruism preference.
- In Rock-Paper-Scissors, GPT-4 consistently took correct actions after about 3 rounds against constant opponents and showed rising payoff on loop patterns, while GPT-3 performed close to random guessing on the constant pattern.
- In the ring-network game, GPT-4 accuracy for the optimal action was about 0.70 under explicit belief decomposition, versus near-zero under implicit belief, with belief accuracy above 0.95.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Assign uncommon preferences (CI or AL) instead of common preferences (EQ or SI) | GPT-3, GPT-3.5, and GPT-4 · Dictator game | preference-consistent choice accuracy | Hurt |
| Assign AL preference rather than a common preference | GPT-3 · Dictator game | preference-consistent choice accuracy: 0.0, 0.0, 0.1 | Hurt |
| Use explicit belief decomposition rather than implicit belief-to-action prompting | LLMs in the ring-network game · Ring-network game | optimal-action accuracy: 0.10 -> 0.75; 0.00 -> 0.60; 0.00 -> 0.65; 0.00 -> 0.75 | Helped |
| Provide the correct belief rather than having the model refine it in the dialogue | GPT-4 · Ring-network game | optimal-action accuracy: 0.75 -> 1.00; 0.60 -> 1.00; 0.65 -> 1.00; 0.75 -> 1.00 | Helped |
| Provide the correct belief rather than having the model refine it in the dialogue | GPT-3.5 · Ring-network game | optimal-action accuracy: 0.60 -> 0.85; 0.65 -> 0.95; 0.25 -> 0.90; 0.35 -> 0.80 | Helped |
| Use explicit belief-to-action prompting instead of implicit belief-to-action prompting | GPT-4 · Ring-network game | optimal-action accuracy: 0.10 -> 0.75; 0.00 -> 0.60; 0.00 -> 0.65; 0.00 -> 0.75 | Helped |
Surprising findings
- LLMs accurately refine beliefs (accuracy above 0.95) yet overlook or modify those refined beliefs when taking the subsequent action.
- GPT-4 was almost completely unable to take the optimal action when given the payoff matrix without explicit belief decomposition.
Limitations
- Games used are relatively simple and not close to real-world game scenarios.
- Only the principle of rationality is considered as the evaluation perspective.
- Analysis is rough, lacking comparative and ablation experiments.
Experimental setup
Benchmarks: Dictator game (custom preference setup) Rock-Paper-Scissors (custom opponent patterns) Ring-network game (custom payoff matrices)
Metrics: accuracy average payoff
Baselines: Human behavior (reference) Random guessing
Builds on: Chain-of-thought prompting
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- STEER: Assessing the Economic Rationality of Large Language Models (ICML 2024 · similarity 0.87)
- Decision-Making Behavior Evaluation Framework for LLMs under Uncertain Context (NeurIPS 2024 · similarity 0.87)
- Large Language Models Assume People are More Rational than We Really are (ICLR 2025 · similarity 0.87)
- Evaluating LLMs in Open-Source Games (NeurIPS 2025 · similarity 0.87)
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