Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis

TL;DR

This paper systematically probes whether large language models can function as rational players in game theory by evaluating three core rationality components—desire construction, belief refinement, and action selection—across dictator, Rock-Paper-Scissors, and ring-network games. It reveals that LLMs can form clear desires with common preferences but struggle with uncommon ones, have limited ability to refine beliefs across patterns, and differ in their capacity to translate refined beliefs into optimal actions depending on how the game process is decomposed. The findings underscore substantial gaps between LLMs and human rationality in game contexts and advocate for cautious, explicitly decomposed prompts and scenarios when employing LLMs in social science experiments. The work highlights the need for targeted improvements and more rigorous benchmarking to harness LLMs effectively in game-theoretic research.

Abstract

Game theory, as an analytical tool, is frequently utilized to analyze human behavior in social science research. With the high alignment between the behavior of Large Language Models (LLMs) and humans, a promising research direction is to employ LLMs as substitutes for humans in game experiments, enabling social science research. However, despite numerous empirical researches on the combination of LLMs and game theory, the capability boundaries of LLMs in game theory remain unclear. In this research, we endeavor to systematically analyze LLMs in the context of game theory. Specifically, rationality, as the fundamental principle of game theory, serves as the metric for evaluating players' behavior -- building a clear desire, refining belief about uncertainty, and taking optimal actions. Accordingly, we select three classical games (dictator game, Rock-Paper-Scissors, and ring-network game) to analyze to what extent LLMs can achieve rationality in these three aspects. The experimental results indicate that even the current state-of-the-art LLM (GPT-4) exhibits substantial disparities compared to humans in game theory. For instance, LLMs struggle to build desires based on uncommon preferences, fail to refine belief from many simple patterns, and may overlook or modify refined belief when taking actions. Therefore, we consider that introducing LLMs into game experiments in the field of social science should be approached with greater caution.

Figures (7)

• Figure 1: Overview of a player's behavior in game theory.
• Figure 2: A case of the dictator game. All LLMs are assigned the preference AL, and the allocation options are AL-CI.
• Figure 3: Average payoff of LLMs for each round in R-S-P.
• Figure 4: Analysis of LLMs on loop-3. The symbols under the round axis indicate the opponent's action for each round.
• Figure 5: Overview of ring-network game, where red numbers / blue numbers represent the player's and opponent's payoffs, and $D_m(\cdot)$ and $D_o(\cdot)$ represent the player's and opponent's desire functions.