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Apr 15

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

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.

  • 4 authors
·
Dec 9, 2023

Fluctuations and correlations in chemical reaction kinetics and population dynamics

This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or epidemics. After reviewing the assumptions and mean-field type approximations involved in the construction of chemical rate equations for uniform reactant densities, we first discuss spatial clustering in birth-death systems, where non-linearities are introduced through either density-limiting pair reactions, or equivalently via local imposition of finite carrying capacities. The competition of offspring production, death, and non-linear inhibition induces a population extinction threshold, which represents a non-equilibrium phase transition that separates active from absorbing states. This continuous transition is characterized by the universal scaling exponents of critical directed percolation clusters. Next we focus on the emergence of depletion zones in single-species annihilation processes and spatial population segregation with the associated reaction fronts in two-species pair annihilation. These strong (anti-)correlation effects are dynamically generated by the underlying stochastic kinetics. Finally, we address noise-induced and fluctuation-stabilized spatio-temporal patterns in basic predator-prey systems, exemplified by spreading activity fronts in the two-species Lotka-Volterra model as well as spiral structures in the May-Leonard variant of cyclically competing three-species systems akin to rock-paper-scissors games.

  • 1 authors
·
Jul 3, 2018

SirLLM: Streaming Infinite Retentive LLM

As Large Language Models (LLMs) become increasingly prevalent in various domains, their ability to process inputs of any length and maintain a degree of memory becomes essential. However, the one-off input of overly long texts is limited, as studies have shown that when input lengths exceed the LLMs' pre-trained text length, there is a dramatic decline in text generation capabilities. Moreover, simply extending the length of pre-training texts is impractical due to the difficulty in obtaining long text data and the substantial memory consumption costs this would entail for LLMs. Recent efforts have employed streaming inputs to alleviate the pressure of excessively long text inputs, but this approach can significantly impair the model's long-term memory capabilities. Motivated by this challenge, we introduce Streaming Infinite Retentive LLM (SirLLM), which allows LLMs to maintain longer memory during infinite-length dialogues without the need for fine-tuning. SirLLM utilizes the Token Entropy metric and a memory decay mechanism to filter key phrases, endowing LLMs with both long-lasting and flexible memory. We designed three distinct tasks and constructed three datasets to measure the effectiveness of SirLLM from various angles: (1) DailyDialog; (2) Grocery Shopping; (3) Rock-Paper-Scissors. Our experimental results robustly demonstrate that SirLLM can achieve stable and significant improvements across different LLMs and tasks, compellingly proving its effectiveness. When having a coversation, "A sir could forget himself," but SirLLM never does! Our code is publicly available at https://github.com/Zoeyyao27/SirLLM

  • 3 authors
·
May 21, 2024