Abstract:

Chess, a symbolic game of human intellectual competition, provides valuable behavioral insights into players’ cognition, creativity, and strategic thinking, making it an ideal subject for studying human decision-making patterns. Leveraging the vast chess game dataset from Kaggle, this study conducts an empirical analysis of the scale-free characteristics (Zipf’s law) of the popularity of games across different skill levels and explores the underlying patterns of decision-making behavior. Our empirical results indicate that the popularity of chess games follows a multi-scaling law correlated with player ratings. Specifically, the Zipf exponent of highly rated players is lower than that of lower-rated players in the opening stage, whereas this trend reverses as the game proceeds to the mid-game stage, which suggests a starkly opposite decision-making diversity of the two types of players in cases of different complexity. This difference in behavior may stem from the heterogeneity in the capacities of strategic sets and the fuzziness of payoffs and identify two independent variables that can quantitatively express the Zipf exponent. Furthermore, we find that the similarity between chess games exhibits long-term correlations, with Hurst exponents increasing alongside player ratings, indicating a locally rapid growth in popularity dynamics. These findings establish a critical foundation for understanding and predicting individual decision-making behaviors in complex scenarios.

Key words: chess, chess tree, decision-making, Zipf’s law, long-term correlation