In the field of bounded rationality research, accurately characterizing the behavioral patterns of players has long stood as a core concern in academic circles. To address the limitations of existing models regarding scope definition and parameter estimation accuracy, this study endeavors to construct a hierarchical quantal response function and proposes the k-level Quantal Response Equilibrium Model (k-QREM). Leveraging a "tower-like" vertical structure, the model organically embeds CHM and QRE, fully accounting for the behavioral heterogeneity of players both across and within levels. In terms of parameter estimation, this work breaks free from the constraints of the traditional maximum likelihood method and introduces a multi-stage hybrid optimization algorithm: by integrating the global search superiority of the Genetic Algorithm (GA) with the local optimization capability of Sequential Quadratic Programming (SQP), the algorithm effectively overcomes the convergence and accuracy challenges encountered in scenarios involving scarce samples and multi-parameter estimation. To validate the model’s effectiveness, two sets of distinct numerical examples are selected for testing of k-QREM. Beyond comparing its output with that of traditional models, simulation validation and stability analysis are concurrently performed based on these examples. The findings indicate that k-QREM significantly outperforms traditional models in overall fitting and predictive performance, enabling more precise explanation and prediction of bounded rational behaviors. It is particularly well-suited for analyzing strategic interactions among groups of players with significant cognitive disparities. Meanwhile, the test results confirm that the proposed parameter estimation method exhibits excellent convergence stability, and k-QREM demonstrates robust performance under given scenarios.
Lai et al. (Sat,) studied this question.