Dynamic Cognitive Hierarchy Model with Regret Minimization for Two-Player Extensive-Form Games

This paper introduces a dynamic cognitive hierarchy model with regret minimization (DCH-RM), a bounded-rational decision model for extensive-form two-player games. Existing approaches often assume perfect rationality, overlooking the effects of limited reasoning abilities and heterogeneous behaviors, which reduces their empirical relevance. DCH-RM combines cognitive hierarchy reasoning with regret-minimization dynamics to relax the perfect-rationality assumption while capturing adaptive and diverse opponent behavior. Compared to traditional Nash equilibrium-based decision models, DCH-RM (i) enables tractable opponent modeling, (ii) predicts systematic behavioral deviations caused by different game representations, and (iii) supports strategy optimization under bounded rationality. Empirical evaluation on practical Centipede Game data verifies the model’s accurate representation and demonstrates its superiority over baseline models, while an urban attack–defense scenario highlights its applicability under limited data and reduced exploitability.