Dynamics of counterfactual attribution regret minimization in spatial public goods games

The spatial public goods game is widely regarded as a foundational framework for exploring the evolutionary dynamics of cooperation. However, existing strategy update rules, which are a crucial component of these games, typically rely on social imitation or reinforcement learning and overlook the intricate cognitive processes inherent in human decision making. Here, we propose a novel strategy update mechanism, Counterfactual Attribution Regret Minimization (CARM), that more effectively reflects the genuine cognitive processes that drive human decisions. CARM is based on the mechanisms of regret accumulation and regret matching, integrating three psychological weights that modulate how agents assess counterfactual scenarios. These weights correspond to accessibility, causal attribution, and an asymmetric emotional response to regret and relief. Through extensive Monte Carlo simulations, we demonstrate that CARM can generate a rich spectrum of collective behaviors, including absorbing states of cooperation and defection, stable coexistence, and complex bistable oscillations. A systematic sensitivity analysis further reveals how the core cognitive parameters independently and collaboratively influence the cooperation threshold, the steady-state level, and the system's dynamic stability. Intriguingly, our results show that macroscopic coexistence under CARM is maintained through a dynamic equilibrium of constantly oscillating individual strategies. This phenomenon differs from traditional models, which depend on the formation of static cooperative clusters to defend against invasion by defectors. Our model provides a new perspective on how cooperation can emerge and be sustained within the context of spatial evolutionary games.