Memory-based involution dilemma on square lattices

When involution affects individuals, their efforts do not augment resources but merely compete for limited resources. From entrance exams to company overtime, such efforts lead to unnecessary costs, undermining group welfare. Meanwhile, the individual advantages or collective disadvantages from this unnecessary effort may accumulate over time, such as the long-term validity of test scores. To identify the role of this memory factor, we propose a memory-based involution game model. In a more competitive environment, our findings suggest: (i) with scant social resources, increasing memory length curbs involution, (ii) with moderate resources, increasing memory length initially intensifies involution but later reduces it, and (iii) with abundant social resources, increasing memory length amplifies involution. Conversely, in a less competitive environment, involution consistently decreases with a larger memory length. Our research provides insights into mitigating involution by considering memory effects.