Involution game with migration and spatial heterogeneity of social resources

Abstract

Involution -- a phenomenon of excessive competition with diminishing returns -- has become a pressing socio-economic concern in contemporary China, prompting both academic inquiry and policy interventions. This paper proposes an evolutionary game model of involution that incorporates agent migration and spatial heterogeneity in resource distribution. The model captures realistic features such as effort-based resource allocation, local interactions on a lattice, and mobility driven by payoff comparisons. We explore how varying conditions of migration and resource allocation influence the dynamics of involution. The key findings from our simulations are as follows: when total resources are held constant, similar resource levels across different regions tend to suppress involution, whereas a large disparity between regions promotes it. Furthermore, increasing the total amount of resources exacerbates involution. In addition, the probability of migration does not significantly affect the final evolutionary outcome. We further identify threshold effects in the effort ratio and utility multiplier, revealing critical conditions under which involution emerges or subsides. To further elucidate these simulation results, we conduct a theoretical analysis using mean-field theory, which provides analytical expressions for the equilibria and stability conditions. The theoretical predictions are in excellent qualitative agreement with simulation outcomes. Finally, we discuss real-world counterparts of the model, including competition among food delivery riders and between stores offering similar services.