Involution game with migration and spatial heterogeneity of social resources

TL;DR

This paper develops an evolutionary game model incorporating migration and spatial resource heterogeneity to analyze involution, revealing how resource distribution and effort thresholds influence socio-economic competition dynamics.

Contribution

It introduces a novel model combining migration, effort, and spatial heterogeneity, and provides both simulation and theoretical analysis of involution phenomena.

Findings

Similar resource levels suppress involution

Increased total resources exacerbate involution

Migration probability has little effect on outcomes

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; conversely, an increase in total resources exacerbates it. 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.