Evolutionary Dynamics of an Other-Regarding Preferences-Based Involution Game in Networked and Well-Mixed Populations

Involution, characterized by intensified competition for limited social resources without generating additional societal value, has become a critical issue in modern social systems. This study aims to investigate effective mechanisms to mitigate involution by incorporating other-regarding preferences (ORP) into evolutionary game dynamics on complex networks and in well-mixed populations. Through numerical simulations conducted on square lattices and small-world networks, we systematically analyze the combined effects of crucial parameters including total social resources, the cost of more effort, fairness in resource distribution, and the intensity of ORP on the evolutionary dynamics of involution. Our findings reveal that increasing social resources generally exacerbates involution, whereas greater fairness in resource distribution alleviates it. Notably, the influence of more effort costs on involution is nonlinear and context-dependent, modulated by the interaction between resource abundance and ORP intensity. Critically, ORP emerges as a decisive factor: stronger ORP substantially suppresses involution, promotes the emergence and spatial stability of cooperative clusters, and reduces the equilibrium proportion of defectors. Theoretical analysis based on replicator dynamics validate our simulation results, providing robust theoretical benchmarks for the observed phenomena. This study not only advances the theoretical understanding of involution dynamics but also offers practical insights for addressing involution in real-world social systems. It highlights the importance of cultivating altruistic social norms and ensuring fairness in resource allocation to effectively mitigate involution.