Modeling Involution: An Evolutionary Game Theory Analysis of Arms-Race Effort Competitions

Abstract

Involution—socially inefficient intensification of individual effort in competitive areas like work and education—arises from individually optimal arms-race dynamics that are collectively suboptimal. To explore the phenomenon, the current study sets up a dynamic model, thinking of involution as an evolutionary game under replicator dynamics. A two-strategy model—High Effort (H) and Low Effort (L)—is set up with payoff externalities reflecting congestion and relative-performance rewards. The model generates a high-effort dominant attractor or an interior evolutionarily stable state, depending on parameters. Closed-form solutions are derived for the selection gradient, interior equilibrium, comparative statics, local stability, and social optimum maximizing average payoff. The analysis connects the mathematics to real examples of schooling, firms, and industries and calculates shortrun benefits (peak performance, tournament selection) and major costs (welfare loss, stagnation of innovation, burnout, inequality). Policy and institutional recommendations are then transformed into a revision of the revenue matrix and information structure, so as to guide the system from the “prisoner’s dilemma” pattern to a coordinated game or a quality-based competition pattern. The study further proposed a formalized diagnostic framework to describe the “inner volume trap” and formulate corresponding policies to promote more sustainable competition.