Multi-Agent Promotion of Children’s Outdoor Physical Exercise Based on Evolutionary Game Theory: Evidence from China’s “Jiaolianti” Practice

Background: The widespread insufficiency of children’s outdoor physical exercise has become a critical public health challenge. The crux of this problem lies not in the absence of any single actor, but in the lack of a stable coordination mechanism among families, schools, and communities—a classic tripartite coordination failure. Existing research predominantly adopts single-agent perspectives and lacks rigorous game-theoretic analysis of the strategic interactions that produce persistent coordination failure. Methodology: This paper constructs a tripartite evolutionary game model of family–school–community interaction for children’s outdoor physical exercise. The government is positioned as an exogenous regulatory variable influencing pay-off structures through positive incentives (D F , D S , D C) and negative constraints (L F , L S , L C). A community network externality coefficient α C is introduced to endogenize the community’s activation threshold. Replicator dynamics equations are derived, and Jacobian matrix eigenvalue analysis is employed to characterize equilibrium stability. Numerical simulations are conducted using SciPy’s odeint integrator. The model mechanisms are validated against three case studies of China’s 2024 “Education-Community Coalition” (Jiaolianti) policy. Results: The system exhibits a tristable structure with three evolutionarily stable strategies (ESS): E 1 (0, 0, 0) low-level trap, E 5 (1, 1, 0) family–school coordination, and E 8 (1, 1, 1) full coordination. Tristability holds if and only if 0 < G < 0.7α C , where G ≡ (C 1 − C 2) − D C − L C − 0.7(β CF + β CS) − γ C is the community inertia gap. Three policy parameters exhibit differentiated efficacy profiles: D F (family subsidy) functions as a mild accelerator with a tristable interval of [0, 3.0); D C (community support) behaves as a threshold switch with a critical value of ≈ 1.55; and γ (synergy gain) displays a high-threshold, high-return profile with a tristable interval of (0.45, 2.55). Three Jiaolianti case studies—Shunyi Parent– Child Run, Jinan Morning Run Program, and Chongqing Xinghu Jiaolianti— correspond precisely to the E 1 → E 5 , E 5 → E 8 , and E 8 consolidation transition pathways, respectively. Conclusions: The tristable structure provides a mechanistic explanation for the empirically pervasive “stunted coordination” phenomenon in children’s outdoor exercise provision. Community-side activation, requiring concentrated investment to cross the D C threshold, represents the core bottleneck in policy implementation. A four-phase “Diagnose–Activate–Break Through–Consolidate” policy pathway is proposed, with budgetary priority assigned to breaking through the community bottleneck. The theoretical framework can be extended to other public governance domains involving network externalities and multi-agent coordination.