Demand-Aware Subsidy Optimization for Community-Based Elderly Care Services: A Data-Driven Stackelberg Game Model

Source abstract

Efficient subsidy allocation for heterogeneous community-based elderly care services requires identifying latent service demand and optimizing service providers’ responses under fiscal constraints. To address this problem, this study develops a data-driven Stackelberg game framework for demand-aware subsidy optimization. The framework transforms unstructured user-generated reviews into empirical demand-priority weights through Latent Dirichlet Allocation (LDA) topic modeling and incorporates these data-derived parameters into a budget-constrained Stackelberg game to optimize differentiated subsidy decisions. A total of 11,257 elderly care-related reviews from e-commerce platforms were collected and refined into 3907 valid samples. Six major service needs were identified: Daily Living Care, Meals and Nutrition, Smart Safety Monitoring, Medical Assistance, Professional Nursing, and Home Rehabilitation. These demand weights were incorporated into the optimization model to characterize heterogeneous service priorities and determine equilibrium subsidy decisions. The numerical experiments show that differentiated subsidies substantially improve demand-weighted service coverage compared with demand-unaware allocation under the same fiscal constraint. At a budget of RMB 300,000, the demand-aware model achieves a demand-weighted coverage of 0.8328, compared with 0.7309 for the demand-unaware model. Budget sensitivity analysis further shows diminishing marginal returns to fiscal expansion, with full potential demand reached at the model-based threshold of RMB 479,500. Robustness analysis indicates that the main allocation results remain stable under perturbations of the empirically derived demand-priority weights.