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AI investment decision in digital home-based elderly care service: A mean field game analysis

Author

Listed:
  • Wang, Yanying
  • Xin, Baogui
  • Peng, Wei
  • Tan, Hui
  • Sun, Minghe

Abstract

How artificial intelligence (AI) can transform elderly care services in response to rapid population aging is a timely and important issue that remains underexplored. This study examines AI investment decision-making in smart home-based elderly care services and develops a dual-incentive mechanism that addresses livelihood needs while promoting the intelligent transformation of social security systems. First, we construct a mean field game model involving a large number of elderly care service firms engaged in AI investment in the smart home-based elderly care market. Second, we formulate the model through a coupled system consisting of the forward Kolmogorov equation and the backward Hamilton-Jacobi-Bellman equation. Third, we employ stochastic differential equations to analyze the model's properties and derive the optimal control strategy for AI investment as well as the static equilibrium solution. Finally, numerical experiments provide quantitative insights into the system's dynamics. The simulation results reveal that higher market uncertainty leads to a flatter stationary price distribution, thereby increasing price dispersion. Moreover, the analysis identifies a critical threshold for the AI investment expenditure coefficient; specifically, the market achieves a stable equilibrium only when the investment cost parameter exceeds this critical value. This study provides theoretical support for improving AI investment mechanisms in smart home-based elderly care and for facilitating the intelligent transformation of social security systems to meet the growing demand for elderly care services.

Suggested Citation

  • Wang, Yanying & Xin, Baogui & Peng, Wei & Tan, Hui & Sun, Minghe, 2026. "AI investment decision in digital home-based elderly care service: A mean field game analysis," Technovation, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:techno:v:154:y:2026:i:c:s0166497226000842
    DOI: 10.1016/j.technovation.2026.103549
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