Price-induced stable matching in shared healthcare

Xiaowei Lin; Yun Wei; Xiaowei Lin; Yun Wei

doi:10.3934/jimo.2026165

Journal of Industrial and Management Optimization

2026, Volume 22, Issue 10: 4770-4795. doi: 10.3934/jimo.2026165

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Research article

Price-induced stable matching in shared healthcare

Xiaowei Lin ¹,
Yun Wei ^{2
,
,}

1.
Department of Fundamental Courses, Nanjing University of Industry Technology, Nanjing, Jiangsu, 210023, China
2.
Nursing Division of the Department of Cardiology, Nanjing Drum Tower Hospital Affiliated to Nanjing University Medical School, Nanjing, Jiangsu, 210008, China

Received: 18 April 2026 Revised: 17 August 2026 Accepted: 01 September 2026 Published: 08 September 2026
91B68, 90B80, 91B24, 90B90

Platform-mediated home healthcare requires coordinated pricing and assignment among clinically and geographically heterogeneous patients and nurses. We develop a price-induced stable matching (PISM) model for a medical institution-affiliated platform that posts a service fee, applies a fixed nurse compensation share, and computes a stable one-to-one assignment. In the single-tier setting, price changes bilateral participation and the mutually acceptable graph without reordering within-tier preferences. On a finite admissible price grid, an optimal fee exists; under explicit local fluid conditions, the profit benchmark exceeds the volume benchmark; and platform profit is invariant across patient- and nurse-proposing stable mechanisms when margins depend only on price and service type. A tiered extension shows how compensation differences can reorder advanced nurses' cross-tier preferences and generate downward substitution. Externally anchored synthetic experiments across six supply–demand and spatial configurations yield nurse rule-conditional price-induced welfare losses of 1.47%–14.41%. Hospital-clustered nurse origins materially increase travel but change the profit-optimal fee only modestly, whereas valuation dispersion has stronger effects on price and completed volume. A two-dimensional price search reveals a nonmonotone relationship between the compensation premium and downward substitution.
- shared healthcare,
- two-sided matching,
- spatial pricing,
- price-induced stability,
- downward substitution,
- gig economy,
- operations management
Citation: Xiaowei Lin, Yun Wei. Price-induced stable matching in shared healthcare[J]. Journal of Industrial and Management Optimization, 2026, 22(10): 4770-4795. doi: 10.3934/jimo.2026165

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Abstract

Platform-mediated home healthcare requires coordinated pricing and assignment among clinically and geographically heterogeneous patients and nurses. We develop a price-induced stable matching (PISM) model for a medical institution-affiliated platform that posts a service fee, applies a fixed nurse compensation share, and computes a stable one-to-one assignment. In the single-tier setting, price changes bilateral participation and the mutually acceptable graph without reordering within-tier preferences. On a finite admissible price grid, an optimal fee exists; under explicit local fluid conditions, the profit benchmark exceeds the volume benchmark; and platform profit is invariant across patient- and nurse-proposing stable mechanisms when margins depend only on price and service type. A tiered extension shows how compensation differences can reorder advanced nurses' cross-tier preferences and generate downward substitution. Externally anchored synthetic experiments across six supply–demand and spatial configurations yield nurse rule-conditional price-induced welfare losses of 1.47%–14.41%. Hospital-clustered nurse origins materially increase travel but change the profit-optimal fee only modestly, whereas valuation dispersion has stronger effects on price and completed volume. A two-dimensional price search reveals a nonmonotone relationship between the compensation premium and downward substitution.

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