Liability Sharing and Staffing in AI-Assisted Online Medical Consultation

Liability sharing and staffing jointly determine service quality in AI-assisted online medical consultation, yet their interaction is rarely examined in an integrated framework linking contracts to congestion via physician responses. This paper develops a Stackelberg queueing model where the platform selects a liability share and a staffing level while physicians choose between AI-assisted and independent diagnostic modes. Physician mode choice exhibits a threshold structure, with the critical liability share decreasing in loss severity and increasing in the effort cost of independent diagnosis. Optimal platform policy sets liability below this threshold to trade off risk transfer against compliance costs, revealing that liability sharing and staffing function as substitute safety mechanisms. Higher congestion or staffing costs tilt optimal policy toward AI-assisted operation, whereas elevated loss severity shifts the preferred regime toward independent diagnosis. The welfare gap between platform and social optima widens with loss severity, suggesting greater scope for incentive alignment in high-stakes settings. By endogenizing physician mode choice within a congested service system, this study clarifies how liability design propagates through queueing dynamics, offering guidance for calibrating contracts and capacity in AI-assisted medical consultation.