Liability Sharing and Staffing in AI-Assisted Online Medical Consultation

TL;DR

A Stackelberg queueing model is developed where the platform selects a liability share and a staffing level while physicians choose between AI-assisted and independent diagnostic modes, clarifying how liability design propagates through queueing dynamics.

Abstract

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.

Figures (10)

• Figure 1: Queueing system nonlinearity illustrated through the Erlang C delay probability as a function of server utilization. The delay probability exhibits modest values for utilization below 0.8 but rises sharply as the system approaches saturation, creating an amplification mechanism whereby liability-induced mode switching generates disproportionate congestion effects.
• Figure 2: Physician best response and threshold structure. The intersection of Mode A and Mode I utility curves at $\theta^D = 0.60$ determines physician mode selection. Below the threshold, effort savings dominate liability costs, inducing AI-assisted mode; above the threshold, liability costs dominate, inducing independent diagnosis.
• Figure 3: Sensitivity of physician threshold $\theta^D$ to model parameters. Panel (a): Higher loss severity $L$ reduces the threshold, making physicians more responsive to liability incentives. Panel (b): Higher effort differential $k_I - k_A$ raises the threshold, requiring greater liability exposure to induce independent diagnosis.
• Figure 4: Platform cost structure under AI-assisted mode (Regime A) with $N = 5$ physicians. The optimal liability share $\theta^* = 0.40$ represents an interior solution balancing decreasing risk cost against increasing compliance cost. The threshold $\theta^D = 0.60$ marks the boundary beyond which physicians would switch to independent diagnosis.
• Figure 5: Optimal staffing requirements by diagnostic mode as a function of patient arrival rate. AI-assisted mode (Mode A) achieves substantial staffing savings relative to independent diagnosis (Mode I), with the differential representing the capacity benefit of higher service rate $\mu_A > \mu_I$.

Theorems & Definitions (5)

• Proposition 4.1: Physician best response
• Proposition 4.2: Threshold comparative statics
• Definition 5.1: Policy regimes
• Proposition 5.2: Strict convexity in liability
• Theorem 5.3: Decomposition theorem