Incentives, Equilibria, and the Limits of Healthcare AI: A Game-Theoretic Perspective

AI tools increasingly drive targeted interventions in various service settings, including healthcare, education, and public services. Algorithms score individuals, trigger outreach to those above a threshold (e.g., high-risk or high-value), and encourage them to request service; then providers deliver service to those who request. Much of the work in this area has focused on improving predictive accuracy, implicitly assuming that better predictions lead to better outcomes. We show that predictions are only one component of a larger service system: when service capacity is limited and behavioral responses to outreach are probabilistic, system efficacy depends on operational forces that predictive accuracy does not capture. In such settings, the optimal score threshold must balance two effects: ensuring all capacity is filled (utilization) and, when capacity is constrained, preventing low-value requests from crowding out high-value ones (cannibalization). We characterize the optimal threshold and prove that thresholds based solely on predictive accuracy are generally suboptimal. Further, algorithm selection metrics such as AUC can be misaligned with operational performance: they weight all thresholds equally, while optimal deployment uses a subset of thresholds that depends on both capacity and compliance behavior. We introduce a new metric, Operational AUC (OpAUC), and show that it identifies the efficacy-optimal algorithm. Finally, we conduct a case study on sepsis early warning data that illustrates the magnitude of the improvement available from better threshold selection and shows that a predictor with lower AUC can achieve higher system efficacy under optimal deployment.

Healthcare productivity is shaped not only by clinical complexity but by the costs of coordinating work under uncertainty. Transaction-cost economics offers a theory of these coordination frictions, yet has rarely been operationalised at task level across health occupations. Using task statements and frequency weights from the O*NET occupational database, we characterised healthcare work at task granularity and coded each unique task using a constrained large language model into one dominant transaction-cost category (information search, decision and bargaining, monitoring and enforcement, or adaptation and coordination) together with an overall transaction-cost intensity score. Aggregating to the occupation level, clinician roles exhibited substantially higher transaction-cost intensity than non-clinician roles, driven primarily by greater burdens of information search and decision-related coordination, while dispersion of transaction costs within occupations did not differ. These findings demonstrate systematic heterogeneity in the nature of coordination work across healthcare roles and suggest that the opportunities for digital and AI interventions are unevenly distributed, shaped less by technical task complexity than by underlying coordination structure.

Healthcare mechanisms are inseparable from the strategic provider response they induce: existing healthcare AI benchmarks hold this response fixed and so cannot evaluate mechanisms by the equilibrium they produce. We recast hospital mechanism design as program synthesis for language models: typed, inspectable rule programs are executed and scored by Medi-Sim, a multi-agent simulator with five strategic provider channels (coding, selection, delay, effort, triage). An incentive sweep recovers classical health-economics findings as adjacent regimes -- up-coding and low-complexity-patient selection under profit pressure, and Goodhart-style drift where measured performance becomes anti-correlated with true outcomes -- and a single audit lever exposes pressure migration: closing the coding channel more than doubles low-complexity selection. LLM-guided evolutionary code search over the same rule-program space then synthesizes an inspectable mixed-objective program that eliminates up-coding, halves rejection, and retains most of the profit-oriented baseline's funds.