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.

翻译：医疗机制与其所引发的战略提供方响应密不可分：现有的医疗人工智能基准测试固化了这一响应，因此无法根据其产生的均衡来评估机制。我们将医院机制设计重构为语言模型的程序合成：类型化、可检查的规则程序由多智能体模拟器Medi-Sim执行并评分，该模拟器包含五种战略提供方渠道（编码、选择、延迟、努力、分诊）。激励扫描将健康经济学的经典发现恢复为相邻机制——利润压力下的向上编码和低复杂度患者选择，以及古德哈特式漂移（测量绩效与真实结果呈反相关）——而单一的审计杠杆揭示了压力迁移：关闭编码渠道会使低复杂度选择增加一倍以上。随后，在相同规则程序空间中进行的大语言模型引导的进化代码搜索，合成了一种可检查的混合目标程序，该程序消除了向上编码，将拒绝率减半，并保留了大部分以利润为导向的基线的资金。