Optimal Liability Design for Medical AI

Artificial intelligence (AI) is increasingly integrated into medical decision-making, yet its liability implications remain complex, particularly when physicians differ in diagnostic skills and their quality is unobservable. This paper develops a principal-agent model in which a social planner designs medical liability to regulate a physician with private quality information who chooses between a standard treatment, a personalized judgment-based treatment, or following an imperfect AI recommendation. Our analysis yields several novel insights. First, we show that the optimal mechanism under asymmetric information is surprisingly simple: a uniform, one-size-fits-all liability level for all physician types who deviate from the standard of care. Despite physician heterogeneity, this simple policy often achieves the full-information first-best outcome, particularly when standard care is reliable or AI is highly accurate. Second, the relationship between AI accuracy and optimal liability is non-monotonic. Contrary to common intuition, better AI does not always imply more relaxed liability. As AI accuracy increases, the optimal liability either decreases monotonically or follows an inverted-U pattern, depending on the uncertainty of the standard treatment. Third, asymmetric information does not universally reduce social welfare. Welfare loss arises only when standard care is unreliable and AI accuracy is too low; even then, its magnitude follows an inverted U-shape, initially increasing as AI complicates the regulatory problem, but declining as more accurate AI helps mitigate it. Finally, we find that information asymmetry is a double-edged sword in the presence of AI, and greater transparency does not benefit all stakeholders equally.

Learning Fair Demand Models

Data-driven pricing is increasingly prevalent in sectors such as airlines, lending, insurance, and retail. By learning demand models from customer features and setting prices accordingly, these systems may generate discriminatory outcomes that raise fairness concerns. This leads to fundamental questions - how and where should systems incorporate fairness considerations in the pricing pipeline, and how does it ultimately affect societal outcomes? To answer these, we study a stylized model where a seller has a two-stage decision pipeline comprising linear demand model estimation followed by price optimization. The seller considers fairness notions in training loss, price, and demand, under both parity-wise and Rawlsian perspectives. We show that equalizing training loss across consumer groups leads to multiple solutions, which in turn can result in undesirable outcomes despite being a standard approach in fair machine learning. Focusing instead on fairness applied directly to prices or demand, we compare two strategies that enforce fairness in either the demand estimation stage or the price optimization stage. For parity-wise fairness, we characterize when each strategy yields higher social welfare under small fairness levels. We show that when market sizes and prices in the dataset are similar, imposing price fairness in the estimation stage is more beneficial to consumers, whereas imposing demand fairness in the optimization stage yields better consumer outcomes. For Rawlsian fairness, the two strategies coincide exactly. Lastly, we extend our model to alternate demand functions and conduct a case study using real-world vaccine pricing data.