Dynamic treatment regimes improve health outcomes by tailoring each treatment to a patient’s evolving condition, but they also allow providers to learn and game the system over time. How should insurers pay? We study this new class of reimbursement problems, where the provider can privately learn and manipulate the progression of the patient’s condition. (i) We characterize the optimal payment policy: it internalizes two intertemporal effects of each treatment, and rewards provider honesty with incentive pay; moreover, it admits a simple implementation of risk-adjusted cost-sharing policy. (ii) We show that, ignoring dynamic learning and gaming, the existing payment models may have overestimated the harm of information asymmetry. Using the optimal policy, insurers only need to pay for initial private information; they can exploit provider uncertainty and elicit future private information at no cost. (iii) Our study informs U.S. healthcare payment reform with new insights; using two sets of real data, our study also quantifies when and why the optimal policy outperforms the existing ones. By highlighting the critical role of dynamic learning and gaming, this study advances our understanding of healthcare payment theory and practice.
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