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Prolonged waiting to access health care is a primary concern for nations aiming for comprehensive effective care, due to its adverse effects on mortality, quality of life, and government approval. Here, we propose two novel bargaining frameworks to reduce waiting lists in two-tier health care systems with local and regional actors. In particular, we assess the impact of 1) trading patients on waiting lists among hospitals, the 2) introduction of the role of private hospitals in capturing unfulfilled demand, and the 3) hospitals’ willingness to share capacity on the system performance. We calibrated our models with 2008–2018 Chilean waiting list data. If hospitals trade unattended patients, our game-theoretic models indicate a potential reduction of waiting lists of up to 37%. However, when private hospitals are introduced into the system, we found a possible reduction of waiting lists of up to 60%. Further analyses …