Dynamic multi-criteria ordinal game in public-private partnerships for mental health programmes

Despite the increasing interest in public-private partnerships (PPPs) in healthcare delivery, especially between NGOs and government entities, a significant gap remains in systematically predicting optimal partnerships by concurrently addressing the dynamic nature of partnership environments and the diverse objectives and preferences of both sectors. This study develops a novel decision-support framework to forecast optimal partnerships between government organizations (GOs) and non-government organizations (NGOs) in the mental health sector. Grounded in an ordinal game theory structure, the framework integrates the Analytic Hierarchy Process (AHP) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to evaluate multiple criteria—population, health service capacity, health infrastructure, and distance—across 31 non-partnered local government units (LGUs) in Cebu, Philippines. A key feature is the dynamic recalibration of distance criterion and alternative pools, enabling the model to capture how optimal partnerships evolve as NGOs form new collaborations over time. Case study results for the Philippine Mental Health Association (PMHA) and Americares Philippines (AP) reveal a gradual and strategic partnership growth throughout four successive periods, with decisions aligning closely to each NGO's objectives and priorities. Although focused on a specific sector and regional context, the framework can be adapted to broader applications with caution. Future research could explore relational dynamics and multi-player interactions, and uncertainty handling. Overall, the proposed framework offers a flexible and adaptive tool for strategic GO-NGO partnership planning in public health systems or PPPs, in general.