This article proposes an analytical framework to reinterpret the segmentation and fragmentation of health systems in Latin America and the Caribbean, focusing on the asymmetric relationships between actors as a structural cause of inefficiencies and inequities. In contrast to the traditional approach, which attributes these problems to the mere coexistence of multiple financing and delivery schemes, the present proposal combines the structure-behavior-performance (SBP) paradigm from industrial economics with an analysis of the selection dilemma to explain how strategic incentives and power dynamics shape the functioning of the system. The framework shows that the expansion of the private sector in the region has accentuated asymmetries among insurers, providers, and the population, giving rise to practices such as population skimming and the prioritization of profitable services. These strategic behaviors, when interacting with segmented and fragmented market structures and weak regulatory frameworks, deepen inequalities and reduce the system's allocative efficiency. Effective regulation must go beyond institutional control: it must intervene in the strategic relationships between actors and modify both structures and behaviors. The framework identifies critical points for regulatory intervention and proposes tools to align incentives with equity and efficiency objectives. Finally, it should be noted that integrating systems institutionally is not enough if the relationships between actors are not regulated and the structural asymmetries that underlie the problems of access, quality, and sustainability in health are not addressed. This perspective offers a useful guide for redesigning more effective public policies in the region.