  Space-air-ground integrated networks (SAGINs) will play a pivotal role in 6G
communication systems. They are considered a promising technology for enhancing
network capacity in densely populated urban areas and extending connectivity to
rural regions. However, the complex, multi-layered, and heterogeneous nature of
SAGINs demands an innovative approach to designing their multi-tier
associations. In this context, we propose a modeling of the SAGINs association
problem using multi-sided matching theory. Our objective is to devise a
reliable, asynchronous, and fully distributed approach that associates nodes
across the layers to maximize the total end-to-end rate of the assigned agents.
To achieve this, our problem is formulated as a multi-sided many-to-one
matching game. We introduce a randomized matching algorithm with minimal
information exchange. The algorithm is shown to reach an efficient and stable
association between nodes in adjacent layers. Simulation results show that our
proposed approach yields significant gains compared to both greedy and
distance-based algorithms.
