Matching models with a conservation law: The existence and global structure of the set of stationary equilibria

We study random matching models where there is a set of infinitely lived agents, and in each period agents are pairwise matched to each other and play a stage game. We investigate the basic structure of equilibria in such models: the existence of equilibria and the global structure of the set of equilibria. Specifically, we focus on models with a conservation law, which typically holds in economies having some assets, such as money. In such models, under certain regularity conditions the set of equilibria is one-dimensional and each connected component of it is a piecewise smooth one-dimensional manifold being homeomorphic to either the unit circle or the unit interval. Moreover, in an endpoint of an interval all agents have the same amount of assets.