Stable allocations in discrete economies

We study discrete allocation problems, as in the textbook notion of an exchange economy, but with indivisible goods. The problem is well-known to be difficult. The model is rich enough to encode some of the most pathological bargaining configurations in game theory, like the roommate problem. Our contribution is to show the existence of stable allocations (outcomes in the weak core, or in the bargaining set) under different sets of assumptions. Specifically, we consider dichotomous preferences, categorical economies, and discrete TU markets. The paper uses varied techniques, from Scarf's balanced games to a generalization of the TTC algorithm by means of Tarski fixed points.