Stable sets of allocations and the provision of public goods

In a market model with public projects, we introduce and study von Neumann–Morgenstern stable sets. Stability concepts derive from a procedure in which the blocking coalitions are responsible for a share of the total cost of the public project. This share is determined by a contribution measure. Moreover, the analysis is extended to the case in which traders can join a coalition with a grade of membership. In this framework, under proper assumptions, we provide a correspondence between stable sets of an economy with finitely many types and stable sets of an associated finite economy and prove uniqueness of stable sets when the dominance is defined over a suitable family of coalitions.