  We study a matching problem between agents and public goods, in settings
without monetary transfers. Since goods are public, they have no capacity
constraints. There is no exogenously defined budget of goods to be provided.
Rather, each provided good must justify its cost, leading to strong
complementarities in the "preferences" of goods. Furthermore, goods that are in
high demand given other already-provided goods must also be provided. The
question of the existence of a stable solution (a menu of public goods to be
provided) exhibits a rich combinatorial structure. We uncover sufficient
conditions and necessary conditions for guaranteeing the existence of a stable
solution, and derive both positive and negative results for strategyproof
stable matching.
