Regular population monotonic allocation schemes

The paper introduces a refinement of the notion of population monotonic allocation scheme, called regular population monotonic allocation scheme (regular pmas). This refinement is based on economic situations in which players may have to select new partners from a set of potential players and in which there exist certain capacity constraints. A sufficient condition for the existence of a regular pmas is given. For the class of games with regular pmas, we prove that the core coincides with the Davis and Maschler and the Mas-Colell bargaining sets.