Inessentiality of Large Groups and the Approximate Core Property: An Equivalence Theorem.

Inessentiality of large groups or, in other words, effectiveness of small groups, means that almost all gains to group formation can be realized by partitions of the players into groups bounded in absolute size. The approximate cores property is that all sufficiently large games have nonempty approximate cores. I consider these properties in a framework of games in characteristic function form satisfying a mild boundedness condition where, when the games have many players, most players have many substitutes. I show that large (finite) games satisfy inessentially of large groups if and only if they satisfy the approximate core property.