Within the context of transferable utility (TU) games derived from cooperative pregames, this paper demonstrates the equivalence of two properties:
- Small group effectiveness – that all, or almost all gains to collective activities can be realized by cooperation only within relatively small groups of players.
- Small group effectiveness of improvement – that all or almost all improvement can be realized by relatively small groupsof players.
With many players, small group effectiveness ensures that diverse economies, including those with local public goods, clubs, indivisibilities and non-monotonicities are competitive; there exists price-taking economic equilibrium and the outcomes in the core and of price-taking equilibrium are equivalent and have the equal-treatment property. The results of this paper thus show that small group effectiveness for improvement provides an alternative characterization of the conditions underlying perfect competition.