Information and small group effectiveness in large quasilinear economies

In large quasilinear economies, we provide sufficient conditions to establish the nonemptiness of several versions of approximate interim cores with endogenous communication. This is done by proving nonemptiness of approximate ex post cores satisfying incentive compatibility. When the number of agents with private information remains finite, the main argument relies on an adaptation of the small group effectiveness condition, previously proposed for games of complete information. The result goes through when all agents are informationally small.