Expectations, cores, and strategy-proofness under externalities

We study the connection between cores and strategy-proofness in environments with externalities. With this objective in mind, we present a new concept of the core that relies on agents' expectations about their peers' reactions to group deviations. It encompasses several core consistent solutions previously proposed in the literature for environments with externalities. It allows us to prove that essentially single-valued cores are necessary and sufficient for the existence of strategy-proof, efficient, and individually rational mechanisms.