An appropriate (interim) notion of the core for an economy with incomplete information depends on the amount of information that coalitions can share. The coarse and fine core, as originally defined by Wilson (1978), correspond to two polar cases, involving no information sharing and arbitrary information sharing, respectively. We propose a new core notion, the credible core, which incorporates incentive compatibility constraints, and is based on the idea that a coalition can coordinate its potential objection to a status-quo over an event that can be credibly inferred from the nature of the objection being contemplated. We provide sufficient conditions ensuring non-emptiness of the credible core.