In this paper, we re-examine the classical questions of implementation theory under complete information in a setting where coalitions are fundamental behavioral units, and the outcomes of their interactions are predicted by applying the solution concept of the core. The planner's exercise includes designing a code of rights that specifies the collection of coalitions having the right to block one outcome by moving to another. A code of individual rights is a code of rights in which only unit coalitions may have blocking powers. We provide the necessary and sufficient conditions for implementation (under core equilibria) by codes of rights, as well as by codes of individual rights. We also show that these two modes of implementation are not equivalent. The results are robust and extend to alternative notions of core, such as an externally stable core. Therefore, coalitions are shown to bring value added to institutional design. The characterization results address the limitations that restrict the relevance of the existing implementation theory. (C) 2019 Elsevier Inc. All rights reserved.