This paper investigates solution concepts for coalitional games. Several solution concepts are characterized, such as the core, Shapley value, bargaining set, stable set, nucleolus, and kernel. We look at recent developments of succinct representations of coalitional games, such as weighted voting games, coalitional resource games, cooperative boolean games, and marginal contribution nets. Existing solution concepts have prohibitive complexity requirements even for very simple classes of games. We discuss an agenda for finding an equilibrium solution concept that is as appealing as the core, but that is tractable and guaranteed to exist.