Cooperation among automated agents is becoming increasingly important in various artificial intelligence applications. Coalitional (i.e., cooperative) game theory supplies conceptual and mathematical tools useful in the analysis of such interactions, and in particular in the achievement of stable outcomes among self-interested agents. Here, we study the minimal external subsidy required to stabilize the core of a coalitional game. Following the Cost of Stability (CoS) model introduced by Bachrach et al. [2009a], we give tight bounds on the required subsidy under various restrictions on the social structure of the game. We then compare the extended core induced by subsidies with the least core of the game, proving tight bounds on the ratio between the minimal subsidy and the minimal demand relaxation that each lead to stability.