This paper examines recent theoretical developments of the theory of coalition stability. It focuses on the relationship between the incentives to defect from a coalition, the size of the resulting equilibrium coalition structure, and the different assumptions on membership rules, coalition behaviour, players' conjectures, etc. The paper considers several cases. Simultaneous vs. sequential moves, linear vs. circular order of moves, Nash vs. rational conjectures, open vs. exclusive membership, monotonic vs. non monotonic payoff functions, and orthogonal vs. non-orthogonal reaction functions. The profitable and stable coalition will be derived for each possible configuration of the rules of the game, the payoff functions and the membership rules. The results show that the size of the profitable and stable coalition highly depends on the chosen configuration and that the equilibrium outcome ranges from a small coalition with a few signatories to full cooperation. The paper explores under which conditions a large stable coalition is likely to emerge, and identifies the institutional setting that favours the emergence of such coalition.