Coalition formation games with separable preferences

We provide sufficient conditions for the existence of stable coalitional structures in a purely hedonic game, that is in a coalition formation game such that players’ preferences over coalitions are completely determined by the members of the coalition to which they belong. First, we show that the existence of core stable and Nash stable solutions for the game depends on certain vector decompositions of the utility functions representing additively separable and symmetric preferences. Then, we generalize the results obtained and show that equilibria with the same qualitative features exist under much weaker restrictions on agents’ preferences. Finally, we examine the relationships between the properties we introduce and other conditions, already known in the literature, that guarantee the existence of stable partitions.