Individual Rationality in Constrained Hedonic Games: Friends, Enemies, and Neutrals
This study investigates the computational complexity of individually rational coalition structures in hedonic games under size constraints. Through classical and parameterized complexity analyses combined with graph coloring reductions, it reveals that adversarial structures fundamentally drive intractability in friend-oriented models. The research comprehensively characterizes the boundary conditions under which symmetry and size constraints influence complexity, establishing a systematic taxonomy of computational hardness. It identifies the critical structural properties responsible for NP-hardness while delineating tractable cases solvable in polynomial time. These findings provide a rigorous theoretical foundation for algorithm design in constrained cooperative games, clarifying precisely when efficient computation is feasible versus inherently intractable within this important class of hedonic game models.