Hedonic Games with Fixed-Size Coalitions

In hedonic games, a set of n agents, having preferences over all possible coalition structures, needs to agree on stable outcome. this work, we initiate the study games with fixed-size coalitions, where structures is restricted as follows: there are k each has fixed size, and sum sizes coalitions equals n. We focus basic model additively separable symmetric preferences, an agent's preference captured by utility function which sums up contribution due any other agent in same coalition. setting, outcome if no pair agents can exchange improve their utilities. Conditioned definition improvement, three stability notions arise: swap under transferable utilities, requires utilities both stability, one without decreasing one, strict requiring simultaneously. analyse fundamental questions existence, complexity efficiency outcomes, that social optimum.