Boolean Hedonic Games
This work addresses computational and representational challenges in cooperative game theory for researchers and practitioners, though it appears incremental as it builds on existing hedonic game frameworks with a specific preference structure.
The paper tackles the problem of representing and analyzing hedonic games with dichotomous preferences by developing a succinct representation using propositional formulas, and shows how solution concepts for these games can be characterized by such formulas.
We study hedonic games with dichotomous preferences. Hedonic games are cooperative games in which players desire to form coalitions, but only care about the makeup of the coalitions of which they are members; they are indifferent about the makeup of other coalitions. The assumption of dichotomous preferences means that, additionally, each player's preference relation partitions the set of coalitions of which that player is a member into just two equivalence classes: satisfactory and unsatisfactory. A player is indifferent between satisfactory coalitions, and is indifferent between unsatisfactory coalitions, but strictly prefers any satisfactory coalition over any unsatisfactory coalition. We develop a succinct representation for such games, in which each player's preference relation is represented by a propositional formula. We show how solution concepts for hedonic games with dichotomous preferences are characterised by propositional formulas.