Local Fairness in Hedonic Games via Individual Threshold Coalitions

Hedonic games are coalition formation games where players only specify preferences over coalitions they are part of. We introduce and systematically study local fairness notions in hedonic games by suitably adapting fairness notions from fair division. In particular, we introduce three notions that assign to each player a threshold coalition that only depends on the player's individual preferences. A coalition structure (i.e., a partition of the players into coalitions) is considered locally fair if all players' coalitions in this structure are each at least as good as their threshold coalitions. We relate our notions to previously studied concepts and show that our fairness notions form a proper hierarchy. We also study the computational aspects of finding threshold coalitions and of deciding whether fair coalition structures exist in additively separable hedonic games. At last, we investigate the price of fairness.