Local fairness in hedonic games via individual threshold coalitions

Abstract

Hedonic games are coalition formation games where players only specify preferences over coalitions they are part of. We introduce and systematically study three local fairness notions in hedonic games called max-min fairness, grand-coalition fairness, and min-max fairness. To this end, we define suitable threshold coalitions for these three concepts. 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. Based on this approach, we then introduce three specific notions of local fairness by suitably adapting fairness notions from fair division. We show that they form a proper hierarchy and how they are related to previously studied solution concepts in hedonic games. We also study the computational aspects of finding threshold coalitions and of deciding whether fair coalition structures exist in additively separable hedonic games, and we investigate the related price of local fairness.