Representing and Solving Hedonic Games with Ordinal Preferences and Thresholds

We propose a new representation setting for hedonic games, where each agent partitions the set of other agents into friends, enemies, and neutral agents, with friends and enemies being ranked. Under the assumption that preferences are monotonic (respectively, antimonotonic) with respect to the addition of friends (respectively, enemies), we propose a bipolar extension of the Bossong-Schweigert extension principle, and use this principle to derive the (partial) preferences of agents over coalitions. Then, for a number of solution concepts, we characterize partitions that necessarily (respectively, possibly) satisfy them, and identify the computational complexity of the associated decision problems. Alternatively, we suggest cardinal comparability functions in order to extend to complete preference orders consistent with the generalized Bossong-Schweigert order.