In this paper, we examine in which each player's preferences over partitions of players depend only on the members of his coalition. We present three main results in which restrictions on the preferences of the players guarantee the existence of stable partitions for various notions of stability. The preference restrictions pertain to and which model optimistic and pessimistic behavior of players respectively. The existence results apply to natural subclasses of and . It is also shown that our existence results cannot be strengthened to the case of stronger known stability concepts.
proposed a natural preference restriction called top responsiveness which is based on the idea that players value other players on how they could complement them in research teams. They showed that there exists an algorithm called the which finds a core stable partition for top responsive hedonic games. The Top Covering Algorithm can be seen as a generalization of @cite_0 . simplified the Top Covering Algorithm and proved that top responsiveness implies non-emptiness of the strict core and if mutuality is additionally satisfied, then a Nash stable partition exists.
@cite_0
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Abstract An economic model of trading in commodities that are inherently indivisible, like houses, is investigated from a game-theoretic point of view. The concepts of balanced game and core are developed, and a general theorem of Scarf's is applied to prove that the market in question has a nonempty core, that is, at least one outcome that no subset of traders can improve upon. A number of examples are discussed, and the final section reviews a series of other models involving indivisible commodities, with references to the literature.