On Myopic Stability Concepts for Hedonic Games

Abstract

We present a unified look at myopic stability concepts for hedonic games, and discuss the status of the existence problems of stable coalition structures. In particular, we show that contractual strictly core stable coalition structures always exist, and present a sufficient condition for the existence of contractually Nash stable coalition structures on the class of separable games. Copyright Springer Science+Business Media, LLC 2007coalition formation, hedonic games, separability, taxonomy, C71, A14, D20,

Computing desirable partitions in additively separable hedonic games

“…The main focus in hedonic games has been on notions of stability for coalition structures such as Nash stability, individual stability, contractual individual stability, or core stability and characterizing conditions under which the set of stable partitions is guaranteed to be non-empty (see, e.g., Bogomolnaia and Jackson, 2002; Burani and Zwicker, 2003). Sung and Dimitrov (2007b) presented a taxonomy of stability concepts which includes the contractual strict core, the most general stability concept that is guaranteed to exist. A wellstudied special case of hedonic games are two-sided matching games in which only coalitions of size two are admissible (Roth and Sotomayor, 1990).…”

Hedonic coalition formation games: A new stability notion

“…4 The aim of this paper is to study coalitional extension of Nash stability under FX-FE membership rights, referred to as strong Nash stability, which has not been studied yet. Note that strong Nash stability is not defined in Sung and Dimitrov (2007) but they identified some weaker versions of strong Nash stability.…”

“…They showed that if a 4 Other stability concepts that consider individual deviations under different membership rights have already been studied in the literature. That is, individual stability is defined under FX-AE membership rights (see Bogomolnaia and Jackson (2002)), contractual Nash stability is defined under AX-FE membership rights (see Sung and Dimitrov (2007)), and contractual individual stability is defined under AX-AE membership rights (see Bogomolnaia and Jackson (2002) and Ballester (2004)).…”

“…It is shown that under FX-AE membership rights, a partition is FX-AE strictly strongly Nash stable if and only if it is strictly core stable (Proposition 3), showing that core stability entails an FX-AE rights structure. Sung and Dimitrov (2007) defined contractual strict core stability and showed that for any hedonic game such a partition always exists. It is proved that under AX-AE membership rights, a partition is AX-AE strictly strongly Nash stable if and only if it is contractual strictly core stable (Proposition 4).…”

Government versus Opposition: Who Should be Who in the 16th German Bundestag?

“…In Section 2 we introduce some basic notions from the theory of simple games and hedonic games, and discuss different stability concepts for hedonic games (see also Sung and Dimitrov (2005)). In Section 3 we first define the simple game that corresponds to the distribution of seats in the 16th German Bundestag and then induce a hedonic game by using the Shapley value of all subgames of the simple game.…”