The egalitarian sharing rule in provision of public projects

In this note we consider a society that partitions itself into disjoint jurisdictions, each choosing a location of its public project and a taxation scheme to finance it. The set of public project is multi-dimensional, and their costs could vary from jurisdiction to jurisdiction. We impose two principles, egalitarianism, that requires the equalization of the total cost for all agents in the same jurisdiction, and efficiency, that implies the minimization of the aggregate total cost within jurisdiction. We show that these two principles always yield a core-stable partition but a Nash stable partition may fail to exist.Comment: 7 page

Top coalitions, common rankings, and semistrict core stability

The top coalition property of Banerjee et al. (2001) and the common ranking property of Farrell and Scotchmer (1988) are sufficient conditions for core stability in hedonic games. We introduce the semistrict core as a stronger stability concept than the core, and show that the top coalition property guarantees the existence of semistrictly core stable coalition structures. Moreover, for each game satisfying the common ranking property, the core and the semistrict core coincide.coalition formation

On core membership testing for hedonic coalition formation games

We are concerned with the problem of core membership testing for hedonic coalition formation games, which is to decide whether a certain coalition structure belongs to the core of a given game. We show that this problem is co-NP complete when players' preferences are additive.additivity, coalition formation, core, co-NP completeness, hedonic games

The Egalitarian sharing rule in provision of public goods

In this note we consider a society that partitions itself into disjoint jurisdictions, each choosing a location of its public project and a taxation scheme to finance it. The set of public project is multi-dimensional, and their costs could vary from jurisdiction to jurisdiction. We impose two principles, egalitarianism, that requires the equalization of the total cost for all agents in the same jurisdiction, and efficiency, that implies the minimization of the aggregate total cost within jurisdiction. We show that these two principles always yield a core-stable partition but a Nash stable partition may fail to exist. We demonstrate moreover that stable partitions are not necessarily consecutive.

On the Impossibility of Strategy-Proof Coalition Formation Rules

We analyze simple coalition formation problems in which a group of agents is partitioned into coalitions and agents' preferences only depend on the identity of the members of the coalition to which they belong. We study coaltion formation rules that associate to each profile of agents'' preferences a partition of the group of agents. Assuming that agents'' preferences are separable, we show that no coalition formation rule can satisfy the joint requirements of strategy-proofness, individual rationality, non-bossiness, and voters'' sovereignty.Coalition Formation Rule

Government versus opposition: Who should be who in the 16th German Bundestag?

We model the process of coalition formation in the 16th German Bundestag as a hedonic coalition formation game. In order to induce players' preferences in the game we apply the Shapley value of the simple game describing all winning coalitions in the Bundestag. Using different stability notions for hedonic games we prove that the "most" stable government is formed by the Union Parties together with the Social Democratic Party.coalition formation, Shapley value, simple games, winning coalitions

A note on the paradox of smaller coalitions

We consider hedonic coalition formation games that are induced by a simple TU-game and a cooperative solution. For such models, Shenoy's (1979) absence of the paradox of smaller coalitions provides a sufficient condition for core existence. We present three different versions of his condition in order to compare it to the top coalition property of Banerjee et al. (2001) that guarantees nonemptiness of the core in more general models. As it turns out, the top coalition property implies a condition in which Shenoy's paradox is not present for at least one minimal winning coalition. Conversely, if for each non-null player Shenoy's paradox is not present for at least one minimal winning coalition containing that player, then the induced hedonic game satisfies the top coalition property.coalition formation, core, paradox of smaller coalitions, simple games, top coalition property