Hedonic coalition formation games: A new stability notion (original) (raw)

Top responsiveness and stable partitions in coalition formation games

2005

Top responsiveness is introduced by Alcalde and Revilla [Journal of Mathematical Economics 40 (2004) 869-887] as a property which induces a rich domain on playerss preferences in hedonic games, and guarantees the existence of core stable partitions. We strengthen this observation by proving the existence of strict core stable partitions, and when a mutuality condition is imposed as well, the

The Stability of Hedonic Coalition Structures

1998

We consider the partitioning of a society into coalitions in purely hedonic settings, i.e., where each player's payoff is completely determined by the identity of other members of her coalition. We first discuss how hedonic and nonhedonic settings differ and some sufficient conditions for the existence of core stable coalition partitions in hedonic settings. We then focus on a weaker stability condition: individual stability, where no player can benefit from moving to another coalition while not hurting the members of that new coalition. We show that if coalitions can be ordered according to some characteristic over which players have single-peaked preferences, or where players have symmetric and additively separable preferences, then there exists an individually stable coalition partition. Examples show that without these conditions, individually stable coalition partitions may not exist. We also discuss some other stability concepts, and the incompatibility of stability with other normative properties. Journal of Economic Literature Classification Numbers: C71, A14, D20.  2002 Elsevier Science Weber for very helpful conversations and suggestions. We are also grateful for the comments of two anonymous referees that have helped in the rewriting of the paper. 2

On the stability of an Optimal Coalition Structure

The two main questions in coalition games are 1) what coalitions should form and 2) how to distribute the value of each coalition between its members. When a game is not superadditive, other coalition structures (CSs) may be more attractive than the grand coalition. For example, if the agents care about the total payoff generated by the entire society, CSs that maximize utilitarian social welfare are of interest. The search for such optimal CSs has been a very active area of research. Stability concepts have been defined for games with coalition structure, under the assumption that the agents agree first on a CS, and then the members of each coalition decide on how to share the value of their coalition. An agent can refer to the values of coalitions with agents outside of its current coalition to argue for a larger share of the coalition payoff. To use this approach, one can find the CS s★ with optimal value and use one of these stability concepts for the game with s★. However, it m...

Noncooperative formation of coalitions in hedonic games

International Journal of Game Theory - INT J GAME THEORY, 2011

We study a bargaining procedure of coalition formation in the class of hedonic games, where players’ preferences depend solely on the coalition they belong to. We provide an example of nonexistence of a pure strategy stationary perfect equilibrium, and a necessary and sufficient condition for existence. We show that when the game is totally stable (the game and all its restrictions have a nonempty core), there always exists a no-delay equilibrium generating core outcomes. Other equilibria exhibiting delay or resulting in unstable outcomes can also exist. If the core of the hedonic game and its restrictions always consist of a single point, we show that the bargaining game admits a unique stationary perfect equilibrium, resulting in the immediate formation of the core coalition structure.

Stable decompositions of coalition formation games

2020

It is known that a coalition formation game may not have a stable coalition structure. In this study we propose a new solution concept for these games, which we call “stable decomposition”, and show that each game has at least one. This solution consists of a collection of coalitions organized in sets that “protect” each other in a stable way. When sets of this collection are singletons, the stable decomposition can be identified with a stable coalition structure. As an application, we study convergence to stability in coalition formation games. JEL classification: C71, C78.

Stable Coalition Structures with Fixed Decision Scheme

Lecture Notes in Economics and Mathematical Systems, 2001

in Aix-en-Provence, and particularly Hideo Konishi for comments and suggestions that greatly improved the exposition of this work are gratefuly acknowledged. Part of this work was done while I was visiting the Institute of Mathematical Economics at Bielefeld University under the European research programme "Game-theoretic approaches to cooperation and exchange of information, with economic applications." Financial support from the European Commission, contract number HPMF-CT-1999-00284, is gratefuly acknowledged. All remaining errors are mine.

Strategy-proof coalition formation

International Journal of Game Theory, 2009

We analyze 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 they are members of. We study rules that associate to each profile of agents' preferences a partition of the society. We are interested in rules that never provide incentives for the agents to misrepresent their preferences. Hence, we analyze strategy-proof rules and we focus on restricted domains of preferences, as the domain of additively representable or separable preferences.

E ciency in Coalition Games with Externalities

2006

A natural,extension,of superadditivity,is not su¢ cient to imply that the grand,coalition is e¢ cient when,externalities are present. We provide a con- dition –analogous,to convexity–that,is su¢ cient for the grand coalition to be e¢ cient and show,that this also implies that the (appropriately de…ned) core is nonempty. Moreover, we propose a mechanism which implements the most e¢ cient partition for all coalition formation,games,and characterize the payo¤ division of the mechanism. JEL Classi…cation Numbers: C71, C72, D62 Keywords: Coalition formation, externalities, partition function games, Shapley value, implementation.