Hedonic coalition formation games: A new stability notion

Social Choice and Welfare, 2006

This paper studies a class of NTU coalition formation game in which every player's payo® depends only on the members of her coalition. We provide three conditions under which the core of such games is non-empty. The three properties identi¯ed are called Union Responsiveness, Intersection Responsiveness, and Essentiality. All three are restrictions on individuals' preferences and stable allocations always exist under each of them.

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.

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.

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.

HAL (Le Centre pour la Communication Scientifique Directe), 2022

A social ranking (solution) over a set N is defined as a map assigning to each coalitional relation (i.e. a ranking over subsets of N ) another ranking over the single elements in N . Differently, coalition formation situations, and, in particular, hedonic games, mainly focus on partitions of the set N into disjoint coalitions, which are in general referred to as coalition structures. A coalition structure may be stable according to various notions of stability and the objective is to understand under which conditions a coalition structure is stable. In this paper we merge the framework of coalition formation with the one of social rankings to keep into account the effect of hierarchies within coalitions on the stability of coalition structures. We consider alternative classes of coalition formation games where the preferences of the players over coalitions are induced by a social ranking. More precisely, players compare coalition structures keeping into account both the relative ranking of coalitions to which they belong (according to a coalitional relation) and their position in the social ranking within each coalition. Constructive characterizations of the set of stable coalition structures are provided for alternative classes of hedonic games, together with an impossibility result on the existence of stable coalition structures for (non-hedonic) coalition formation situations.

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.

Mathematical Social Sciences, 2003

We define a solution to the problem of coalition formation that applies to purely hedonic games. Coalition structures satisfying our requirements are called durable, and we interpret them as much more likely to last than those coalition structures not satisfying the requirements, which we call transient. Durability results from a combination of foresight and extreme risk aversion on the part of agents, when considering to join others to disrupt an existing structure in search of higher gains. Agents' calculations are also constrained to satisfy a strong consistency requirement, which is reflected in the recursive structure of our definition. We prove that durable coalition structures always exist, and we provide examples of hedonic games where our solutions apply nicely. 

Lecture Notes in Computer Science, 2009

A key question in cooperative game theory is that of coalitional stability, usually captured by the notion of the core-the set of outcomes such that no subgroup of players has an incentive to deviate. However, some coalitional games have empty cores, and any outcome in such a game is unstable.

ArXiv, 2020

We study the problem of convergence to stability in coalition formation games in which the strategies of each agent are coalitions in which she can participate and outcomes are coalition structures. Given a natural blocking dynamic, an absorbing set is a minimum set of coalition structures that once reached is never abandoned. The coexistence of single and non-single absorbing sets is what causes lack of convergence to stability. To characterize games in which both types of set are present, we first relate circularity among coalitions in preferences (rings) with circularity among coalition structures (cycles) and show that there is a ring in preferences if and only if there is a cycle in coalition structures. Then we identify a special configuration of overlapping rings in preferences characterizing games that lack convergence to stability. Finally, we apply our findings to the study of games induced by sharing rules.

Journal of Economic Theory, 1987

for helpful comments. The third author gratefully acknowledges support from the Sloan Foundation, through its grant to the MIT Department of Economics. The notion of Coalition-Proof Nash Equilibria was developed independently by Peleg [S] and Bernheim and Whinston [3]; the current paper represents a synthesis of that work.