On coalition formation: durable coalition structures.
type: Item
instance of: scholarly article
title: On coalition formation: durable coalition structures.
zbMATH Open document ID: 1045.91002
DOI: 10.1016/S0165-4896(03)00025-8
author: Anke Gerber
author: Salvador Barberà
published in: Mathematical Social Sciences
publication date: 2003-07-29T00:00:00Z
review text: A hedonic game consists of a finite set of players and, for each one of them, a preference relation (complete preordering) on the set of coalitions to which the player belongs. The concept is hereditary for subsets of players. A coalition structure (CS, in the sequel) is a partition of the player set. By induction on the number of players, the notion of durable CS is introduced. To this end, the key idea is the disruption of a CS by means of some coalitions, a process that leads to other CSs and can be iterated. It naturally gives rise to speak of transient or (oppositely) durable CSs. Although rigorously formalized, the topic admits a helpful intuitive view. The main results are the following. (a) From any transient CS a durable one can be always obtained, and this guarantees the existence of some durable CS for any hedonic game. (b) All core CSs are durable, and all durable CSs are individually rational -no player strictly prefers being alone instead of the coalition he belongs to in the given CS. (c) If there is just one durable CS, it is the only member of the core of the hedonic game; for example, this is the case if the top-coalition property is satisfied and preferences are strict. Interesting numerical examples are also provided. Cases with empty core or where the core is nonempty but a strict subset of the set of durable CSs and, especially, three detailed samples of one-to-one and many-to-one matching problems, which are interpreted as hedonic games by assuming that all unfeasible coalitions are not individually rational.
reviewed by: Francesc Carreras
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 1956089
zbMATH Keywords: hedonic game
zbMATH Keywords: coalition structure
zbMATH Keywords: core
zbMATH Keywords: durability
MaRDI profile type: Publication
cites work: Core in a simple coalition formation game
cites work: Bargaining in cooperative games
cites work: Coalition-proof Nash equilibria. I: Concepts
cites work: Coalitional stability with a credibility constraint
cites work: The stability of hedonic coalition structures
cites work: Farsighted coalitional stability
cites work: Intermediate preferences and stable coalition structures
cites work: Farsighted stability in hedonic games
cites work: Hedonic Coalitions: Optimality and Stability
cites work: Stability of matchings when individuals have preferences over colleagues
cites work: A consistent bargaining set
cites work: College Admissions and the Stability of Marriage
cites work: Q3378952
cites work: Strong Tiebout equilibrium under restricted preferences domain
cites work: Stable coalition structures with a unidimensional set of alternatives
cites work: Second best taxation as a game
cites work: Endogenous Formation of Coalitions
cites work: The stability set as a social choice correspondence.
cites work: Credible coalitions and the core
cites work: Equilibrium binding agreements
cites work: Stability of decision systems under majority rule
cites work: On coalition formation: A game-theoretical approach
cites work: Q5844986
cites work: Coalitional stability under perfect foresight
cites work: A new bargaining set of an \(N\)-person game and endogenous coalition formation
full work available at URL: s0165-4896(03)00025-8
OpenAlex ID: W2017005962
description: scientific article; zbMATH DE number 1956089