Balancedness, nonemptiness of the core and the existence of a majority equilibrium
type: Item
instance of: scholarly article
title: Balancedness, nonemptiness of the core and the existence of a majority equilibrium
zbMATH Open document ID: 0537.90004
DOI: 10.1007/BF01769816
author: Joseph Greenberg
author: Shlomo Weber
published in: International Journal of Game Theory
publication date: 1984-01-01T00:00:00Z
review text: Consider a society with a finite number, n, of individuals who have to choose an alternative from a compact, convex set A in the m-dimensional Euclidean space, \({\mathbb{R}}^ m\). Assume that the preference relation over A of every individual is represented by a quasi-concave and continuous function. If the set of winning coalitions (i.e. those that have the veto power) consists of all coalitions with more than \(mn/(m+1)\) individuals, then there exists an alternative a*\(\in A\) which is a majority equilibrium, or equivalently, that the core of the induced game is nonempty. The main step of the proof is to show that the game is balanced. This is a slight strengthening of a previous result by the first author.
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 3854741
zbMATH Keywords: balanced games
zbMATH Keywords: voting games
zbMATH Keywords: social choice
zbMATH Keywords: nonemptiness result
zbMATH Keywords: winning coalitions
zbMATH Keywords: majority equilibrium
zbMATH Keywords: core
reviewed by: David Schmeidler
MaRDI profile type: Publication
cites work: Q3260984
cites work: Consistent Majority Rules over Compact Sets of Alternatives
cites work: The Core of an N Person Game
description: scientific article; zbMATH DE number 3854741