A note on the permutationally convex games
type: Item
instance of: scholarly article
title: A note on the permutationally convex games
zbMATH Open document ID: 0742.90091
DOI: 10.1007/BF00134118
author: Bahram Alidaee
published in: Theory and Decision
publication date: 1992-06-25T00:00:00Z
review text: An \(n\)-person side-payment game \(v\) is called permutationally convex with an ordering \(\pi\) on the player set, if \[ v(P^ \pi_ j\cup\{j\}\cup S)-v(P^ \pi_ j\cup\{j\})\leq v(P^ \pi_ k\cup\{k\}\cup S)-v(P^ \pi_ k\cup\{k\}) \] for all \(k\geq j\) and \(S\subset N\backslash[P^ \pi_ k\cup\{k\}]\), where \(P^ \pi_ j:=\{i\mid\pi(i)<\pi(j)\}\). It is well-known that a permutationally convex game with an ordering \(\pi\) has its marginal worth vector with respect to \(\pi\) as a member of the core. This paper shows by an example that the converse is false.
reviewed by: Tatsuro Ichiishi
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 9436
zbMATH Keywords: \(n\)-person side-payment game
zbMATH Keywords: permutationally convex game
zbMATH Keywords: marginal worth vector
zbMATH Keywords: core
MaRDI profile type: Publication
cites work: The Relationship Between Convex Games and Minimum Cost Spanning Tree Games: A Case for Permutationally Convex Games
cites work: Super-modularity: Applications to convex games and to the greedy algorithm for LP
cites work: Cores of convex games
full work available at URL: https://doi.org/10.1007/bf00134118
OpenAlex ID: W2983841391
description: scientific article; zbMATH DE number 9436