Prosperty properties of TU-games
type: Item
instance of: scholarly article
title: Prosperty properties of TU-games
zbMATH Open document ID: 0941.91008
author: J. R. G. van Gellekom
author: J. H. Reijnierse
author: Jos Potters
published in: International Journal of Game Theory
publication date: 1999-10-05T00:00:00Z
review text: The problem of core-stability, i.e., the existence of Von Neumann-Morgenstern solution for cooperative games in the characteristic function form is considered. The authors define prosperity properties in order to obtain new sufficient conditions for the core stability. A survey of sufficient conditions for the core stability, which are known from the scientific literature, is given. The prosperity properties mean the following. If we start with an arbitrary cooperative game and increase the value of the characteristic function of the grand coalition (the coalition of all players) only, then the property, once arising, will be kept till infinity. The threshold number is denoted by \(\alpha\). Also a weaker kind of prosperity is introduced. The largeness of the core is proved to be a prosperity property. The core stability is proved to be a weak prosperity property. The prosperity of some other properties of the core such as exactness, TB-exactness (exactness of the totally balanced cover), balancedness, extendability, and subconvexity is investigated. The main result is a relation between \(\alpha\)'s for various properties. For the inequality relations, the examples of strict inequality cases are given. Thus, some relations between the aforesaid properties are obtained.
Mathematics Subject Classification ID: 91A12
zbMATH DE Number: 1308995
zbMATH Keywords: cooperative games
zbMATH Keywords: transferable utility game
zbMATH Keywords: characteristic function form
zbMATH Keywords: stable core
zbMATH Keywords: Von Neumann-Morgenstern solution
zbMATH Keywords: large core
zbMATH Keywords: prosperity
reviewed by: N. M. Novikova
MaRDI profile type: Publication
full work available at URL: s001820050106
OpenAlex ID: W2056481063
DOI: 10.1007/S001820050106
description: scientific article; zbMATH DE number 1308995