Prosperty properties of TU-games
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.
scientific article; zbMATH DE number 1308995