Preliminaries

Abstract

Cooperative game theory is dealing with set functions that are essentially non-additive. A game (with side payments) is regarded as a tripel $\Lambda = \left( {\Omega ,\underline{\underline B} ,v} \right)$ where Ω is a set (“the players”) ${\underline{\underline B} }$ a system of subsets off) (“the admissible coalitions”) and $\begin{array}{*{20}c} {v:\underline{\underline B} \to \mathbb{R}^ + ,} {v\left( \varphi \right) = 0} \\ \end{array}$, is a mapping. (v(S) is a “utility” or “monetary value” that coalition S € $S \in \underline{\underline B}$ can achieve by cooperation), ∧ is said to be “superadditive”, “convex”,... etc., if ∨ is a superadditive, convex,... etc. set function.