Resumen de Extendability, convexity and PMAS

Jesús Getán Oliván, Jesús Montes Peral

• The extendability notion for cooperative games is introduced by Kikuta and Shapley (1986). They show that extendability implies stability of the core. Moreover, they prove that all games with large core are extendable. The monotonic core of a cooperative game is the set formed by all its Population Monotonic Allocation Schemes (PMAS), cf. Moulin (1990) and Sprumont (1990). The games with large monotonic core are introduced by Moulin (1990), who obtains the convexity of these games in the case of three-players.

  The almost convex games are introduced by Nu~nez-Rafels (1998), who obtain the extreme points of the core of such games. In this paper we show that all games with large monotonic core are convex, we introduce the concept of games PMAS-extendable, and we prove that these games are exactly the convex games. Moreover, we show that the properties of convexity, largeness of the core, extendability and stability of the core are equivalent for balanced almost convex games.