Homogeneous Games: Recursive Structure and Computation

The structure of a homogeneous weighted majority game in general not constant-sum is analyzed via the concepts of characters of types and of satellite games being played by smaller players in order to replace larger ones. Two proofs for the existence of the minimal representation see Ostmann [Ostmann, A. On the Minimal Representation of Homogeneous Games. Internal. J. Game Theory to appear.] are given. An algorithm to construct the satellite games, the characters and the minimal representation directly from any homogeneous representation is described.