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.