The Modified Nucleolus as Canonical Representation of Weighted Majority Games

Abstract

A new solution concept for cooperative transferable utility games is introduced, which is strongly related to the nucleolus and therefore called modified nucleolus. It has many properties in common with the prenucleolus and can be considered as the canonical restriction of the prenucleolus of a certain replicated game. For weighted majority games this solution concept induces a representation of the game. In the special case of weighted majority constant-sum games and homogeneous games respectively the nucleolus and the minimal integer representation respectively are adequate candidates for a canonical representation (see Peleg [Peleg, B. 1968. On weights of constant-sum majority games. SIAM J. Appl. Math. 16 527–532.] and Ostman [Ostmann, A. 1987a. On the numerical representation of homogeneous games. Int. J. Game Theory 16 69–81.]). Fortunately the modified nucleolus coincides with the just mentioned solutions in these special cases and can, therefore, be seen as a canonical representation in the general weighted majority case.