Combinations and transformations of some general coalition-games

The general coalition-game model suggested in [2] is considered, and a few types of combinations and transformations of such games are investigated. It is shown that a conjunction, disjunction, and combination of two general coalition-games is, under natural conditions, also a general coalition-game. Also the main relations between the solutions of the original games and the resulting one are derived. The general conditions under which a transformation of the imputation space preserves the existence of general coalition-games were presented in [5]. It is shown in this paper that the same conditions are sufficient for the preservation of some important special properties of the games like their superadditivity, subadditivity and additivity. Also the preservation of the convexity, concavity or linearity of the sets of available imputations is connected with the same conditions.