Values and potential of games with cooperation structure

Games with cooperation structure are cooperative games with a family of feasible coalitions, that describes which coalitions can negotiate in the game. We study a model of cooperation structure and the corresponding restricted game, in which the feasible coalitions are those belonging to a partition system. First, we study a recursive procedure for computing the Hart and Mas-Colell potential of these games and we develop the relation between the dividends of Harsanyi in the restricted game and the worths in the original game. The properties of partition convex geometries are used to obtain formulas for the Shapley and Banzhaf values of the players in the restricted game $v^{ \cal L}$, in terms of the original game v. Finally, we consider the Owen multilinear extension for the restricted game.