Values and potential of games with cooperation structure

Games with cooperation structure are cooperative games with a family offeasible coalitions, that describes which coalitions can negotiate in the game. We study a model ofcooperation structure and the corresponding restricted game, in which the feasible coalitions are those belonging to apartition 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 ofpartition convex geometries are used to obtain formulas for theShapley andBanzhaf values of the players in the restricted game in terms of the original gamev. Finally, we consider the Owen multilinear extension for the restricted game.The author is grateful to Paul Edelman, Ulrich Faigle and the referees for their comments and suggestions. The proof of Theorem 1 was proposed by the associate editor's referee.