A NEW METHOD TO CONSTRUCT SOLUTION CONCEPTS FOR COOPERATIVE GAMES WITH COALITION STRUCTURE BASED ON MARGINAL CONTRIBUTIONS

The semivalues are solution concepts for cooperative games that assign to each player a weighted sum of his/her marginal contributions to the coalitions, where the weights only depend on the coalition size. The solutions introduced here are modifications of the semivalues when we consider a priori coalition blocks in the player set. A first semivalue is used among the coalition blocks and a second semivalue arts within each block. For all these solutions, we offer a computation procedure based on suitable modifications of the multilinear extension of the game and a product of matrices.