Cooperative games with a priori unions: introduction of a wide set of solutions

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Giménez Pradales, José Miguel (2006)
  • Subject: Cooperative Game | Solution | :Matemàtiques i estadística::Investigació operativa::Teoria de jocs [Àrees temàtiques de la UPC] | Semivalue | Game theory | Coalition Structure | Multilinear Function | :91 Game theory, economics, social and behavioral sciences::91A Game theory [Classificació AMS] | Teoria de jocs
    acm: TheoryofComputation_GENERAL

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 Shapley value and the Banzhaf value are semivalues. 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 acts 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.
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