New values for cooperative games: two approaches from the filtration theory

In this paper, we give a different vision of a cooperative game inspired by the filtration theory for simplicial complexes. Two important elements are introduced for a filtration associated with a game: bases and vercets. Each of them determines the definition of one new value for cooperative games. We show the kind of situations where both can be applied, with examples. We also introduce operations and algorithms of filtration manipulation to give an axiomatization of the defined values.