Cel The main goal of this project is to study ordered algebraic structures with regard to their applications in game theory. Theory of Riesz spaces, groups, and MV-algebras provide the tools necessary for modeling important aspects of mathematical games, such as economic rationality, strategic invariance, or fairness. This is already witnessed by many parts of game theory: for example, Aumann-Shapley value is a positive equivariant linear operator into the Riesz space of measures and MV-algebras model many coalition games. Our objective is to employ the methods, which were developed for solving deep algebraic and logical problems, in several important game-theoretic problems. Specifically, we will study the class of piecewise linear continuous strategic games by using the polyhedral representation of free MV-algebras and Baker-Beynon duality for unital free vector lattices, with the goal to show the existence of finitely-supported mixed strategy equilibria. We will investigate MV-algebras and their measures in order to model coalition games and their solutions. The motivation is to generalize the Danilov-Koshevoy representation of core by the convex Minkowski combination of simplices for larger classes of games. This inevitably leads to building dual representations of games based on the notion of generalized Moebius transform and the space of filters of an MV-algebra. Each facet of this project is transdisciplinary: the emphasis on algebra and order pervades all the selected game-theoretic scenaria. The presented proposal is an opportunity for the applicant to acquire new mathematical skills under the guidance of a scientist in charge - the specialist in ordered algebraic structures - and achieve thus a unique position in his own research field (game theory, many-valued logics). Dziedzina nauki natural sciencesmathematicspure mathematicsalgebranatural sciencesmathematicsapplied mathematicsgame theory Program(-y) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Temat(-y) FP7-PEOPLE-2013-IEF - Marie-Curie Action: "Intra-European fellowships for career development" Zaproszenie do składania wniosków FP7-PEOPLE-2013-IEF Zobacz inne projekty w ramach tego zaproszenia System finansowania MC-IEF - Intra-European Fellowships (IEF) Koordynator UNIVERSITA DEGLI STUDI DI MILANO Wkład UE € 241 567,60 Adres Via Festa Del Perdono 7 20122 Milano Włochy Zobacz na mapie Region Nord-Ovest Lombardia Milano Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Luisa Mondina (Dr.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych