In this paper, we study the properties of Germeier’s scalarization applied for solving multicriteria games. The equilibria and equilibrium values such games, as a rule, make sets, problems parametrizing approximating these sets arise. Shapley proved that Nash matrix game can be found by two-parametric family scalar games obtained with help linear criteria vector. We show parametrizes using one-...

In this paper, we propose a new combined scalarization method of multi-objective optimization problems by using the surplus variables and generalized Tchebycheff norm then use it to obtain some equivalent characterizations (weakly, strictly, properly) efficient solutions adjusting range parameters. These results do not need any convexity assumption conditions object...

Keisuke Taniguchi,1 Masaru Shibata,2 and Alessandra Buonanno3,4 1Graduate School of Arts and Sciences, University of Tokyo, Komaba, Meguro, Tokyo, 153-8902, Japan 2Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan 3Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, Potsdam-Golm, 14476, Germany 4Department of Physics, Uni...

ISBN 88-7088-483-X (Bibliopolis, Napoli, 2005) http://www.bibliopolis.it These notes originated out of a set of lectures in Quantum Optics and Quantum Information given by one of us (MGAP) at the University of Napoli and the University of Milano. A quite broad set of issues are covered, ranging from elementary concepts to current research topics, and from fundamental concepts to applications. A...