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...

We propose a class of higher-derivative gravities that can be viewed as the Gauss-Bonnet extension Starobinsky model. The theory admits Minkowski spacetime vacuum whose linear spectrum consists graviton and massive scalar mode. In addition to usual Schwarzschild black hole, we use numerical analysis establish in some suitable mass range, new holes carrying hair emerge. hole serves "wall" separa...