Abstract: The primary objective of this study is to enhance the game-theoretical approach for the optimization of structural design in contexts characterized by uncertainty regarding external loads. The game formulation finds application in game structural optimization with distributed control functions. A game on a unit square necessitates a minimum of two levels due to the fundamental requirement of the optimization process. These levels are designated as the substratum and superstratum levels of the stratified game. At the substratum level, the optimization criterion functions as the payoff function, with "ordinal players" striving to minimize or maximize the respective payoff functions. The strategies employed by these "ordinal players" are constrained by limited resources, and the value of the substratum game on the unit square is reflected in these strategies. At the upper substratum level, the value of the game is contingent upon the design parameters. The "designer," or cardinal player, exerts control over these design parameters. In the event of multiple cardinal players with conflicting objectives, the game task resolves their interests. Conversely, in the event of a sole cardinal player, the search for the extremum of the value of the superstratum game reduces to conventional optimization. The lecture presents some representative solutions for game optimization formulations in matrix convention.

Biography: Vladimir Kobelev, Dr. rer. nat. habil, received the title of Dipl.-Physicist in 1982 and his PhD in 1984 at the Faculty of Aerophysics and Space Research, Moscow Institute of Physics and Technology, Dolgoprudny, Russia.
Since 2000 he has been a private lecturer and APL professor at the Department of Mechanical Engineering at the University of Siegen, Germany.
Author of the works: “Fundamentals of Spring Mechanics” (Springer, 2024), “Fundamentals of structural optimization. Stability and contact mechanics” (Springer, 2023), “Fundamentals of Structural Optimization (II).Shape, Anisotropy, Topology” (Springer, 2024) and “Design and Analysis of Composite Structures for Automotive Applications” (Wiley, 2019). https://orcid.org/0000-0002-2653-6853
https://www.researchgate.net/profile/Vladimir-Kobelev