Game-Theoretical Viewpoint to Optimal Design

Abstract:

The main goal of this study is to improve the game-theoretical approach for making the best structural design choices in situations where we are not sure what the external loads will be. The game formulation is used to improve games with different control functions. A game on a unit square needs at least two levels because of the basic need for optimization. In a stratified game, the levels are called the substratum and superstratum levels. At the basic level, the way to improve something is like the payoff function, with "ordinal players" trying to make the respective payoff functions as small or as big as possible. The strategies used by these "ordinal players" are limited by their resources, and the value of the substratum game on the unit square is reflected in these strategies. At the upper level of the game, its value depends on the design parameters. The "designer," or the main player, controls these design parameters. If there are multiple players with different goals, the game decides how to handle that. On the other hand, if there is only one cardinal player, finding the maximum value of the superstratum game is the same as a regular optimization. The following text will give you all the information you need. The text presents the exact solutions for two different types of quadratic game formulations: the matrix game and the game on the unit square

• Periodical: Engineering Innovations (Volume 16)
• Pages: 127-138
• DOI: https://doi.org/10.4028/p-M6fTQm
• Online since: January 2026
• Authors: Vladimir Kobelev*
• Keywords: Continuous Game Theory, Game Formulation for a Potential Asteroid Impact, Games on Unit Square, Optimal Design with Uncertainties, Quadratic Games Unit Square

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