On the Game-Based Approach to Optimal Design

A game problem of structural design is defined as a problem of playing against external circumstances. The scalar criterion serves the function of the payoff function. There are two classes of players, the “ordinal” and “cardinal” players. The ordinal players, designated as the "operator" and "nature," endeavor to respectively minimize or maximize the payoff function, operating within the constraints of limited resources. The fundamental premise of this study is that the probability distribution governing nature's "choice" of states remains unknown. Statistical decision theory addresses decision-making scenarios where these probabilities, whether or not they are known, must be considered. The solution to the substratum game is expressed as a value of the game. The value of the game is contingent upon the design parameters. The cardinal players, "designers", oversee the design parameters. For the se single cardinal player, the pursuit of the maximum and minimum values of the game reduces to the problem of optimal design. In the event that there are multiple cardinal players with conflicting objectives, a superstratum game emerges, which addresses the interests of the superstratum players. The optimal design problems for games with closed forms are presented. The game formulations could be applied for optimal design with uncertain loading.