A study of optimal design under conflict using models of multi-player games

In the broad context of modelling for system design, it is normally assumed that all decision-makers cooperate fully and thus avoid conflict. However, this is not always possible, in which case the design process is best modelled and studied as a multi-player game. The objective in this paper is to present and illustrate such a general game-theoretic framework for design modelling. In particular, explicit solutions are computed and interpreted for conservative or minmax, Pareto, Nash and Stackelberg games in a simple pressure vessel design example in which two players interact strategically, one of whom wants to minimize the weight and the other wishes to maximize the volume. In another example in which a rotating disk is to be optimized for two objectives related to its design and manufacture, the Pareto solutions show how a novel manufacturing cost function can improve, under assumptions of a cooperative game, the optimal shape that was obtained under a single objective formulation related to design alone.