Pareto optima and Nash equilibria

Abstract

PurposeThis paper seeks to describe an approach to multi‐objective optimization problems (MOOPs) based on game theory (GT) and to provide a comparison with the more standard Pareto approach on a real design problem.Design/methodology/approachThe GT is first briefly presented, then a possible recasting of MOOPs in terms of GT is described, where players from GT are associated with single objectives and strategies to the choice of degrees of freedom. A comparison with the Pareto approach is performed on the optimized design of a superconducting synchronous generator.FindingsIt was shown that the GT can be applied to the optimized design of real world devices, with results that present a different viewpoint on the problem, yet with device performance comparable with those obtained by standard approaches.Research limitations/implicationsOnly the Nash approach to non‐cooperative games has been applied; the conditions for the solution found using GT to belong to the Pareto front have not been fully explored.Practical implicationsDesigners and engineers interested in optimal design are presented with a new design technique able to get a balance among conflicting partial objectives, that can also be used to select among different possible designs obtained in other ways (e.g. using the Pareto front approach).Originality/valueThe paper demonstrates the possibility of using GT in the design of real world electromagnetic devices, with reference to the optimal shape design of a high temperature superconducting single‐phase synchronous generator.