Game-Theoretic Models for Cooperative Equilibrium Solutions of Interacting Engineering Sub-Systems

Although game-theoretical models to study social and economic problems have existed for a long time, they have been sparsely used for the design of engineering systems. This is due to the significant theoretical hurdles posed by game formulations for real engineering environments /problems. In this study we show our first attempt at adapting the frame-work of game-theoretical models for engineering problems, in particular the aero-mechanical optimization of a notional turbine blade. We pose the design problem as a series of games, starting with the determination of the Pareto front, the non-cooperative (disagreement) point and the optimal solution as the tangent intersection of the Pareto front and contours of the overall system objective. We present gradient-based algorithms that determine the Pareto front, the non-cooperative solution and the tangent solution. The solution to this series of games provides the basis of a new equilibrium concept namely, System Optimal Cooperative Solution (SOCS), which is the central theme of this paper. Finally we compare the SOCS solution against other cooperative solutions like Nash-Bargaining [1]. The results of this study show that in engineering environments previously known cooperative solutions like Nash-Bargaining and Kalai-Smordinsky [2] are not that important while the notion of a System Optimal Cooperative Solution, SOCS, is the equilibrium solution of relevance. For the particular example we consider, the SOCS is shown to be more favoring the aerodynamic performance when compared against the Nash-Bargaining equilibrium solution.