Methodology From an Equilibria Viewpoints

Since the Stackelberg game model (von Stackelberg, The theory of the market economy. Oxford University Press, New York, 1952) was proposed by German economist Heinrich Freiherr von Stackelberg in 1934, it has been widely applied (Peng and Lu, Appl Math Comput 271(C):259–268, 2015; Simaan and Cruz, J Optim Theory Appl 11(5):533–555, 1973; Shi et al., Ind Manag Data Syst 116(3):350–368, 2016; von Stengel, Games Econ Behav 69(2):512–516, 2010). The main idea of the Stackelberg game is equilibrium, which is the achievement of a state whereby the conflicting parties are in balance and do not seek any further changes. In real-world problems, decision makers often have several concurrent objectives, which are often in conflict and cannot be easily measured. Therefore, decision makers must consider trade-offs across the objectives. In addition to the hierarchical structure and the diverse objectives, imprecise data, inaccurate human decision making judgments, the decision maker’s bounded rationality, and the decision making uncertainties all need to be taken into account. In this book, we focus on random-like phenomena, including random phenomena, the Ra-Ra phenomenon, and the Ra-Fu phenomenon, the latter two of which are considered to be two-fold uncertain phenomena. In the conclusion, Chap. 5 summarizes the methodologies adopted in this monograph from an equilibria viewpoint, including equilibrium motivation, equilibrium in real-world problems, model system in equilibrium, equilibrium algorithms, and perspectives for the models, theories, algorithms and applications.