Stochastic Nash Equilibrium Problems: Models, Analysis, and Algorithms

Decision making under uncertainty has been studied extensively over the last 70 years, if not earlier. In the field of optimization, models for two-stage, stochastic, linear programming, presented by Dantzig [1] and Beale [2], are often viewed as the basis for the subsequent development of the field of stochastic optimization. This subfield of optimization now encompasses a breadth of models that can accommodate both convexity and nonconvexity, probabilistic constraints, risk-aversion, discreteness, and multistage decision-making (compare [3], [4]). Similarly, stochastic control [5] has proven to be an enormously impactful subarea of control theory. When one extends the decision-making paradigm to multiple self-interested decision makers, then the resulting problem can be viewed as a noncooperative game that is rooted in the groundbreaking text by Von Neumann and Morgenstern [6].