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].

中文翻译：

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随机纳什均衡问题：模型、分析和算法


在过去 70 年（甚至更早）中，人们对不确定性下的决策进行了广泛的研究。在优化领域，由 Dantzig [1] 和 Beale [2] 提出的两阶段随机线性规划模型通常被视为随机优化领域后续发展的基础。这个优化子领域现在涵盖了广泛的模型，可以适应凸性和非凸性、概率约束、风险规避、离散性和多阶段决策（比较[3]、[4]）。同样，随机控制 [5] 已被证明是控制理论中一个具有巨大影响力的子领域。当一个人将决策范式扩展到多个自利决策者时，所产生的问题可以被视为一种非合作博弈，它植根于冯·诺依曼和摩根斯特恩的开创性文本[6]。