基于向量优化的纳什均衡集表征与计算

IF 0.7 4区管理学 Q3 Engineering

Military Operations Research Pub Date : 2021-09-30 DOI:10.1287/opre.2023.2457

Zachary Feinstein, Birgit Rudloff

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引用次数: 6

摘要

纳什均衡和帕累托最优点之间的关系是什么?众所周知，纳什均衡不一定是帕累托最优，帕累托点也不一定是纳什均衡。然而，Feinstein和Rudloff的论文“通过向量优化表征和计算纳什均衡集”对这种关系进行了更深入的研究。证明了可以将所有纳什均衡的集合表征为某向量优化问题的所有帕累托最优解的集合。这是通过仔细设计矢量优化问题的目标函数和排序锥，使两者重合来实现的。这一特征适用于所有非合作博弈(非凸、凸、线性)。它开辟了一种计算纳什均衡的新方法，因为人们现在可以使用向量优化的技术和算法来计算所有纳什均衡的集合，这与经典的定点迭代只找到一个纳什均衡形成了对比。

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Characterizing and Computing the Set of Nash Equilibria via Vector Optimization

What is the relation between the notion of Nash equilibria and Pareto-optimal points? It is well known that Nash equilibria do not need to be Pareto optimal, and Pareto points do not need to be Nash equilibria. However, the paper “Characterizing and Computing the Set of Nash Equilibria via Vector Optimization” by Feinstein and Rudloff takes a deeper look at the relation. It is shown that it is possible to characterize the set of all Nash equilibria as the set of all Pareto-optimal solutions of a certain vector optimization problem. This is accomplished by carefully designing the objective function and the ordering cone of the vector optimization problem such that both notions coincide. This characterization holds for all noncooperative games (nonconvex, convex, linear). It opens up a new way of computing Nash equilibria, as one can now use techniques and algorithms from vector optimization to compute the set of all Nash equilibria, which is in contrast to the classical fixed-point iterations that find just a single Nash equilibrium.

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来源期刊

Military Operations Research 管理科学-运筹学与管理科学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Military Operations Research is a peer-reviewed journal of high academic quality. The Journal publishes articles that describe operations research (OR) methodologies and theories used in key military and national security applications. Of particular interest are papers that present: Case studies showing innovative OR applications Apply OR to major policy issues Introduce interesting new problems areas Highlight education issues Document the history of military and national security OR.