论文标题
多项式的NASH平衡问题
Nash Equilibrium Problems of Polynomials
论文作者
论文摘要
本文研究了由多项式函数给出的NASH平衡问题。我们为计算纳什均衡的有效多项式优化问题。套索型瞬间SOS松弛用于解决它们。在通用假设下，该方法可以找到NASH平衡，如果有一个。此外，如果其中有很多纳什的平衡，它可以找到所有纳什均衡。如果没有NASH平衡，该方法还可以检测不存在。
This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Lasserre type Moment-SOS relaxations are used to solve them. Under generic assumptions, the method can find a Nash equilibrium if there is one. Moreover, it can find all Nash equilibria if there are finitely many ones of them. The method can also detect nonexistence if there is no Nash equilibrium.
