Nash Equilibrium Problems of Polynomials
研究由多项式函数定义的纳什均衡问题，提出用矩-平方和松弛方法高效求解，可找到一个或所有均衡，也能判断无解。
This paper studies Nash equilibrium problems that are given by polynomial functions. We formulate efficient polynomial optimization problems for computing Nash equilibria. The Moment-sum-of-squares 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. Funding: J. Nie was supported by the National Science Foundation [Grant DMS-2110780].