论文标题
广义NASH平衡问题的代数程度
Algebraic Degrees of Generalized Nash Equilibrium Problems
论文作者
论文摘要
本文研究了多项式给出的广义NASH平衡问题（GNEP）的代数程度。他们的广义纳什均衡（GNE）及其KKT或Fritz-John点是定义多项式系数的代数函数。我们研究这些代数函数的程度，这些函数还计算了复杂的KKT或Fritz-John点的数量。在某些通用假设下，我们表明GNEP只有许多复杂的Fritz-John点有限，而每个Fritz-John点都是KKT点。我们还给出了GNEP的代数度的公式，该公式计算了通用病例的复杂Fritz-John点的数量。
This paper studies algebraic degree of generalized Nash equilibrium problems (GNEPs) given by polynomials. Their generalized Nash equilibria (GNEs), as well as their KKT or Fritz-John points, are algebraic functions in the coefficients of defining polynomials. We study the degrees of these algebraic functions, which also counts the numbers of complex KKT or Fritz-John points. Under some genericity assumptions, we show that a GNEP has only finitely many complex Fritz-John points and every Fritz-John point is a KKT point. We also give formulae for algebraic degrees of GNEPs, which count the numbers of complex Fritz-John points for generic cases.
