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arXiv · 2208.00357

Algebraic Degrees of Generalized Nash Equilibrium Problems

Jiawang Nie·Kristian Ranestad·Xindong Tang
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Abstract

This paper studies the 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 count 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.

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Jiawang Nie, Kristian Ranestad, Xindong Tang. 2022-07-31. Algebraic Degrees of Generalized Nash Equilibrium Problems. https://arxiv.org/abs/2208.00357

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