TY - JOUR
T1 - Nash Equilibrium Problems of Polynomials
AU - Nie, Jiawang
AU - Tang, Xindong
N1 - J. Nie was supported by the National Science Foundation [Grant DMS-2110780].
Publisher Copyright:
Copyright: © 2023 INFORMS.
PY - 2024/5
Y1 - 2024/5
N2 - 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.
AB - 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.
KW - Lagrange multiplier expression
KW - Moment-SOS relaxation
KW - Nash equilibrium
KW - Primary: 90C23, 90C33, 91A10, 65K05
KW - polynomial optimization
KW - tight relaxation
UR - http://www.scopus.com/inward/record.url?scp=85194296893&partnerID=8YFLogxK
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=hkbuirimsintegration2023&SrcAuth=WosAPI&KeyUT=WOS:001029595100001&DestLinkType=FullRecord&DestApp=WOS
U2 - 10.1287/moor.2022.0334
DO - 10.1287/moor.2022.0334
M3 - Journal article
SN - 0364-765X
VL - 49
SP - 1065
EP - 1090
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
IS - 2
ER -