  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.
