Nash equilibrium problems (NEPs) are games for several players . A Nash Equilibrium (NE) is a tuple of strategies such that each player's benefits cannot be improved when the other players' strategies are fixed. For NEPs given by polynomial functions, we formulate efficient polynomial optimization problems for computing NEs. The Moment-SOS relaxations are used to solve them. Under genericity assumptions, the method can find a Nash equilibrium if there is one; it can also find all NEs if there are finitely many ones. The method can also detect nonexistence if there is no NE.

This is a joint work with Dr. Xindong Tang.