A New Method to Finding All Nash Equilibria

It is a main concern in applications of game theory to effectively select a Nash equilibrium. All Nash equilibria is often required to be computed for this selection process. However, it is well known that the problem of finding only one mixed-strategy Nash equilibrium is a PPAD-complete process. Therefore, it is very hard to find all Nash equilibrium for a certain problem by traditional methods. By exploiting the properties of multilinear terms in the payoff functions, this paper presents a good approximation of the multilinear terms and develops a mixed-integer linear programming for finding all mixed-strategy Nash equilibria. An example of this method will be given too.