# How to determine the complexity of a mixed strategy NASH equilibrium problem

How to determine a complete-information mixed strategy NASH equilibrium problem with finite numbers of players and strategies? That is, there exists a payoff matrix which shows all the relation among all the player's profile. For example, 5 player all have 5 strategies, and all of them know the results for all 5*5*5*5*5 strategy combinations.

Another question: If I concatenate all player's the KKT conditons to solve this problem, what is the complexity of the problem?