Sizhong Lan 1 1 China Mobile Research Institute, Beijing 100053, China a) (Dated: September 24, 2019) It had been proved that every non-cooperative game had a Nash equilibrium point. Although many existing algorithms are capable of finding equilibrium points, it is still unclear what force is driving the players to them in the real world. We show that, the players' immediately and constantly pursuing profitable strategies is sufficient for the game to evolve towards equilibrium point, and meanwhile the game needs minimum information exchange among players and no mediation from beyond players. Accordingly, we suggest that in reality the tendency towards Nash equilibrium could be more pervasive and irresistible than expected. Technically, the players' pursuit of profitable strategies gives rise to a sequence of adjusted strategies for our study its approximation to the true equilibrium point. And the sequence can be nicely visualized as a clear path towards an equilibrium point. Our theory has limitations in optimizing the accuracy of equilibrium point approximation. I. INTRODUCTION In 1951 John Nash proved that every non-cooperative game has an equilibrium point 1 by using Brouwer's fixed point theorem 2 . Nash's proof is existential for equilibrium point and yet non-constructive for finding one.