The Path to Nash Equilibrium
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It has been proved that every non-cooperative game has 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 the limitation in optimizing the accuracy of equilibrium point approximation.
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