The concept of NE is intuitively appealing. Indeed, it is a self-fulfilling
prophecy. To explain, suppose a player were to guess the strategies of
the other players. A guess would be consistent with payoff maximization
and therefore would be reasonable only if it presumes that strategies
are chosen to maximize every player’s payoff given the chosen strategies.
In other words, with any set of strategies that is not a NE there exists
at least one player that is choosing a non payoff maximizing strategy.
Moreover, the NE has a self-enforcing property: no player wants to unilaterally
deviate from it since such behavior would lead to lower payoffs.
Hence NE seems to be the necessary condition for the prediction of any
rational behavior by players3.