The classical game theory considers rational players and proposes Nash equilibrium (NE) as the solution. However, real-world scenarios rarely feature rational players; instead, players make inconsistent and irrational decisions. Often, irrational players exhibit herding behaviour by simply following the majority. In this paper, we consider a mean-field game with \(\alpha \) -fraction of rational players and the rest being herding-irrational players. For such a game, we introduce a novel concept of equilibrium named \(\alpha \) -Rational NE (in short, \(\alpha \) -RNE). We extensively analyze the \(\alpha \) -RNEs and their implications in games with two actions. Due to herding-irrational players, new equilibria may arise, and some classical NEs may be deleted. We establish that the rational players are not harmed but benefit from the presence of irrational players. More interestingly, in some examples, the rational players attain higher utility (under \(\alpha \) -RNE) than even the social optimal utility (in the classical setting), by leveraging upon the herding behaviour of irrational players. Surprisingly, the irrational players may also benefit by not being rational. We observe that irrational players do not lose compared to some classical NEs for participation and bandwidth-sharing games. Importantly, in bandwidth-sharing game, the irrational players also receive utility near social optimal utility. Such examples indicate that it may sometimes be ‘rational’ to be irrational.