Two Choice Behavioral Game Dynamics with Myopic-Rational and Herding Players

In classical game theory, the players are assumed to be rational and intelligent, which is often contradictory to reality. We consider more realistic behavioral game dynamics where the players choose actions in a turn-by-turn manner and exhibit two prominent behavioral traits --- α-fraction of them are myopic who strategically choose optimal actions against the empirical distribution of the previous plays, while others herd towards the most popular action till then. Our analysis focuses on scenarios when players encounter two possible choices and get to play only once. We constructively derive the almost sure mean-field limits of such dynamics. Further, we provide comparisons across various levels and types of rationality. Our framework extends naturally to model avoid-the-crowd behavior. Finally, we illustrate our results with two practical examples: the participation game and the routing game.