Social herding in mean field games

In this paper, we consider a mean field model of social behavior where there are an infinite number of players, each of whom observes a type privately that represents her preference, and publicly observes a mean field state of types and actions of the players in the society. The types (and equivalently preferences) of the players are dynamically evolving. Each player is fully rational and forward-looking and makes a decision in each round t to buy a product. She receives a higher utility if the product she bought is aligned with her current preference and if there is a higher fraction of people who bought that product (thus a game of strategic complementarity). We show that for certain parameters when the weight of strategic complementarity is high, players eventually herd towards one of the actions with probability 1 which is when each player buys a product irrespective of her preference.