Characterizing Non-Myopic Information Cascades in Bayesian Learning

We consider an environment where many players need to decide whether to buy a certain product (or adopt a trend) or not. The product is either good or bad, but its true value is not known to the players. Instead, each player has his own private information on the quality of the product. Each player can observe the previous actions of other players and deduce the quality of the product. A player can only buy the product once. In contrast to the existing literature on informational cascades, in this work players get more than one opportunity to act. In each turn, a player is chosen uniformly at random from all players and can decide to buy or not to buy. His utility is the total expected discounted reward, and thus myopic strategies may not be best responses. We provide a characterization of structured perfect Bayesian equilibria (PBE) with non-myopic strategies through a fixed-point equation of dimensionality that grows only polynomially with the number of players. Based on this characterization we study informational cascades and show that they happen with high probability for a large number of players. Furthermore, only a small portion of the total information in the system is revealed before a cascade occurs.