Informational cascades can be avoided with non-myopic agents

We study informational cascades in a scenario where a finite number of players need to decide whether to buy a product, which is either good or bad, or not. The true value of the product is not known to the players, but each player has her own private information on it. Each player observes the previous actions of other players and forms a belief on the quality of the product. In this work, players get more than one opportunity to act, although, a player can only buy the product once. This is in contrast to the existing literature on informational cascades, where each player only acts once. We consider an exogenous random process for choosing the players to act in each turn. We provide a characterization of structured perfect Bayesian equilibria (sPBE) with forward-looking strategies through a fixed-point equation of dimensionality that grows only quadratically with the number of players. We show the existence of sPBE and prove that bad informational cascades can be avoided entirely for infinitely patient players when the product is bad. Furthermore, we show that for sufficiently patient players, bad informational cascades happen only when at least half of the players have revealed their private information.