  We consider an environment where players need to decide whether to buy a
certain product (or adopt a technology) or not. The product is either good or
bad, but its true value is unknown to the players. Instead, each player has her
own private information on its quality. Each player can observe the previous
actions of other players and estimate the quality of the product. A classic
result in the literature shows that in similar settings informational cascades
occur where learning stops for the whole network and players repeat the actions
of their predecessors. In contrast to this literature, 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 the product and
leave the market or wait. Her utility is the total expected discounted reward,
and thus myopic strategies may not constitute equilibria. We provide a
characterization of perfect Bayesian equilibria (PBE) with forward-looking
strategies through a fixed-point equation of dimensionality that grows only
quadratically with the number of players. Using this tractable fixed-point
equation, we show the existence of a PBE and characterize PBE with threshold
strategies. Based on this characterization we study informational cascades in
two regimes. First, we show that for a discount factor {\delta} strictly
smaller than one, informational cascades happen with high probability as the
number of players N increases. Furthermore, only a small portion of the total
information in the system is revealed before a cascade occurs ...
