  We study the problem of Bayesian learning in a dynamical system involving
strategic agents with asymmetric information. In a series of seminal papers in
the literature, this problem has been investigated under a simplifying model
where myopically selfish players appear sequentially and act once in the game,
based on private noisy observations of the system state and public observation
of past players' actions. It has been shown that there exist information
cascades where users discard their private information and mimic the action of
their predecessor. In this paper, we provide a framework for studying Bayesian
learning dynamics in a more general setting than the one described above. In
particular, our model incorporates cases where players are non-myopic and
strategically participate for the whole duration of the game, and cases where
an endogenous process selects which subset of players will act at each time
instance. The proposed framework hinges on a sequential decomposition
methodology for finding structured perfect Bayesian equilibria (PBE) of a
general class of dynamic games with asymmetric information, where user-specific
states evolve as conditionally independent Markov processes and users make
independent noisy observations of their states. Using this methodology, we
study a specific dynamic learning model where players make decisions about
public investment based on their estimates of everyone's types. We characterize
a set of informational cascades for this problem where learning stops for the
team as a whole. We show that in such cascades, all players' estimates of other
players' types freeze even though each individual player asymptotically learns
its own true type.
